DPPs Physics (11th) PDF

CHAPTERS PG 1: Mathematics in Physics 2 2: Units and Dimensions 27 3: Motion In One Dimension 50 4: Motion In Two Dimensions 79 5: Laws of Motion 107 6: Work Power Energy...

CHAPTERS PG 1: Mathematics in Physics 2 2: Units and Dimensions 27 3: Motion In One Dimension 50 4: Motion In Two Dimensions 79 5: Laws of Motion 107 6: Work Power Energy 140 7: Center of Mass Momentum and Collision 166 8: Rotational Motion 195 9: Gravitation 224 10: Mechanical Properties of Solids 253 11: Mechanical Properties of Fluids 280 12: Thermal Properties of Matter 305 13: Thermodynamics 329 14: Kinetic Theory of Gases 362 15: Oscillations 386 16: Waves and Sound 418  Marks Premium DPPs - Physics (11th) Mathematics in Physics Easy Questions Question 1 The expression A(A ¯ simplifies to ¯ + B) + (B + AA)(A + B) A. A) A + B B. B) AB C. C) A + B – D. D) A ¯+B ¯ Question 2 The percentage errors in quantities P , Q, R and S are 0. 5%, 1%, 3% and 1. 5% respectively in the measurement of a physical quantity A= √. The maximum percentage error in the P 3 Q2 RS value of A will be: A. A) 6.5 % B. B) 7.5 % C. C) 6.0 % D. D) 8.5 % Question 3 A particle is moving with a uniform speed v in a circular path of radius r with the centre at O. When the particle moves from a point P to Q on the circle such that ∠P OQ = θ, then the magnitude of the change in velocity is A. A) 2v sin(2θ) B. B) zero C. C) 2v sin ( 2θ ) D. D) 2v cos ( 2θ ) Question 4 A potential difference V = 100 ± 5 V, when applied across a resistance, gives a current I = 10 ± 0.2 A. What is the percentage error in R ? A. A) 2% B. B) 5% C. C) 7% D. D) 8% Question 5 The velocity of a projectile at the initial point A is (2ˆi − 3ˆj) m s −1. Its velocity (in m s −1 ) at point B is A. A) −2ˆi − 3ˆj B. B) −2ˆi + 3ˆj C. C) 2ˆi − 3ˆj D. D) 2ˆi + 3ˆj Question 6 In an experiment of simple pendulum, the errors in the measurement of length of the pendulum (L) and time period (T ) are 3% and 2%, respectively. The maximum percentage error in the value of TL2 is A. A) 5% B. B) 7% C. C) 8% D. D) 1% Question 7 A physical quantity X is given by X = 2k l The percentage error in the measurements of k, 3 2 m√n l, m and n are 1%, 2%, 3% and 4% respectively. The value of X is uncertain by  A. A) 8% B. B) 10% C. C) 12% D. D) none of these Question 8 If a vector 2^i + 3^ ^ is perpendicular to the vector 4^i − 4^j + αk j + 8k ^, then value of α is A. A) −1 B. B) 12 C. C) − 12 D. D) 1 Question 9 → A particle moving with velocity V is acted by three forces shown by the vector triangle P QR. The velocity of the particle will A. A) increase B. B) decrease C. C) remain constant − → D. D) change according to the smallest force QR Question 10 The heat generated in a circuit is given by Q = I 2 Rt, where I is current, R is resistance and tis time. If the percentage errors in measuring I. R and t are 2%, 1% and 1% respectively, then the maximum error in measuring heat will be A. A) 2% B. B) 3% C. C) 4% D. D) 6% Question 11 → B Vectors A, → , and C→ are such A→ ⋅ B → = 0 A→ ⋅ C→ = 0. Then the vector parallel is A→ is: →×B A. A) A → → × C→ B. B) B → × C→ C. C) B → and C→ D. D) B Question 12 The vector sum of two forces is perpendicular to their vector differences. In that case, the force: A. A) are equal to each other B. B) are equal to each other in magnitude C. C) are not equal to each other in magnitude D. D) cannot be predicted Question 13 If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be A. A) 2% B. B) 4% C. C) 6% D. D) 8% Question 14 If vectors P→ = a^i + a^ ^ and Q = a^i − 2^j − k j + 3k ^ are perpendicular to each other, then the positive value of a is A. A) 3 B. B) 1 C. C) 2 D. D) 0. Question 15 Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is A. A) 6% B. B) zero C. C) 1% D. D) 3% Question 16 The decimal number equivalent to a binary number 1011001 is A. A) 13 B. B) 17 C. C) 89 D. D) 178 Question 17 If a wire is stretched to make it 0.1% longer, its resistance will : A. A) increase by 0.2% B. B) decrease by 0.2% C. C) decrease by 0.05% D. D) increases by 0.05% Question 18 A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are (√3, 3). The path of the particle makes with the x-axis an angle of: A. A) 45 ∘ B. B) 60 ∘ C. C) 0 ∘ D. D) 30 ∘ Question 19 Assertion : The cross product of a vector with itself is a null vector. Reason : The cross product of two vectors results in a vector quantity. A. A) If both assertion and reason are true and reason is the correct explanation of assertion. B. B) If both assertion and reason are true but reason is not the correct explanation of assertion. C. C) If assertion is true but reason is false. D. D) If both assertion and reason are false. Question 20 → → → → → Given that A + B = R and A 2 + B 2 = R 2. The angle between A and B is A. A) 0 B. B) π/4 C. C) π/2 D. D) π Question 21 → through f→ have the magnitudes and directions indicated in the figure. Which of the Six vectors a following statements is true? A. A) → b + c→ = f→ B. B) d→ + c→ = f→ → = f→ C. C) d→ + e D. D) → b + e→ = f→ Question 22 → and B If A → are non-zero vectors which obey the relation |A→ + B| → = |A→ − B| → , then the angle between them is A. A) 0 ∘ B. B) 60 ∘ C. C) 90 ∘ D. D) 120 ∘ Question 23 The vectors are given by A ^ and B = 3^i + 6^j + 2k. Another vector C has the ˙ = ^i + 2^j + 2k same magnitude as B but has the same direction as A. Then which of the following vectors represents C? A. A) 73 (^i + 2^j + 2k) ^ B. B) 37 (i − 2^ ^ j + 2k) C. C) 79 (i − 2^ ^ j + 2k) D. D) 97 (→i + 2^ ^ j + 2k) Question 24 The period of oscillation of a simple pendulum is T = 2π√ gl. Measured value of l is 20. 0 cm, known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s resolution. The accuracy in the determination of g is A. A) 5% B. B) 4% C. C) 3% D. D) 1% Question 25 The value of ' λ ' for which the two vectors a ^ and →b = ^i − 2^j + k → = 5^i + λ^j + k ^ are perpendicular to each other is A. A) 2 B. B) -2 C. C) 3 D. D) -3 Question 26 An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be : A. A) 4.4% B. B) 2.27% C. C) 1.7% D. D) 2.7% Question 27 The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is the total mass of the box and the difference in the masses of the pieces to correct significant figures? A. A) 2.34 kg, 0 g B. B) 2.3 kg, 0.02 g C. C) 2.34 kg, 0.02 g D. D) 2.3 kg, 0 g Question 28 → → → → → The two vectors A and B are drawn from a common point and C = A + B, then angle → → between A and B is - (1) 90 if C 2 = A 2 + B 2 (2) greater than 90 if C 2 < A 2 + B 2 (3) ∘ ∘ greater than 90 ∘ if C 2 > A 2 + B 2 (4) less than 90 ∘ if C 2 > A 2 + B 2 Correct options are - A. A) 1,2 B. B) 1,2,3,4 C. C) 2,3,4 D. D) 1,2,4 Question 29 → → → → → → → → Given C = A × B and D = B × A. What is the angle between C and D ? A. A) 30 ∘ B. B) 60 ∘ C. C) 90 ∘ D. D) 180 ∘ Question 30 → → → → Given A = 2^i + 3^j and B = ^i + ^j. The component of vector A along vector B is A. A) 1 √2 B. B) 3 √2 C. C) 5 √2 D. D) 7 √2 Moderate Questions Question 31 In the measurement of a physical quantity X = CA1/3B. The percentage errors introduced in 2 D3 the measurements of the quantities A, B, C , and D are 2%, 2%, 4% and 5%, respectively. Then, the minimum amount of percentage error in the measurement of X is contributed by A. A) A B. B) B C. C) C D. D) D Question 32 A→ and B → are two vectors given by A→ = 2^i + 3^j and B → = ^i + ^j. The magnitude of the component of A → along B → is A. A) 5 √2 B. B) 3 √2 C. C) 7 √2 D. D) 1 √2 Question 33 A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be: A. A) 92 ± 1.8 s B. B) 92 ± 3 s C. C) 92 ± 2 s D. D) 92 ± 5.0 s Question 34 → The moment of the force, F = 4ˆi + 5ˆj − 6ˆ k at (2, 0, −3), about the point (2, −2, −2), is given by A. A) −7^i − 8^j − 4ˆ k B. B) −4^i − ^j − 8ˆ k C. C) −8^i − 4^j − 7k ^ D. D) −7^i − 4^j − 8ˆ k Question 35 A metal wire has mass (0. 4 ± 0. 002) g, radius (0. 3 ± 0. 001) mm and length (5 ± 0. 02) cm. The maximum possible percentage error in the measurement of density will nearly be: A. A) 1. 4% B. B) 1. 2% C. C) 1. 3% D. D) 1. 6% Question 36 Assertion : If dot product and cross product of P→ and Q → are zero, it implies that one of the vector P→ and Q → must be null vector. Reason : A null vector is a vector of zero magnitude. A. A) If both assertion and reason are true and reason is the correct explanation of assertion. B. B) If both assertion and reason are true but reason is not the correct explanation of assertion. C. C) If assertion is true but reason is false. D. D) If both assertion and reason are false. Question 37 Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is A. A) 0.5 N B. B) 1.5 N C. C) 43 N √ D. D) √3 N Question 38 Force F→ applied on a body is written as F = (^ → → ^ n + G, where n nF)^ ^ is a unit vector The vector → is equal to G → A. A) n ^×F → B. B) n ^ × (^ n × F) → → → C. C) (^ n × F) × F/|F| → D. D) (^ n × F) × n ^ Question 39 The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is A. A) 11% B. B) 21% C. C) 42% D. D) 10% Question 40 Two forces P and Q, of magnitude 2F and 3F , respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is: A. A) 120 ° B. B) 60 ° C. C) 30 ° D. D) 90 ° Question 41 The length and width of a rectangular room are measured to be 3.95 ± 0.05 m and 3.05 ± 0.05 m, respectively, the area of the floor is A. A) 12.05 ± 0.01 m 2 B. B) 12.05 ± 0.005 m 2 C. C) 12.05 ± 0.34 m 2 D. D) 12.05 ± 0.40 m 2 Question 42 In an experiment of simple pendulum, the errors in the measurement of length of the pendulum (L) and time period (T ) are 3% and 2%, respectively. The maximum percentage error in the value of TL2 is A. A) 5% B. B) 7% C. C) 8% D. D) 1% Question 43 The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 × 10 −2 m rise of water, h = 1.45 × 10 −2 m Using g = 9.80 m s −2 and the simplified relation T = 2 × 10 3 N m −1 the possible error in rhg surface tension is closest to: A. A) 10% B. B) 0. 15% C. C) 1. 5% D. D) 2. 4% Question 44 A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e 1 and e 2 respectively, the percentage error in the estimation of g is A. A) e 2 − e 1 B. B) e 1 + 2e 2 C. C) e 1 + e 2 D. D) e 1 − 2e 2 Question 45 The error in the measurement of the length and the breadth of a rectangular table is 1%. If the length and breadth of the table are 1 m and 50 cm respectively, then the area of the table including error is A. A) (0.5 ± 0.1)m 2 B. B) (0.5 ± 0.01)m 2 C. C) (5000 ± 10)cm 2 D. D) (5000 ± 1)cm 2 Question 46 In a triangle ABC , the sides AB and AC are represented by the vectors 3i + j + k and i + 2j + k, respectively. Calculate the angle ∠ABC A. A) cos −1 √ 11 5 B. B) cos −1 √ 11 6 C. C) (90 ∘ − cos −1 √ 11 5 ) D. D) (180 ∘ − cos −1 √ 11 5 ) Question 47 Three vectors A = ai + j + k; B = i + bj + k and C = i + j + ck are mutually perpendicular (i, j and k are unit vectors along X, Y and Z axes respectively). The respective values of a, b and c are A. A) 0,0,0 B. B) − 12 , − 12 , − 12 C. C) 1,-1,1 D. D) 12 , 12 , 12 Question 48 An ant starts from the origin and crawls 10 cm along the x-axis and then 20 cm along the y- axis. The dot product of the ant's displacement vector with the position vector of a point that makes 45° with the x-axis and has a magnitude of √2 cm is A. A) 30 cm B. B) 30√2 cm C. C) √ 30 cm 2 D. D) 15 cm Question 49  → → → Consider the vectors A = ^i + ^j − k, ^. What is the ^ C = 1 (^i − 2^j + 2k) ^ B = 2^i − ^j + k, √5 → → → value of C. (A × B)? A. A) 1 B. B) 0 C. C) 3√2 D. D) 18√5 Question 50 A force F is applied on a square plate of length L. If the percentage error in the determination of L is 3% and in F is 4%, then permissible error in the calculation of pressure is A. A) 13% B. B) 10% C. C) 7% D. D) 12% Question 51 The vectors A and B are such that |A + B| = |A − B|. The angle between the two vectors will be A. A) 0 ∘ B. B) 60 ∘ C. C) 90 ∘ D. D) 45 ∘ Question 52 ^, then the scalar and vector products of F→ and r→ have → If F = 2^i + ^ ^ and r→ = 3^i + 2^j − 2k j−k the magnitudes respectively as: A. A) 5, √3 B. B) 4, √5 C. C) 10, √2 D. D) 10, 2 Question 53 The decimal equivalent of the binary number (11010.101) 2 is A. A) 9.625 B. B) 25.265 C. C) 26.625 D. D) 26.265 Question 54 A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is A. A) 1 m/s 2 towards north-east √2 B. B) 1 2 m/s 2 towards north. C. C) zero D. D) 1 m/s 2 towards north-west √2 Question 55 The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are 0.3% and 0.2% respectively, the maximum error in the estimation of the density of the cube is approximately. A. A) 1.1% B. B) 0.5% C. C) 0.9% D. D) 0.7% Question 56 Assertion : The first derivative of a vector of constant magnitude (either zero or a nonzero) is perpendicular to the vector itself. Reason : Scalar product of two vectors obeys commutative law. A. A) If both assertion and reason are true and reason is the correct explanation of assertion. B. B) If both assertion and reason are true but reason is not the correct explanation of assertion. C. C) If assertion is true but reason is false. D. D) If both assertion and reason are false. Question 57  → → → → Two vectors A and B have equal magnitudes. The magnitude of (A + B) is ' n ' times the → → → → magnitude of (A − B). The angle between A and B is: A. A) cos −1 [ nn2 −1 2 +1 ] B. B) sin −1 [ n−1 n+1 ] C. C) cos −1 [ n−1 n+1 ] D. D) sin −1 [ nn2 −1 2 +1 ] Question 58 Consider a series of measurements of the length of a box in an experiment. The readings are 2.4 m, 2.5 m, 2.6 m, 2.8 m, 3.0 m. What would be the relative error? A. A) 0.110 B. B) 0.089 C. C) 0.079 D. D) 0.072 Question 59 The heat produced in a long wire is characterised by resistance, current and time through which the current passes. If the errors in measuring these quantities are respectively 1%, 2% and 1% , then total error in calculating the energy produced is A. A) 4% B. B) 6% C. C) 4/3% D. D) 8% Question 60 If A = B + C have scalar magnitudes of 5,4,3 units respectively, then the angle between A and C is A. A) cos −1 (3/5) B. B) cos −1 (4/5) C. C) π/2 D. D) sin −1 (3/4) Hard Questions Question 61 A physical quantity P is related to four observables a, b, c and d as P = (α is constant) √ab⋅d α √c The percentage errors in a, b, c and d are 0.5% in each. If the percentage error in P is 2%, then α is A. A) 52 B. B) 25 C. C) 34 D. D) 32 Question 62 Two intervals of time are measured as Δt 1 = (2.00 ± 0.02)s and Δt 2 = (4.00 ± 0.02)s. The value of √(Δt 1 ) (Δt 2 ) with correct significant figures and error is A. A) (2.828 ± 0.01)s B. B) (2.83 ± 0.01)s C. C) (2.828 ± 0.0075)s D. D) (2.83 ± 0.0075)s Question 63 A particle moves in XY -plane with x and y varying with time t as x(t) = 5t, y(t) = 5t (27 − t 2 ). At what time in seconds, the direction of velocity and acceleration will be perpendicular to each other? A. A) 5√ 27 2 B. B) 5 C. C) 5√12 D. D) 3 Question 64 In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5. 25 mm and apparent thickness of the glass slab at 5. 00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is 10 x × 10 −3 , where x is ______ Question 65 Two resistances are given as R 1 = (10± 0.5)Ω and R 2 = (15 ± 0.5)Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is A. A) 6.33 B. B) 2.33 C. C) 4.33 D. D) 5.33 Question 66 A particle is projected with velocity v 0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e. a = −x 2. The distance at which particle stops is - A. A) √ 3v2 0 1 v 20 /3 B. B) ( 3 ) 1 2v 20 /3 C. C) ( 3 ) 1 3v 20 /3 D. D) ( 2 ) Question 67 A physical quantity Q is found to depend on quantities a, b, c by the relation Q = ac2b. The 4 3 percentage error in a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is: A. A) 66% B. B) 43% C. C) 34% D. D) 14% Question 68 → → → Given that A + B + C = 0. Out of three vectors, two are equal in magnitude and the magnitude of third vector is √2 times that of either of the two having equal magnitude. Then the angle between vectors are given by A. A) 45 o , 45 o , 90 o B. B) 90 o , 135 o , 135 o C. C) 30 o , 60 o , 90 o D. D) 45 o , 60 o , 90 o Question 69 A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with a velocity pointed in the same direction. Then the electron will be A. A) Be deflected to the left without increase in speed B. B) Be deflected to the right without increase in speed C. C) Not be deflected but its speed will decrease D. D) Not be deflected but its speed will increase Question 70 A current carrying conductor obeys Ohm's law (V = RI). If the current passing through the conductor is I = (5 ± 0.2) A and voltage developed is V = (60 ± 6)V, then find the percentage of error is resistance, R A. A) 18 B. B) 6 C. C) 14 D. D) 2 Question 71 →→ → Which of the following is not true about vectors A, B and C ? → → → → A. A) (A ⋅ A)(B ⋅ C) is a scalar value. → → → → B. B) (A × B) ⋅ (B × C) is a scalar value. → → → → C. C) (A × C) × (B × C) is a scalar value. → → → D. D) A × (B × C) is a vector value. Question 72 If N A , N B and N C are the number of significant figures in A = 0. 001204 m, B = 43120000 m, and C = 1. 200 m respectively then A. A) N A = N B = N C B. B) N A > N B > N C C. C) N A < N B < N C D. D) N A > N B < N C Question 73 Sum of magnitude of two forces is 25 N. The resultant of these forces is normal to the smaller force and has a magnitude of 10 N. Then the two forces are A. A) 14.5 N, 10.5 N B. B) 16 N, 9 N C. C) 13 N, 12 N D. D) 20 N, 5 N Question 74 Find the angle between the vectors A = 2^i + 4^j + 4k ^ and B = 4^i + 2^j − 4k ^. A. A) 0 ∘ B. B) 45 ∘ C. C) 60 ∘ D. D) 90 ∘ Question 75 The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r = (0.35 ±0.05) cm, R = (100 ± 10) ohm, l = (15 ± 0.2) cm The percentage error in resistivity of the material of the wire is : A. A) 25. 6% B. B) 39.9 % C. C) 37. 3% D. D) 35.6 % Question 76 A vector P directed along the X-axis is added to vector Q which has a magnitude of 10 m. The resultant vector is directed along the Y -axis, with a magnitude that is 2 times that of P. The magnitude of P is A. A) √10 m B. B) 5√2 m C. C) 6 m D. D) 2√5 m Question 77 → A force given by F = f xˆi + f yˆj + f z ˆ k acts on a particle which moves from (a, b, c) to (d, e, f). The work done by the force F is : (Here A 1 , A 2 , A 3 are magnitude of area bounded) A. A) A 1 +A 2 +A 3 B. B) A 1 − A 2 − A 3 C. C) -A 1 +A 2 -A 3 D. D) A 1 -A 2 +A 3 Question 78 The algebraic sum of two co-initial vectors is 16 units. Their vector sum is 8 units and the resultant of the vectors are perpendicular to the smaller vector. Then magnitudes of the two vectors are - A. A) 2 unit & 14 unit B. B) 4 unit & 12 unit C. C) 6 unit & 10 unit D. D) 8 unit & 8 unit Question 79 In the measurement of a physical quantity X = CA1/3B. The percentage errors introduced in 2 D3 the measurements of the quantities A, B, C , and D are 2%, 2%, 4% and 5%, respectively. Then, the minimum amount of percentage error in the measurement of X is contributed by A. A) A B. B) B C. C) C D. D) D Question 80 → → A vector A is rotated by a small angle Δθ radians (Δθ ≪ 1) to get a new vector B. In that → → case B − A is : → (Δθ) 2 A. A) A [1 − 2 ] B. B) 0 → C. C) A Δ θ → → D. D) B Δ θ − A Question 81 Students A, B and C measure the length of a room using 25 m long measuring tape of least count (LC) 0. 5 cm, meter-scale of LC 0. 1 cm and a foot-scale of LC 0. 05 cm, respectively. If the specified length of the room is 9. 5 m, then which of the following students will report the lowest relative error in the measured length? A. A) Student A D. D) ∣ B. B) Student B C. C) Student C D. D) Both, student B and C Question 82 If two vectors A and B are mutually perpendicular, then the component of A − B along the direction of A + B is A. A) √|A| 2 + |B| 2 B. B) √|A| 2 − |B| 2 C. C) |A| 2 −|B| 2 √|A| 2 +|B| 2 |A| 2 +|B| 2 √|A| 2 −|B| 2 Question 83 If a vector 2^i + 3^ A. A) 12 B. B) − 12 ^ is perpendicular to the vector 4^j − 4^i + αk j + 8k ^ then the value of α is: C. C) 1 D. D) -1 Question 84 A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ±0.01 mm. Take g = 9.8 m/s 2 (exact). The Young's modulus obtained from the reading is A. A) (2.0 ± 0.3)10 11 N/m 2 B. B) (2.0 ± 0.2) × 10 11 N/m 2 C. C) (2.0 ± 0.1) × 10 11 N/m 2 D. D) (2.0 ± 0.05) × 10 11 N/m 2 Question 85 Vector A has a magnitude of 10 units and makes an angle of 30 ∘ with the positive X-axis. Vector B has a magnitude of 20 units and makes an angle of 30 ∘ with the negative X-axis. What is the magnitude of the resultant between these two vectors? A. A) 20√3 B. B) 35 C. C) 15√3 D. D) 10√3 Question 86 Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are A. A) 12 N, 6 N B. B) 13 N, 5 N C. C) 10 N, 8 N D. D) 16 N, 2 N Question 87 A thin 1 m long rod has a radius of 5 mm. A force of 50π×10 N is applied at one end to 3 determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0. 01 mm, which of the following statements is false?  A. A) The maximum value of Y that can be determined is 2 × 10 14 N m −2 B. B) ΔY Y gets minimum contribution from the uncertainty in the length. C. C) ΔY Y gets its maximum contribution from the uncertainty in strain. D. D) The figure of merit is the largest for the length of the rod. Question 88 The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would A. A) first increases then decrease back to the original value B. B) first decreases then increase back to the original value C. C) remains unchanged D. D) increases towards a saturation value Question 89 In an octagon ABCDEF GH of equal side, what is the sum of − − − − − − − −→ → → → → → → → AB + AC + AD + AE + AF + AG + AH, if, AO = 2ˆi + 3ˆj − 4ˆ k A. A) 16ˆi + 24ˆj − 32ˆ k B. B) 16ˆi − 24ˆj + 32ˆ k C. C) 16ˆi + 24ˆj + 32ˆ k D. D) −16ˆi − 24ˆj + 32ˆ k Question 90 A jet plane of wing span 20 m is travelling towards west at a speed of 400 ms −1. If the earth's total magnetic field is 4 × 10 −4 T and the dip angle is 30 ∘ , at that place, the voltage difference developed across the ends of the wing is A. A) 1.6 V B. B) 3.2 V C. C) 0.8 V D. D) 6.4 V Correct Answers for this Chapter Q1 - A Q31 - C Q61 - A Q2 - A Q32 - A Q62 - B Q3 - C Q33 - C Q63 - D Q4 - C Q34 - D Q64 - 41 (Num) Q5 - D Q35 - D Q65 - C Q6 - B Q36 - B Q66 - D Q7 - C Q37 - A Q67 - C Q8 - B Q38 - D Q68 - B Q9 - C Q39 - D Q69 - C Q10 - D Q40 - A Q70 - C Q11 - C Q41 - C Q71 - C Q12 - B Q42 - B Q72 - A Q13 - C Q43 - C Q73 - A Q14 - A Q44 - B Q74 - D Q15 - A Q45 - B Q75 - B Q16 - C Q46 - A Q76 - D Q17 - A Q47 - B Q77 - B Q18 - B Q48 - A Q78 - C Q19 - B Q49 - B Q79 - C Q20 - C Q50 - B Q80 - C Q21 - C Q51 - C Q81 - A Q22 - C Q52 - C Q82 - C Q23 - A Q53 - C Q83 - B Q24 - C Q54 - D Q84 - B Q25 - C Q55 - C Q85 - D Q26 - D Q56 - B Q86 - B Q27 - B Q57 - A Q87 - A Q28 - D Q58 - D Q88 - A Q29 - D Q59 - B Q89 - A  Q30 - C Q60 - A Q90 - A Units and Dimensions Easy Questions Question 1 [L 2 M 1 T −2 ] are the dimension of A. A) Torque B. B) Force C. C) Angular acceleration D. D) Angular momentum Question 2 The dimension of torque is A. A) [MT −2 ] B. B) [ML −1 T −1 ] C. C) [ML 2 T −2 ] D. D) [ML 3 T −3 ]. Question 3 Using mass (M), length (L), time (T ) and current (A) as fundamental quantities, the dimension of permeability is A. A) M −1 LT −2 A B. B) ML 2 T −2 A −1 C. C) MLT −2 A −2 D. D) MLT −1 A −1. Question 4 If force (F ), length (L) and time (T ) are assumed to be fundamental units, then the dimensional formula of the mass will be A. A) [FL −1 T 2 ] B. B) [FL −1 T −2 ] C. C) [FL −1 T −1 ] D. D) [FL 2 T 2 ] Question 5 The dimensions of Planck's constant is the same as the product of A. A) force and time B. B) force, displacement and time C. C) force and distance D. D) time and displacement Question 6 The dimensions of universal gravitational constant are: A. A) [M −1 L 3 T −2 ] B. B) [ML 2 T −1 ] C. C) [ML −2 L 3 T −2 ] D. D) [ML −2 L 2 T −1 ] Question 7 The dimensional formula of Planck's constant is A. A) [ML 2 T −1 ] B. B) [ML 2 T −2 ] C. C) [ML 0 T 2 ] D. D) [MLT 2 ] Question 8 Assertion : S.I. units are logical and coherent. Reason : S.I. system of units is a rationalised system. A. A) If both the assertion and reason are true and reason is a correct explanation of the assertion. B. B) If both assertion and reason are true but assertion is not a correct explanation of the assertion. C. C) If the assertion is true but the reason is false. D. D) If both assertion and reason are false. Question 9 The dimensions of self or mutual inductance are given as A. A) [L −2 M 1 T −2 I −2 ] B. B) [L 2 M −2 T −2 I −2 ] C. C) [L 2 M 1 T −2 I −2 ] D. D) [L 2 M 2 T −2 I −2 ] Question 10 The equation of state of a gas is given by (p + va3 ) (V − b 2 ) = cT , where p, V , T are pressure, volume and temperature respectively and a, b, c are constants. The dimensions of a and b are respectively A. A) [ML 8 T −2 and L 3/2 ] B. B) [ML 5 T −2 and L 3 ] C. C) [ML 5 T −2 and L 6 ] D. D) [ML 6 T −2 and L 3/2 ] Question 11 The pair of quantities having same dimensions is: A. A) Impulse and Surface Tension B. B) Angular momentum and Work C. C) Work and Torque D. D) Young's modulus and Energy Question 12 → = ( A2 ^i + B3 ^j). The SI unit of A and B are: Electric field in a certain region is given by E x y A. A) Nm 3 C −1 ; Nm 2 C −1 B. B) Nm 2 C −1 ; Nm 3 C −1 C. C) Nm 3 C; Nm 2 C D. D) Nm 2 C; Nm 3 C Question 13 Dimensions of resistance in an electrical circuit, in terms of dimension of mass M , of length L, of time T and of current I , would be A. A) ML 2 T −2 B. B) ML 2 T −1 I −1 C. C) ML 2 T −3 I −2 D. D) ML 2 T −3 I −1 Question 14 What is the dimensions of magnetic field B in terms of C (= coulomb), M, L, T? A. A) [M 1 L 1 T −2 C] B. B) [M 1 L 0 T −1 C −1 ] C. C) [M 1 L 0 T −2 C] D. D) [M 1 L 0 T −1 C] Question 15 Dimension of electrical resistance is A. A) [ML 2 T −3 A −1 ] B. B) [ML 2 T −3 A −2 ] C. C) [ML 3 T −3 A −2] D. D) [ML −1 L 3 T 3 A 2 ]. Question 16 Let the inductance and resistance be denoted by 'L' and 'R' respectively. The dimensions of ( RL ) are A. A) [L 1 M 0 T 1 ] B. B) [L 0 M 0 T 0 ] C. C) [L 0 M 1 T 0 ] D. D) [L 0 M 0 T 1 ] Question 17 If E and G respectively denote energy and gravitational constant, then G E has the dimensions of: A. A) [M][L 0 ][T 0 ] B. B) [M][L −1 ][T −1 ] C. C) [M 2 ][L −1 ][T 0 ] D. D) [M 2 ][L −2 ][T −1 ] Question 18 The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are A. A) kgms −1 B. B) kgms −2 C. C) kgs −1 D. D) kgs Question 19 If x = at + bt 2 , where x is in metre (m) and t is in hour (h), then unit of b will be A. A) mh 2 B. B) m C. C) m h D. D) hm2 Question 20 The unit of thermal conductivity is A. A) J m K −1 B. B) J m −1 K −1 C. C) W m K −1 D. D) W m −1 K −1 Question 21 The frequency of vibration of string is given by v = 2l [ m ] Here p is number of segments in p F 1/2 the string and l is the length. The dimensional formula for m will be A. A) [M 0 LT −1 ] B. B) [ML 0 T −1 ] C. C) [ML −1 T 0 ] D. D) [M 0 L 0 T 0 ] Question 22 Which of the following is the dimensional formula for electric polarisation? A. A) [M 0 L −2 T 1 I 1 ] B. B) [M −1 L −2 T 1 I −1 ] C. C) [M 0 L −1 T 1 I 1 ] D. D) [M 1 L −2 T 1 I 1 ] Question 23 If T = 2π√ ML 3Yq then find the dimensions of q. Where T is the time period of bar of mass M 3 length L and Young modulus Y. A. A) [L] B. B) [L 2 ] C. C) [L 4 ] D. D) [L 3 ] Question 24 Assertion : Specific gravity of a fluid is a dimensionless quantity. Reason : It is the ratio of density of fluid to the density of water. A. A) If both assertion and reason are true and reason is the correct explanation of assertion B. B) If both assertion and reason are true but reason is not the correct explanation of assertion C. C) If assertion is true but reason is false D. D) If both assertion and reason are false. Question 25 From dimensional analysis, the Rydberg constant can be expressed in terms of electric charge (e), mass (m) and Planck constant ( h ) as [ consider 4πϵ 1 0 ≡ 1 unit ] A. A) me h2 2 B. B) me2 4 h C. C) m2 e4 h2 D. D) None of the above Question 26 Dimension of which base quantity corresponds to that √ Gh c3 =? A. A) Time B. B) Length C. C) Mass D. D) Temperalure Question 27 The correct dimensional formula for impulse is given by A. A) ML 2 T −2 B. B) MLT −1 C. C) ML 2 T −1 D. D) MLT −2 Question 28 If the force is given by F = at + bt 2 with t as time. The dimensions of a and b are A. A) [MLT −4 ] and [MLT −2 ] B. B) [MLT −3 ] and [MLT −4 ] C. C) [ML 2 T −3 ] and [ML 2 T −2 ] D. D) [ML 2 T −3 ] and [ML 3 T −4 ] Question 29 The frequency v of the radiation emitted by an atom when an electron jumps from one orbit to another is given by = kδE, where k is a constant and δE is the change in energy level due to the transition. Then dimension of k is A. A) ML 2 T −2 B. B) the same dimension of angular momentum C. C) ML 2 T −1 D. D) M −1 L −2 T Question 30 In case of dimensions of electric field and electric dipole moment the power of mass is respectively. A. A) 1, 1 B. B) 1, 0 C. C) 0, 1 D. D) 0, 0 Moderate Questions Question 31 If speed V, force F and acceleration a are chosen as the fundamental physical quantities, then the dimension of Young's modulus in terms of V, F and a are A. A) [V −3 Fa] B. B) [V −4 F 2 a 2 ] C. C) [V −4 Fa 2 ] D. D) [V −4 F 2 a] Question 32 If the velocity of light C , the gravitational constant G and Planck's constant h are chosen as the fundamental units, the dimension of density in the new system is A. A) C 3 G −2 h 1 B. B) C 5 G −2 h −1 C. C) C −3/2 G −1/2 h 1/2 D. D) C 9/2 G −1/2 h −1/2 Question 33 Which of the following physical quantities has neither dimensions nor unit? A. A) Angle B. B) Luminous intensity C. C) Coefficient of friction D. D) Current Question 34 If A represents Boltzmann constant, B represents Planck's constant and C represents speed of light in vacuum, then the quantity having the dimensions of A 4 B −3 C −2 is A. A) universal gas constant B. B) specific heat capacity C. C) stefan’s constant D. D) heat energy Question 35 If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension× length) A. A) [E V −2 T −1 ] B. B) [E V −1 T −2 ] C. C) [E V −2 T −2 ] D. D) [E −2 V −1 T −3 ] Question 36 Which of the following is the unit of mobility of a electron in a conductor? A. A) kg −1 s 2 A −1 B. B) kg −1 s 2 A C. C) kg −1 ms 2 A −1 D. D) kgms −1 A −1 Question 37 Select the physical quantities in Column-I and Column-II having same dimensions. The correct answer is $ A B C D $ A. A) III IV I II B. B) IV I III II C. C) II III IV I D. D) II IV III II Question 38 Match List - I with List - II : List - I List - II (a) Gravitational constant (G) (i) [L 2 T −2 ] (b) Gravitational potential energy (ii) [M −1 L 3 T −2 ] (c) Gravitational potential (iii) [LT −2 ] (d) Gravitational intensity (iv) [ML 2 T −2 ] Choose the correct answer from the options given below: A. A) (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii) B. B) (a) - (ii), (b) - (iv), (c) - (iii), (d) - (i) C. C) (a) - (iv), (b) - (ii), (c) - (i), (d) - (iii) D. D) (a)-(ii), (b)-(i), (c) - (iv), (d) - (iii) Question 39 Select the dimensional formula of 2μ B2 0 A. A) [M 1 L 1 T 2 ] B. B) [M −1 L 1 T 2 ] C. C) [M −1 L −1 T −2 ] D. D) [M 1 L −1 T −2 ] Question 40 If the units of mass, length and time are doubled then unit of angular momentum will be A. A) Doubled B. B) Tripled C. C) Quadrupled D. D) Eight times the original value Question 41 The velocity v of a particle at time t is given by v = at + t+c b , where a, b and c are constants. The dimensions of a, b and c are: A. A) L, LT and LT 2 B. B) LT −2 , L and T C. C) L 2 , T and LT 2 D. D) LT 2 , LT and L. Question 42 If the energy, E = G p h q c r , where G is the universal gravitational constant, h is the Planck's constant and c is the velocity of light, then the values of p, q and r are, respectively A. A) −1/2, 1/2 and 5/2 B. B) 1/2, −1/2 and −5/2 C. C) −1/2, 1/2 and 3/2 D. D) 1/2, −1/2 and −3/2 Question 43 A physical quantity of the dimensions of length that can be formed out of c, G and 4πε e2 , where 0 [c is velocity of light, G is universal constant of gravitation, e is charge & ε 0 is permittivity of free space]:  1 A. A) e2 2 1 c2 [G 4πε 0 ] 1 B. B) c [G e2 2 2 4πε 0 ] 1 C. C) e2 2 1 c2 [ G4πε 0 ] D. D) 1c G 4πε e2 0 Question 44 The dimensions of ab , in the equation P = a−t bx , where P is pressure, x is distance and t is 2 time, are A. A) [M 2 LT −3 ] B. B) [MT −2 ] C. C) [ML 3 T −1 ] D. D) [LT −3 ] Question 45 Assertion (A) Energy per unit volume and angular momentum can be added dimensionally. Reason (R) Physical quantities having same dimensions can be added or subtracted. A. A) Both (A) and (R) are true and (R) is the correct explanation of (A) B. B) Both (A) and (R) are true but (R) is not the correct explanation of (A) C. C) (A) is true but (R) is false D. D) (A) is false but (R) is true Question 46 Dimensional analysis of the equation (velocity) x = (pressure difference) 3/2 × (density) −3/2 , gives the value of x as _______. Question 47 If the dimensions of a physical quantity are given by [M a L b T c ], then the physical quantity will be : A. A) Force if a = 0, b = −1, c = −2 B. B) Pressure if a = 1, b = −1, c = −2 C. C) Velocity if a = 1, b = 0, c = −1 D. D) Acceleration if a = 1, b = 1, c = −2 Question 48 A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ? A. A) BD C 2 2 − A CD B. B) A 2 − B 2 C 2 C. C) B A −C D. D) A −AC 2 D Question 49 When a wave traverses a medium, the displacement of a particle located at x at a time t is given by y = a sin(bt − cx), where a, b and c are constants of the wave, which of the following is a quantity with dimensions? A. A) a y B. B) bt C. C) cx D. D) cb Question 50 In a new system of units, the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s. Unit of mass in this system can be expressed as A. A) 10 5 kg B. B) 10 6 kg C. C) 10 2 kg D. D) 10 3 kg Question 51 Which of the following pairs does not have same dimensions ? A. A) impulse and momentum B. B) moment of inertia and moment of force C. C) angular momentum and Planck's constant D. D) work and torque. Question 52 The engine of a truck moving along a straight road delivers constant power. The distance travelled by the truck in time t is proportional to A. A) t B. B) t 2 C. C) √t D. D) t 3/2 Question 53 Consider a spongy block of mass m floating on a flowing river. The maximum mass of the block is related to the speed of the river flow v, acceleration due to gravity g and the density of the block ρ such that m max = kv x g y ρ z (k is constant ). The values of x, y and z should then respectively be (Mass of the spongy block is assumed to vary due to absorption of water by it) A. A) 6, 3, 2 B. B) 6, −3, 1 C. C) 3, 6, 1 D. D) 6, 1, 3 Question 54 In CGS system the magnitude of the force is 100 dynes. In another system where the fundamental physical. quantities are kilogram, meter and minute, the magnitude of the force is A. A) 0.036 B. B) 0.36 C. C) 3.6 D. D) 36 Question 55 The velocity of water waves v may depend upon their wavelength λ , the density of water ρ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as A. A) v 2 ∝ ρg B. B) v 2 ∝ gλρ C. C) v 2 ∝ gλ D. D) v 2 ∝ g −1 λ −3 Question 56 The position of a particle at time t is given by the equation x(t) = A0 (1 − e At )v o = constant v and A > 0. Dimensions of v o and A respectively are A. A) [M 0 LT 0 ] and [M 0 L 0 T −1 ] B. B) [M 0 LT −1 ] and [M 0 LT −2 ] C. C) [M 0 LT −1 ] and [M 0 L 0 T] D. D) [M 0 LT −1 ] and [M 0 L 0 T −1 ] Question 57 A certain physical quantity is calculated from the formula π3 (a 2 − b 2 )hd, where a, b and h are all lengths and d is density. The physical quantity being calculated is A. A) velocity B. B) volume C. C) mass D. D) acceleration Question 58 The speed of ripples (v) on water surface depends on surface tension (σ), density (ρ), and wavelength (λ). Then the square of speed (v) is proportional to A. A) ρλ σ B. B) σλ ρ C. C) σρ λ D. D) √ σ ρλ Question 59 Electric displacement is given by D = εE , here, ε =electric permittivity, E =electric field strength The dimensions of electric displacement are A. A) [ML −2 TA] B. B) [L −2 T −1 A] C. C) [L −2 TA] D. D) None of these Question 60 If C, R, L and I denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are : (1) CR (2) R L (3) √LC (4) LI 2 A. A) (1) and (2) only B. B) (1) and (3) only C. C) (1) and (4) only D. D) (1), (2) and (3) only Hard Questions Question 61 If dimensions of critical velocity, v c of a liquid flowing through a tube are expressed as [η x ρ y r z ], where, η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube, respectively, then, the values of x, y and z are given by A. A) −1, − 1, 1 B. B) −1, − 1, − 1 C. C) 1, 1, 1 D. D) 1, − 1, − 1 Question 62 The dimensions of stefan-Boltzmann constant σ can be written in terms of Planck's constanth' Boltzmann constant K B and the speed of light c as σ = h α K B β C γ. Here A. A) α = 3, β = 4 and γ = −3 B. B) α = 3, β = −4 and γ = 2 C. C) α = −3, β = 4 and γ = −2 D. D) α = 2, β = −3 and γ = −1 Question 63 The efficiency of an engine is given by η = sin θ ⋅ log e kT , where α and β are constants. If T αβ βx is the absolute temperature, k - Boltzmann constant, θ-angular displacement and x is distance, then the incorrect statement is A. A) Dimensions of β are same as that of force B. B) Dimensions of α −1 x are same as that of energy C. C) Dimensions of η −1 sin θ are same as that of αβ D. D) Dimensions of α are same as that of β Question 64 Velocities (V) and accelerations (a) in two systems of units 1 and 2 are related as V 2 = mn2 V 1 and a 2 = mna1 respectively. Here m and n are constants. Dimensionally relations between distances (S 1 and S 2 ) and times (t 1 and t 2 ) in the two systems are respectively. A. A) S 2 = ( m ) S 1 and t 2 = nm t 1 3 2 n B. B) S 2 = ( m ) S 1 and t 2 = nm2 t 1 n 3 C. C) S 2 = nm2 S 1 and t 2 = m 2 t n4 1 D. D) S 2 = nm S 1 and t 2 = m 2 2 t n4 1 Question 65 The dependency of speed of water surface waves (capillary waves) on the density of water (ρ) their wavelength (λ) and surface tension (γ) is - γa A. A) √ ρ γ B. B) √ ρλ 1 γ C. C) ( 3 ρλ ) γ D. D) ρλ Question 66 If p represents radiation pressure, C represents the speed of light and q represents radiation energy striking a unit area per second, then non-zero integers a, b and c are such that p a q b C c is dimensionless, then A. A) a = 1, b = 1, c = −1 B. B) a = 1, b = −1, c = 1 C. C) a = −1, b = 1, c = 1 D. D) a = 1, b = 1, c = 1 Question 67 If E and E 0 denote energies at time t and t 0 respectively, and L and L 0 distance from some point at t and t 0 respectively, then which of the following equations can be declared to be incorrect on dimensional grounds (A) E = 2E 0 L L0 − L2L (B) E = E 0 e 0 −L (C) E = 2Le E0 −L (D) E = 2( L 0 ) × e L0 E 0 A. A) A,B only B. B) A,C only C. C) A,C,D only D. D) C,D only Question 68 Stoke's law states that the viscous drag force F experienced by a sphere of radius a, moving with a speed V through a fluid with coefficient of viscosity η, is given by F = 6 inav. If this fluid is flowing through a cylindrical pipe of radiusr, leng th / and a pressure difference of Pacross its two ends, then the volume of water V which flows through the pipe in time t can be written as = k( Pℓ ) η b r c , where k is a dimensional constant. Correct values of a, b and c are V a t A. A) a = 1, b = −1, c = 4 B. B) a = −1, b = 1, c = 4 C. C) a = 2, b = −1, c = 3 D. D) a = 1, b = −2, c = −4 Question 69 Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses 250 g and 125 g are in the ratio A. A) 2 1/6 B. B) 2 1/3 C. C) 2 1/2 D. D) 2 2/3 Question 70 Number of particles, given by n = −D x22 −x11 , is crossing a unit area perpendicular to x-axis in n −n unit time, where n 1 and n 2 are number of particles per unit volume for the value of x meant to x 2 and x 1. Find dimensions of D, called as diffusion constant. A. A) [M 0 LT 2 ] B. B) [M 0 L 2 T −4 ] C. C) [M 0 LT −3 ] D. D) [M 0 L 2 T −1 ] Question 71 Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS. A. A) A-p, r; B-r, s; C-q; D-p, q B. B) A-p, q; B-r, s; C-r, s; D-r, s C. C) A-q; B-r, s; C-s; D-p, q, r D. D) A-r, s; B-q; C-p; D-p, q, s Question 72 A beaker contains a fluid of density ρ m3 , specific heat S kgJo C and viscosity η. The beaker is kg filled up to height h. To estimate the rate of heat transfer per unit area ( A ) by convection ˙ Q when beaker is put on a hot plate, a student proposes that it should depend on η , ( SΔθ h ) and 1 ( ρg ) when Δθ ( in o C ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for ( A ) is: ˙ Q A. A) ( SΔθ h )η B. B) η( SΔθ 1 h )( ρ g ) C. C) ( SΔθ ηh 1 )( ρg ) D. D) SΔθ ηh Question 73 A massive black hole of mass m and radius R is spinning with angular velocity ω. The power P radiated by it as gravitational waves is given by P = Gc −5 m x R y ω z , where c and G are speed of light in free space, and the universal gravitational constant, respectively. Then A. A) x = −1, y = 2, z = 4 B. B) x = 1, y = 1, z = 4 C. C) x = −1, y = 4, z = 4 D. D) x = 2, y = 4, z = 6 Question 74 Coefficient of thermal conductivity is the product of heat, distance and reciprocal of (area × difference in temperature × time). The new value of a unit of coefficient of thermal conductivity, if fundamental units are 21.6kg, 1 decimetre, 4 K and 1 minute will be ______ ×10 −6 new units. If your answer is K, mark 2K as answer after rounding off to nearest integer. Question 75 If the time period (T ) of vibration of a liquid drop depends on surface tension (S) , radius (r) of the drop and density (ρ) of the liquid, then the expression of T is A. A) T = k√ρr 3 /S B. B) T = k√ρ 1/2 r 3 /S C. C) T = k√ρr 3 /S 1/2 D. D) None of these Question 76 In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0. 1 s respectively. The unit of force in this system will be equivalent to - A. A) 10 1 N B. B) 1 N C. C) 10 N D. D) 100 N Question 77 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T ) of the liquid drop depends on the radius (r) of the drop, density (ρ) and surface tension (S) of the liquid. Which among the following will be a possible expression for the time period? where k is a dimensionless constant. A. A) k√ S ρr B. B) k√ S ρ2 r C. C) k√ S ρr 3 D. D) k√ S 2 ρr 3 Question 78 Using dimensional analysis the resistivity in terms of fundamental constants h, m e , c, e, ε 0 can be expressed as A. A) ε mh ce2 0 e B. B) ε 0 m e ce 2 h C. C) 2 h m e ce 2 D. D) me ε0 ce 2 Question 79 Wave pulse can travel along a tense string like a violin spring. Aseries of experiments showed that the wave velocity V of a pulse depends on the following quantities, the tension T of the string, the cross-section area A of the string and then as per unit volume ρ of the string. Obtain an expression for V in terms of the T, A and ρ using dimensional analysis. A. A) V = k√ Aρ T B. B) V = k√ A T C. C) V = k√ T Aρ D. D) None of these Question 80 The viscosity η of a gas depends on the long-range attractive part of the intermolecular force, which varies with molecular separation r according to F = μr –n where n is a number and μ is a constant. If η is a function of the mass m of the molecules, their mean speed v, and the constant μ then which of following is correct - A. A) η ∝ m n+1 v n+3 μ n−2 B. B) η ∝ m n−1 v n−1 μ n−1 n+1 n+3 −2 C. C) η ∝ m n v −n μ −2 D. D) η ∝ mv μ −n Question 81 A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about its equilibrium shape. By dimensional analysis the ratio v can be (Here σ is surface tension, ρ is density, g is acceleration due to gravity, and k is √σ/ρR 3 arbitrary dimensionless constant)- A. A) kρgR 2 /σ B. B) kρR 2 /gσ C. C) kρR 3 /gσ D. D) kρ/gσ Question 82 The potential energy of a particle varies with distance x from a fixed origin as U = x2 +B A√x where A and B are constants. The dimensions of A are - A. A) [ML 2 T −2 ] 5 B. B) [M 1 L 2 T −2 ] C. C) [M 2 L 2 T −2 ] 3 5 D. D) [M 1 L 2 T −2 ] 7 Question 83 The speed of light (c), gravitational constant (G) and Planck’s constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be: A. A) 1 1 −5 G2 h2 c 2 B. B) −1 1 1 G 2 h2 c2 C. C) 1 1 −3 G2 h2 c 2 D. D) 1 1 1 G2 h2 c2 Question 84 The expressions below give current I through an electronic component as a function of applied potential V. I 0 and V 0 are constants having dimensions of current and potential respectively. 2V Which of the following are dimensionally incorrect? (A) I = I 0 (e V0 + 1) (B) v V V I = I 0 (e 2V0 − 1) (C) I = I 0 V 0 (e V0 − 1) (D) I = I 0 ( VV0 ) (e V0 − 1) A. A) A B. B) B C. C) C D. D) D Question 85 If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ 0 can be expressed in units of: A. A) ( mc 2 he 2 ) B. B) ( me h 2 ) C. C) ( me hc 2 ) D. D) ( ceh2 ) Question 86 If velocity, force and time are taken as the fundamental quantities, then using dimensional analysis choose the correct dimensional formula for mass among the following. [ K is a dimensionless constant] A. A) Q = K v −1 F T B. B) Q = K v 3 F T 2 C. C) Q = 2 K v −1 F T D. D) Q = 3 K v 2 F T Question 87 The dependency of speed of water surface waves (capillary waves) on the density of water (ρ) their wavelength (λ) and surface tension (γ) is - γa A. A) √ ρ γ B. B) √ ρλ 1 γ C. C) ( 3 ρλ ) γ D. D) ρλ Question 88 The force of interaction between two atoms is given by F = αβ exp (− αkT ); where x is the 2 x distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimensions of β is: A. A) M 0 L 2 T −4 B. B) M 2 LT −4 C. C) MLT −2 D. D) M 2 L 2 T −2 Question 89 Due to an explosion underneath water, a bubble started oscillating. If this oscillation has time period T , which is proportional to p α S β E γ , where p is static pressure, S is density of water and E is total energy of explosion. Determine α, β and γ. A. A) α = − 32 , β = 13 , γ = − 56 B. B) α = − 56 , β = 12 , γ = 13 C. C) α = 12 , β = − 56 , γ = 74 D. D) α = 13 , β = 32 , γ = 43 Question 90 A spherical body, of mass m and radius r, is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from 0 to 0. 63 times the terminal velocity (v) is called time constant (τ). Dimensionally τ can be represented as A. A) mr 2 6πη 6πmrη B. B) √ g2 C. C) √ 6πη m rv D. D) None of these Correct Answers for this Chapter Q1 - A Q31 - C Q61 - D Q2 - A Q32 - B Q62 - C Q3 - C Q33 - C Q63 - D Q4 - D Q34 - C Q64 - A Q5 - B Q35 - C Q65 - B Q6 - A Q36 - B Q66 - B Q7 - A Q37 - C Q67 - D Q8 - B Q38 - A Q68 - A Q9 - C Q39 - D Q69 - A Q10 - A Q40 - C Q70 - D Q11 - C Q41 - B Q71 - B Q12 - B Q42 - A Q72 - A  Q13 - C Q43 - A Q73 - D Q14 - B Q44 - B Q74 - 5 (Num) Q15 - B Q45 - D Q75 - A Q16 - D Q46 - 3 (Num) Q76 - A Q17 - C Q47 - B Q77 - C Q18 - C Q48 - D Q78 - C Q19 - D Q49 - D Q79 - A Q20 - D Q50 - A Q80 - B Q21 - C Q51 - B Q81 - A Q22 - A Q52 - D Q82 - D Q23 - C Q53 - B Q83 - A Q24 - A Q54 - C Q84 - C Q25 - D Q55 - C Q85 - D Q26 - B Q56 - D Q86 - A Q27 - B Q57 - C Q87 - B Q28 - B Q58 - A Q88 - B Q29 - D Q59 - C Q89 - B Q30 - B Q60 - D Q90 - D Motion In One Dimension Easy Questions Question 1 An object of mass 3 kg is at rest. Now a force F = 6t 2^i + 4^ j is applied on the object then the velocity of the object at t = 3 s is: A. A) 18^i + 3^ j B. B) 18^i + 6^ j C. C) 3^i + 6^ j D. D) 18^i + 4^ j Question 2 A driver applies the brakes on seeing the red traffic single 400 m ahead. At the time of applying the brakes, the vehicle was moving with 15 m/s and retarding at 0.3 m/s 2. The distance covered by the vehicle from the traffic light 1 minute after the application of brakes is A. A) 25 m B. B) 360 m C. C) 40 m D. D) 375 m Question 3 A 0.2 kg object at rest is subjected to a force (0.3^i − 0.4^ j)N. What is the velocity after 6 s ? A. A) (9^i − 12^ j) B. B) (8^i − 16^ j) C. C) (12^i − 9^ j) D. D) (16^i − 8^ j) Question 4 Assertion : If a = −2t for a particle moving in a straight linestartingwithan initialvelocity 4 m/s from the origin, then distance travelled by it in 2 s is same as displacement. Reason : Velocity changes direction after 2 s only. A. A) If both assertion and reason are true and reason is the correct explanation of assertion. B. B) If both assertion and reason are true but reason is not the correct explanation of assertion. C. C) If assertion is true but reason is false. D. D) If both assertion and reason are false. Question 5 If a ball is thrown vertically with speed u, the distance covered during the last t seconds of its ascent is: A. A) ut B. B) 12 gt 2 C. C) ut − 12 gt 2 D. D) (u + gt)t Question 6 A particle is thrown vertically up with an initial velocity 9 m/s from the surface of Earth (take g = 10 m/s 2 ). The time (in s) taken by the particle to reach a height of 4 m from the surface second time (in seconds) is A. A) 1.3 B. B) 1.2 C. C) 1.1 D. D) 1.0 Question 7 A train accelerating uniformly from rest attains a maximum speed of 40 ms −1 in 20 s. It travels at the speed for 20 s and is brought to rest with uniform retardation in further 40 s. What is the average velocity during the period ? A. A) 80 m/s B. B) 25 m/s C. C) 40 m/s D. D) 30 m/s Question 8 A body starting from rest moves along a straight line with a constant acceleration. The variation of speed (v) with distance (s) is represented by the graph A. A) B. B) C. C) D. D) Question 9 A particle moving along X-axis has acceleration f , at time t given byf = f 0 (1 − Tt ), where f 0 and T are constants. The particle at t = 0 and the instant when f = 0, the particle's velocity v x is A. A) f 0 T B. B) 12 f 0 T 2 C. C) f 0 T 2 D. D) 12 f 0 T Question 10 The acceleration ' a ' (in ms −2 ) of a body, starting from rest varies with time t (in s ) following the equation a = 3t + 4 The velocity of the body at time t = 2 s will be A. A) 10 ms −1 B. B) 18 ms −1 C. C) 14 ms −1 D. D) 26 ms −1 Question 11 A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is A. A) 7 m/s 2 B. B) √7 m/s 2 C. C) 5 m/s 2 D. D) 1 m/s 2 Question 12 A bus is moving with a speed of 10 ms −1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus ? A. A) 10 ms −1 B. B) 20 ms −1 C. C) 40 ms −1 D. D) 25 ms −1 Question 13 A car moves from X to Y with a uniform speed v u. The average speed for this round trip is : A. A) √v u v d B. B) vdd+vuv v v C. C) v u +v d 2 D. D) 2v d v u v d +v u Question 14 A block of mass M is pulled along a smooth horizontal surface with a rope of mass m by force F. The acceleration of the block will be A. A) (M−m) F B. B) (M+m) F C. C) m F D. D) M F Question 15 Two bodies A (of mass 1 kg ) and B (of mass 3 kg ) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is: A. A) 4/5 B. B) 5/4 C. C) 12/5 D. D) 5/12 Question 16 The position of a particle moving in the x − y plane at any time t is given by, x = (3t 3 − 6t) metres; y = (t 2 − 2t) metres. Select the correct statement. A. A) acceleration is zero at t = 0 B. B) velocity is zero at t = 0 C. C) velocity is zero at t = 1 s D. D) velocity and acceleration of the particle are never zero. Question 17 A body moves with uniform acceleration, then which of the following graph is correct? A. A) B. B) C. C) D. D) Question 18 A balloon is rising vertically up with a velocity of 29 ms −1. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was (g = 9.8 ms −2 ) A. A) 100 m B. B) 200 m C. C) 400 m D. D) 150 m Question 19 A particle is moving eastwards with a velocity of 5 m/s. In 10 s, the velocity changes to 5 m/s northwards. The average acceleration in this time is A. A) zero B. B) √1 m s −2 towards north-west 2 C. C) 1 √2 m s −2 towards north-east D. D) 1 √2 m s −2 towards north Question 20 Two trains, each 30 m long are travelling in opposite directions with velocities 5 m/s and 10 m/s. They will cross after A. A) 4 s B. B) 3 s C. C) 2 s D. D) 1 s Question 21 The position x of a particle varies with time (t) as x = At 2 − Bt 3. The acceleration at time t of the particle will be equal to zero. What is the value of t? A. A) 23 A B B. B) A B C. C) 3B A D. D) zero Question 22 A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is s 1 and that covered in the first 20 s is s 2 , then A. A) s 2 = 2 s 1 B. B) s 2 = 3 s 1 C. C) s 2 = 4s 1 D. D) s 2 = s 1 Question 23 The acceleration vs distance graph for a particle moving with initial velocity 5 m/s is shown in the fiture. The velocity of the particle at x = 35 m will be A. A) 20.62 m/s B. B) 20 m/s C. C) 25 m/s D. D) 50 m/s Question 24 The displacement x of a particle varies with time t as x = ae −at + B βx , where a, b, α and β are positive constants. The velocity of the particle will: A. A) be independent of β B. B) drop to zero when α = β C. C) go on decreasing with time D. D) go on increasing with time Question 25 A body is projected horizontally with a velocity of 4√2 m/sec. The velocity of the body after 0.7 seconds will be nearly (Take g = 10 m/sec 2 ) A. A) 10 m/sec B. B) 9 m/sec C. C) 19 m/sec D. D) 11 m/sec Question 26 A particle moves along x -axis and its displacement at any time is given by x(t) = 2t 3 − 3t 2 + 4t in SI units. The velocity of the particle when its acceleration is zero, is A. A) 2.5ms −1 B. B) 3.5ms −1 C. C) 4.54ms −1 D. D) 8.5ms −1 Question 27 Which of the following velocity-time graphs shows a realistic situation for a body in motion? A. A) B. B) C. C) D. D) Question 28 An aeroplane is flying in a horizontal direction with a velocity u and at a height of 2000 m. When it is vertically below a point A on the ground a food packet is released from it. The packet strikes the ground at point B. If AB = 3 km and g = 10 m s −2 , then the value of u is A. A) 54 km h −1 B. B) 540 km h −1 C. C) 150 km h −1 D. D) 300 km h −1 Question 29 A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms −1 to 20 ms −1 while passing through a distance 135 m in t second. The value of t is A. A) 9 B. B) 10 C. C) 1.8 D. D) 12 Question 30 A particle starts from rest and has an acceleration of 2 m/s 2 for 10sec. After that, it travels for 30sec with constant speed and then undergoes a retardation of 4 m/s 2 and comes back to rest. The total distance covered by the particle is A. A) 650 m B. B) 750 m C. C) 700 m D. D) 800 m. Moderate Questions Question 31 A rocket is fired upwards. Its engine explodes fully in 12 s. The height reached by the rocket as calculated from its velocity-time graph is A. A) 79200 m B. B) 158400 m C. C) 18400 m D. D) 15400 m Question 32 A car moves in positive Y -direction with velocity v proportional to distance travelled y as v(y) ∝ y β , where β is a positive constant. The car covers a distance L with average velocity proportional to L as ∝ L 1/3. The constant β is given as A. A) 14 B. B) 13 C. C) 23 D. D) 12 Question 33 The motion of a body falling from rest in a resistive medium is described by the equation dv dt = a − bv, where a and b are constants. The velocity at any time t is A. A) a(1 − b 2t ) B. B) ab (1 − e −bt ) C. C) abe −t D. D) ab 2 (1 − t) Question 34 A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is S 1 , next 10 s is S 2 and the last 10 s is S 3. Then S 1 : S 2 : S 3 is the same as A. A) 1 : 2 : 4 B. B) 1 : 2 : 5 C. C) 1 : 3 : 5 D. D) 1 : 3 : 9 Question 35 A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? A. A) more than 19.6 m/s B. B) at least 9.8 m/s C. C) any speed less than 19.6 m/s D. D) only with speed 19.6 m/s Question 36 The displacement time graph of a particle moving along a straight line is drawn below. A. A) OP PQ QR − 0 + B. B) OP PQ QR + 0 + C. C) OP PQ QR + 0 − D. D) OP PQ QR − 0 − Question 37 A vehicle starts moving in a straight line with an acceleration, a = 4 m/s 2 , with initial velocity equal to zero. After accelerating for time t 1 , the vehicle moves uniformly and for time t 2 , the vehicle finally decelerates for time t 1 eventually coming to a stop. The total time taken during the motion is 10 s and the average velocity during the motion is 5.1 m/s. The time taken by the vehicle during acceleration is A. A) 2 s B. B) 2.5 s C. C) 1.5 s D. D) 1.8 s Question 38 A man runs at a speed of 4 m/s to overtake a standing bus. When he is 6 m behind the door at t = 0, the bus moves forward and continuous with a constant acceleration of 1.2 m/s 2. The man reaches the door in time t. Then, A. A) 4t = 6 + 0.6t 2 B. B) 1.2t 2 = 4t C. C) 4t 2 = 1.2t D. D) 6 + 4t = 0.2t 2 Question 39 Given below are the equations of motion of four particles A, B, C and D x A = 6t − 3; x B = 4t 2 − 2t + 3; x C = 3t 3 − 2t 2 + t − 7; x D = 7 cos 60 o − 3 sin 30 o The particle moving with constant acceleration is A. A) A B. B) B C. C) C D. D) D Question 40 The deceleration of a car traveling on a straight highway is a function of its instantaneous velocity v given by ω = a√v, where a is a constant. If the initial velocity of the car is 60 km/h, the distance of the car will travel and the time it takes before it stops are A. A) 23 m 1 12 s B. B) 2a 3 1 m, 2a s C. C) 3a 2 m, a2 s D. D) 3a 2 m, a2 s Question 41 A ball is dropped from the top of a building 100 m high. At the same instant another ball is thrown upwards with a velocity of 40 m/s from the bottom of the building. The two balls will meet after A. A) 3 s B. B) 2 s C. C) 2.5 s D. D) 5 s Question 42 A particle leaves the origin with an initial velocity v = (3.00ˆi)ms −1 and a constant → acceleration a = (−1.00ˆi − 0.5ˆj)ms −2. When the particle reaches it maximum x- → coordinate, what is the magnitude of its velocity (in m/s) in y-direction? If your answer is K, mark 2K as answer after rounding off to nearest integer. Question 43 An object moves in a straight line with deceleration whose magnitude varies with velocity as 3v 2/3. If at an initial point, the velocity is 8 m/s, then the distance travelled by the object before it stops is A. A) 2 m B. B) 4 m C. C) 6 m D. D) 8 m Question 44 A body is thrown vertically upwards from A, the top of the tower, reaches the ground in time t 1. If it is thrown vertically downwards from A with the same speed, it reaches the ground in time t 2. If it is allowed to fall freely from A, then the time it takes to reach the ground is given by A. A) t = t 1 +t 2 2 B. B) t = t 1 −t 2 2 C. C) t = √t 1 t 2 D. D) t = √ t12 t Question 45 A particle moves with constant acceleration along a straight line. If v 1 , v 2 and v 3 are the average velocities in the three successive intervals t 1 , t 2 and t 3 of time, then the correct relation is A. A) v12 −v23 = t12 +t23 v −v t −t B. B) vv1 −v 2 = tt11−−tt23 2 −v 3 C. C) v12 −v23 = t21− t23 v −v t −t D. D) vv1 −v 2 = tt12 +t 2 2 −v 3 +t 3 Question 46 A particle is travelling along a straight line OX. The distance x (in metre) of the particle from 0 at a time t is given by x = 37 + 27t − t 3 , where t is time in seconds. The distance of the particle from O when it comes to rest is A. A) 81m B. B) 91m C. C) 101m D. D) 111m Question 47 The nature of a graph drawn for a freely falling body with time on the x-axis and speed on the y -axis is (Assuming initial speed to be zero.) A. A) a straight line with positive y-axis intercept. B. B) a straight line passing through the origin. C. C) a parabola. D. D) a straight line parallel to y-axis with positive x-axis intercept. Question 48 Two persons A and B are located in X − Y plane at the points (0, 0) and (0, 10) respectively. (The distances are measured in MKS unit). At a time t = 0, they start moving simultaneously with velocities and v B = 2^ims −1 respectively. The time after which A → → v A = 2jms −1 and B are at their closest distance is A. A) 2.5 s B. B) 4 s C. C) 1 s D. D) √ 10 s 2 Question 49 The displacement of a particle moving in a straight line is given by the expression x = At 3 + Bt 2 + Ct + D in metres, where t is in seconds and A, B, C and D are constants. The ratio between the initial acceleration and initial velocity is A. A) 2C B B. B) 2B C C. C) 2C D. D) 2B C Question 50 Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s2. If after 50 s, the guard of B just brushes past the driver of A and the original distance between them is x, then calculate value of 10 x ? Question 51 A bullet emerges from a barrel of length 1. 2 m with a speed of 640 m s −1. Assuming constant acceleration, the approximate time that is spent in the barrel after the gun is fired is A. A) 4 ms B. B) 40 ms C. C) 400 μs D. D) 1 s Question 52 Consider a vechicle moving with a velocity 54 km/h. At a distance of 400 m, from the traffic light brakes are applied. The acceleration of the vehicle, after the application of brakes is −0.3 m/s 2. The vehicle's position relative to the traffic light is A. A) 25 m B. B) 375 m C. C) 425 m D. D) 30 m Question 53 A balloon rises from rest with a constant acceleration of 8. A stone is released from it when it g has risen to height h. The time taken by the stone to reach the ground is n√ g seconds. Then h what is the value of n? Question 54 A stone is projected with velocity 2√gh, so that it just clears two walls of equal height h, at distance of 2h from each other. The time interval of passing between the two walls is A. A) √ hg B. B) √ 2h g C. C) 2√ hg D. D) 2h g Question 55 A ball is thrown vertically upward from the ground at time, t = 0 s. It passes the top of a tower at t = 3 s and 2 s later it reaches and its maximum height. The height of the tower is (Acceleration due to gravity, g = 10 m/s 2 ) A. A) 105 m B. B) 125 m C. C) 85 m D. D) 65 m Question 56 A particle starts moving rectilinearly at time t = 0 such that its velocity v changes with time t according to the equation v = t 2 − t where t is in seconds and v is in m/s. Find the time interval for which the particle retards. A. A) 12 < t < 1 B. B) 12 > t > 1 C. C) 14 < t < 1 D. D) \(\frac{1}{2} Question 57 A ball is projected vertically upwards from ground. It reaches a height ' h ' in time t 1 , continues its motion and then takes a time t 2 to reach ground. The height h in terms of g, t 1 and t 2 is (g = acceleration due to gravity) A. A) 12 t21 gt B. B) 12 gt 1 t 2 C. C) gt 1 t 2 D. D) 2gt 1 t 2 Question 58 A passenger sitting in a train A moving at 90 km/ h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is : A. A) 80 m B. B) 200 m C. C) 120 m D. D) 320 m Question 59 A particle is moving in a straight line with initial velocity and uniform acceleration a. If the sum of the distance travelled in t th and (t + 1) th seconds is 100 cm, then its velocity after t seconds, in cm/s, is A. A) 80  B. B) 50 C. C) 20 D. D) 30 Question 60 A 2 m wide truck is moving with a uniform speed v 0 = 8 m s −1 along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v moving in a straight line, when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is A. A) √6 m s −1 5 B. B) 4 √5 m s −1 C. C) 8 √5 m s −1 D. D) 2 √5 m s −1 Hard Questions Question 61 Train A and train B are running on parallel tracks in the opposite directions with speed of 36 km hour −1 and 72 km hour −1 , respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1. 8 km hour −1. Speed (in m s −1 ) of this person as observed from train B will be close to: (take the distance between the tracks as negligible) A. A) 29. 5 m s −1 B. B) 28. 5 m s −1 C. C) 31. 5 m s −1 D. D) 30. 5 m s −1 Question 62 A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance travelled is: A. A) (α+β) t 2 4αβ B. B) (α+β) t 2 2αβ C. C) 2(α+β) t 2 αβ D. D) 4(α+β) t 2 αβ Question 63 A particle covers a distance from A to B over a period of time; the distance versus time plot is the shown below. Then which of the following is true for the motion of the particle? A. A) Both average speed and instantaneous speed are always zero. B. B) Average speed is always non-zero but instantaneous speed can be zero. C. C) Instantaneous speed is always non-zero but average speed can be zero. D. D) Both average speed and instantaneous speed are always non-zero. Question 64 A box filled with water has a small hole on its side near the bottom. It is dropped from the top of a tower. As it falls, a camera attached on the side of the box records the shape of the water stream coming out of the hole. The resulting video will show A. A) the water coming down forming a parabolic stream B. B) the water going up forming a parabolic stream C. C) the water coming out in a straight line D. D) no water coming out Question 65 A particle moves in a plane along an elliptic path given by xa2 + b2 = 1. At point (0, b), the x- 2 y2 component of velocity is u. The y-component of acceleration at this point is- A. A) −bu 2 /a 2 B. B) −u 2 /b C. C) −au 2 /b 2 D. D) −u 2 /a Question 66 A body moves on a frictionless plane starting from rest. If S n is distance moved between t = n − 1 and t = n and S n−1 is distance moved between t = n − 2 and t = n − 1, then the ratio Sn−1 is (1 − x2 ) for n = 10. The value of x is ______. S n Question 67 Consider a particle moving along the positive direction of X-axis. The velocity of the particle is given by v = α√x (α is a positive constant). At time t = 0, if the particle is located at x = 0, the time dependence of the velocity and the acceleration of the particle are respectively. A. A) α2 t and α2 2 2 B. B) α 2 t and α 2 C. C) α2 t and α2 D. D) α4 t and α4 2 2 Question 68 A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a. Which of the following relations is true if the police is able to catch the thief? A. A) v 2 < ax B. B) v 2 < 2ax C. C) v 2 ≥ 2ax D. D) v 2 = ax Question 69 The accompanying graph of position x versus time t represents the motion of a particle. If p and q are both positive constants, the expression that best describes the acceleration α of the particle is A. A) a = −p − qt B. B) a = −p + qt C. C) a = p + qt D. D) a = p − qt Question 70 A point particle of mass 0.5 kg is moving along the x-axis under a force described by the potential energy V shown below. It is projected towards the right from the origin with a speed v. What is the minimum value of v for which the particle will escape infinitely fasr away from the origin? A. A) 2√2 ms −1 B. B) 2 ms −1 C. C) 4 ms −1 D. D) The particle will never escape Question 71 The figure shows the acceleration-time graph of a particle. Which of the following represents the corresponding velocity-time graph? ( consider initial velocity zero ) A. A) B. B) C. C) D. D) Question 72 One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance(s) between the two stones varies with time (t) as (before either stone hits the ground) A. A) B. B) C. C) D. D) Question 73 In the follwing displacement (x) vs time (t) graph, at which among the points P , Q, and R is the object's speed increasing? A. A) R only B. B) P only C. C) Q and R only D. D) P , Q, R Question 74 Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below A. A) Statement I is correct but statement II is incorrect B. B) Statement I is incorrect but statement II is correct C. C) Both statement I and Statement II are correct D. D) Both statement I and statement II are incorrect Question 75 A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F 0 [1 − ( t−T T ) ] where F 0 and T 2 are constants. The force acts only for the time interval 2 T. The velocity v of the particle after time 2 T is: A. A) 2 F0 T M B. B) F0 T 2M C. C) 4 F0 T 3M D. D) F0 T 3M Question 76 A body of mass 10 kg is acted upon by a force given by equation F = (3t 2 − 30) newtons. The initial velocity of the body is 10 m/s. The velocity of the body after 5 s is A. A) 4.5 m/s B. B) 6 m/s C. C) 7.5 m/s D. D) 5 m/s Question 77 A rigid ball rolls without slipping on a surface shown below. Which one of the following is the most likely representation of the distance traveled by the ball vs time graph? A. A) B. B) C. C) D. D) Question 78 A stone thrown down with a seed u takes a time t 1 to reach the ground, while another stone, thrown upwards from the same point with the same speed, takes time t 2. The maximum height the second stone reaches from the ground is A. A) 1/2gt 1 t 2 B. B) g/8(t 1 + t 2 ) 2 C. C) g/8(t 1 − t 2 ) 2 D. D) 1/2gt 22 Question 79 Given below are two statements: Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time. Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time. In the light of given statements, choose the correct answer from the options given below. A. A) Both Statement I and Statement II are true B. B) Both Statement I and Statement II are false C. C) Statement I is correct but Statement II is false D. D) Statement I is incorrect but Statement II is true Question 80 A wooden block of mass 10 gm is dropped from the top of a tower 100 m high. Simultaneously, a bullet of mass 10 gm is fired from the foot of the tower vertically upwards with a velocity of 100 m s −1. If the bullet is embedded in it, how high will it rise above the tower before it starts falling? (g = 10 m s −2 ) Question 81 Two skaters P and Q are skating towards each other. Skater P throws a ball towards W every 5 s such that it always leaves her hand with speed 2 ms −1 with respect to the ground. Consider two cases: (I) P runs with speed 1 ms −1 towards Q while Q remains stationary (II) Q runs with speed 1 ms −1 towards P while P remains stationary. Note that irrespective of speed of P, ball always leaves P ′ s hand with speed 2 ms −1 with respect to the ground. Ignore gravity. Balls will be received by Q A. A) one every 2.5 s in case (I) and one every 3.3 s in case (II) B. B) one every 2 s in case (I) and one every 4 s in case (II) C. C) one every 3.3 s in case (I) and one every 2.5 s in case (II) D. D) one every 2.5 s in case (I) and one every 2.5 s in case (II) Question 82 The motion of a particle moving along the y-axis is represented as y = 3(t − 2) + 5(t − 2). 2 Identify the correct statement A. A) the initial (t = 0) velocity of the particle is 3 m s −1 B. B) the acceleration of the particle is 5 m s −1 C. C) the particle is at the origin at t = 2 s D. D) all of the above Question 83 A ball is dropped vertically from a height of h onto a hard surface. If the ball rebounds from the surface with a fraction r of the speed with which it strikes the latter on each impact, what is the net distance traveled by the ball up to the 10 th impact ? A. A) 2 h 1−r 10 1−r B. B) h 1−r 20 1−r 2 C. C) 2 h 1−r 22 1−r 2 −h D. D) 2 h 1−r 20 1−r 2 −h Question 84 A balloon is moving up in air vertically above a point A on the ground. When it is a height h 1 , a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45° with respect to the vertical. When the balloon climbs up a further height h 2 , it is seen at an angle 60° with respect to the vertical if the girl moves further by a distance 2. 464 d (point C). Then the height h 2 is (given tan 30°= 0. 5774): A. A) 1. 464 d B. B) 0. 732 d C. C) 0.464 d D. D) d Question 85 Three balls, A, B and C , are released and all reach the point X (shonw in the figure). Balls A and B are released from two identical structures, one kept on the ground and the other at height, h, from the ground as shown in the figure. They take time t A and t B respectively to reach X (time starts after they leave the end of the horizontal portion of the structure). The ball C is released from a point at height, h, vertically above X and reaches X in time t C. Choose the correct statement. A. A) t C < t A < t C B. B) ta = tb = tc C. C) t C = t A < t C D. D) t B < t A = t C Question 86 A river has a steady speed of v. A man swims upstream at a distance of d and swims back to the starting point in total time t. The man can swim at a speed of 2v in still water. If the time taken by the man in still water is t 0 to complete the same length of swim, then tt is 0 A. A) 12 B. B) 32 C. C) 34 D. D) 43 Question 87 A person walks along a straight road from his house to a market 2.5 km away with a speed of 5 km/h and instantly turns back and reaches his house with a speed of 7.5 km/h. The average speed of the person during the time interval 0 to 50 min is (inm/s) A. A) 4 23 B. B) 53 C. C) 56 D. D) 13 Question 88 A particle of mass 2/3 kg with velocity v = −15 m/s at t = −2 s is acted upon by a force F = k − βt 2. Here, k = 8 N and β = 2 N/s 2. The motion is one-dimensional. Then, the speed at which the particle acceleration is zero again, is A. A) 1 m/s B. B) 16 m/s C. C) 17 m/s D. D) 32 m/s Question 89 Which of the following graphs represents the motion of a particle moving with constant velocity? A. A) graphs (i) and (iii) B. B) graphs (i) and (iv) C. C) graphs (i) and (ii) D. D) graph (i) Question 90 A particle starts from rest and traverses a distance 2x with uniform acceleration, then moves uniformly over a further distance 4x and finally comes to rest after moving a further distance 6x under uniform retardation. Assuming entire motion to be rectilinear motion, the ratio of average speed over the journey to the maximum speed on its way is A. A) 45 B. B) 35 C. C) 25 D. D) 15 Correct Answers for this Chapter  Q1 - B Q31 - A Q61 - A Q2 - C Q32 - B Q62 - C Q3 - A Q33 - B Q63 - B Q4 - B Q34 - C Q64 - D Q5 - B Q35 - A Q65 - A Q6 - D Q36 - C Q66 - 19 (Num) Q7 - B Q37 - C Q67 - A Q8 - B Q38 - A Q68 - C Q9 - D Q39 - B Q69 - D Q10 - C Q40 - D Q70 - B Q11 - C Q41 - C Q71 - B Q12 - B Q42 - 3 (Num) Q72 - A Q13 - D Q43 - B Q73 - A Q14 - B Q44 - C Q74 - A Q15 - A Q45 - D Q75 - C Q16 - C Q46 - B Q76 - C Q17 - C Q47 - B Q77 - D Q18 - B Q48 - B Q78 - B Q19 - B Q49 - B Q79 - D Q20 - A Q50 - 45.00 (Num) Q80 - 75 (Num) Q21 - C Q51 - A Q81 - A Q22 - C Q52 - A Q82 - C Q23 - C Q53 - 2 (Num) Q83 - D Q24 - D Q54 - C Q84 - D Q25 - B Q55 - A Q85 - B Q26 - A Q56 - A Q86 - D Q27 - B Q57 - B Q87 - B Q28 - B Q58 - D Q88 - C Q29 - A Q59 - B Q89 - B Q30 - B Q60 - C Q90 - B Motion In Two Dimensions Easy Questions Question 1 If KE of the particle of mass m performing UCM in a circle of radius r is E. Find the acceleration of the particle A. A) mr 2E B. B) ( mr 2E 2 ) C. C) 2Emr D. D) mr 4E Question 2 Four persons K , L, M , N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M , M directly towards N , and N directly towards K. The four persons will meet at a time A. A) dv B. B) 2v d C. C) 2d v D. D) The four persons will never meet Question 3 A bullet is fired with a velocity u making an angle of 60 ∘ with the horizontal plane. The horizontal component o the velocity of the bullet when it reaches the maximum height is A. A) u B. B) 0 C. C) √3u 2 D. D) u 2 Question 4 A particle is projected from the surface of the earth with a velocity of 5 ms −1 at an angle θ with the horizontal. Another particle is projected on the surface of some other planet with a velocity of 3 ms −1 at the same angle and it follows a trajectory which is identical to the trajectory of the projectile which is fired on earth. The value of the acceleration due to gravity on that planet is [given that the acceleration due to gravity on the surface of earth, g = 9. 8 ms −2 ] A. A) 16. 3 ms −2 B. B) 1. 8 ms −2 C. C) 3. 5 ms −2 D. D) 5. 9 ms −2 Question 5 A particle moves in a circle of radius 5 cm with constant speed and time period 0.2πs. The acceleration of the particle is A. A) 25 m/s 2 B. B) 36 m/s 2 C. C) 5 m/s 2 D. D) 15 m/s 2 Question 6 A particle P is projected from a point on the surface of a smooth inclined plane (see figure). Simultaneously another particle Q is released on the smooth incl