Physics NCERT Fingertips Question Bank PDF

PHYSICS BOOKS - NCERT FINGERTIPS PHYSICS (HINGLISH) SYSTEM OF PARTICLES AND ROTATIONAL MOTIONS Introduction 1. In a spinning top, axis moves around the vertical through its point of contact with the ground sweeping out a cone. This movement of the axis of the top around the vertical is known as A. rotation B. translation C. precession D. rolling Answer: c Watch Video Solution Centre Of Mass 1. The centre of mass of a body A. lies always at the geometrical centre B. lies always inside the body C. lies always outside the body D. may lie within or outside the body Answer: D Watch Video Solution 2. The position of the centre of mass of a cube of uniform mass density will be at A. the centre of one face B. the centre of the interaction of diagonals of one face. C. the geometric centre of the cube D. the edge of a cube Answer: C View Text Solution 3. The reduce mass of two particles having masses m and 2 m is A. 2 m B. 3 m C. 2 m/3 D. m/2 Answer: c Watch Video Solution 4. Three particles of masses 3 1kg, kg, and 2g are located the vertices of 2 an equilateral triangle of side a. The x, y coordinates of the centre of mass are. 5a 2a A. , 9 3√3 2a 5a B. , 3√3 9 5a 2a C. , 9 √3 2a 5a D. , √3 9 Answer: a Watch Video Solution 5. The x, y coordinates of the centre of mass of a uniform L-shaped lamina of mass 3 kg is A. (5/6 m, 5/6 m) B. (1 m, 1 m) C. (6/5 m, 6/5 m) D. (2 m, 2m) Answer: A Watch Video Solution 6. The centre of mass of a system of two particle of masses m 1 and m 2 is at a distance d1 from mass m1 and at a distance d2 from mass m such that. 2 d1 m2 A. = d2 m1 d1 m1 B. = d2 m2 d1 m1 C. = + m2 d2 m1 d1 m2 D. = + m2 d2 m1 Answer: A Watch Video Solution 7. Centre of mass of three particles of masses 1kg, 2kg and 3kg lies at the point (1, 2, 3) and centre of mass of another system of particles 3kg and 2kg lies at the point ( − 1, 3, − 2). Where should we put a particle of mass 5kg so that the centre of mass of entire system lies at the centre of mass of first system ? A. (0, 0, 0) B. (1, 3, 2) C. (-1, 2, 3) D. (3, 1, 8) Answer: D Watch Video Solution 8. Two particles of masses 1 kg and 3 kg have position vectors ˆ ˆ 2 î + 3 ĵ + 4k and − 2 î + 3 ĵ − 4k respectively. The centre of mass has a position vector A. ˆ î + 3 ĵ − 2k B. − î ˆ − 3 ĵ − 2k C. − î ˆ + 3 ĵ + 2k D. − î ˆ + 3 ĵ − 2k Answer: D Watch Video Solution Motion Of Centre Of Mass 1. When an explosive shell travelling in a parabolic path under the effect of gravity explodes in the mid air, the centre of mass of the fragments will move. A. vertically downwards B. along the original parabolic path C. vertically upwards and then vertically downwards D. horizontallly followed by parabolic path Answer: B Watch Video Solution 2. The velocity of centre of mass of the system remains constant, if the total external force acting on the system is. A. minimum B. maximum C. unity D. zero Answer: D Watch Video Solution 3. Two particles of equal mass have velocities and. First particle has an acceleration while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of A. straight line B. parabola C. circle D. ellipse Answer: A View Text Solution 4. A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley + child) will move with a speed : A. zero B. (v + u) C. (v - u) D. v Answer: D Watch Video Solution 5. Two masses m 1 = 1kg and m 2 = 2kg are connected by a light inextensible string and suspended by means of a weightness pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is (T akeg = 10ms −2 ).. A. 20/9 m B. 40/9 m C. 2/3 m D. 1/3 m Answer: A Watch Video Solution 6. The correct relation between linear velocity and angular velocity of a particle is → → v ω A. → → → v = r × ω B. → → → v = ω × r C. → → → ω = r × v D. → → → ω = v × r Answer: B Watch Video Solution 7. The direction of the angular velocity vector is along A. the tangent to the circular path B. the inward radius C. the outward radius D. the axis of rotation Answer: D Watch Video Solution 8. Which of the following statements is correct? View Text Solution 9. What is the value of linear velocity, if and ? → → ˆ ˆ ω = 3 î − 4 ĵ + k r = 5 î − 6 ĵ + 6k A. 6 î ˆ + 2 ĵ − 3k B. 18 î ˆ + 3 ĵ − 2k C. − 18 î ˆ − 13 ĵ + 2k D. 6 î ˆ − 2 ĵ + 8k Answer: c Watch Video Solution 10. A disc rotating about its axis with angular speed ω0 is placed lightly (without any translational pull) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. Will the disc roll in the direction indicated ? A. v A > vB > vC B. v A < vB < vC C. v A = vB < vC D. v A = vB > vC Answer: D Watch Video Solution Torque And Angular Momentum 1. Figure shows a lamina in x − y plane. Two axes z and z' pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following statements is incorrect ? (The point P is closer to z' − aξs than the z- axis).. A. Torque τ caused by F about z axis is along k ˆ. B. Torque τ ′ caused by F about z ′ axis is along − k ˆ. C. Torque caused by F about z axis is greater in magnitude than that about z ′ axis. D. Total torque is given by τ = τ + τ ′. Answer: D Watch Video Solution 2. When a torque acting upon a system is zero, which of the following will be constant ? A. Force B. Linear impulse C. Linear momentum D. Angular momentum Answer: D Watch Video Solution → 3. Let F be a force acting on a particle having positon vector be the torque of this → → r. Let r force about the origin then → A. and F → → → r. τ > 0. τ < 0 → B. and F → → → r. τ = 0. τ = 0 → C. and F → → → r. τ = 0. τ ≠ 0 → D. and F → → → r. τ ≠ =. τ = 0 Answer: B Watch Video Solution 4. Angular momentum of the particle rotating with a central force is constant due to A. constant torque B. constant force C. constant linear momentum D. zero torque Answer: d Watch Video Solution 5. Find the torque of a force ˆ (7 î + 3 ĵ − 5k) about the origin. The force acts on a particle whose position vector is ( î ˆ − ĵ + k). A. 2 î ˆ + 12 ĵ + 10k B. 2 î ˆ + 10 ĵ + 12k C. 2 î ˆ + 10 ĵ + 10k D. 10 î ˆ + 2 ĵ + k Answer: A Watch Video Solution 6. A disc is rotating with angular velocity ω. A force F acts at a point whose position vector with respect to the axis of rotation is r. The power associated with torque due to the force is given by → A. → → ( r × F ). ω → B. → → (r × F ) × ω → C. → → r. (F × ω ) → → D. → r × (F. ω ) Answer: a Watch Video Solution 7. A mass M moving with a constant velocity parlale to the X-axis. Its angular momentum with respect to the origin A. is zero B. remains constant C. goes on increasing D. goes on decreasing Answer: b Watch Video Solution 8. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ω. If the angular momentum of the system. calculated about O → → and P are denoted. by L O and L P respectively, then. Watch Video Solution 9. The position of a particle is given by and momentum → ˆ r = ( î + 2 ĵ − k). The angular → ˆ p = (3 î + 4 ĵ − 2k) momentum is perpendicular to the A. x-axis B. y-axis C. z-axis D. yz-plane Answer: A Watch Video Solution 10. The z component of the angular momentum of a particle whose position vector is View Text Solution 11. Consider a particle of mass m having linear momentum at position relative to the → → p r → origin O. Let L be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate(s) → , and ? → → r p L → → dL dp A. → + r × = 0 dt dt → → dL d r B. → + × p = 0 dt dt → → dL d r C. → − × p = 0 dt dt → → dL dp D. → − r × = 0 dt dt Answer: D Watch Video Solution Equilibrium Of A Rigid Body 1. A rigid body is said to be in partial equilibrium, when it is in A. translational equilibrium only B. rotational equilibrium only C. either (a) and (b) D. neither (a) nor (b) Answer: C Watch Video Solution 2. Moment of couple is called A. angular momentum B. force C. torque D. impulse Answer: C Watch Video Solution 3. A couple produces. A. purely translational motion B. purely rotational motion C. both translational and rotational motion D. no motion Answer: B Watch Video Solution 4. Which of the following statements is incorrect? A. A pair of equal and opposite forces with different lines of action is known as couple. B. A couple produces rotation without translation. C. When we open the lid of a bottle by turning it, our fingers apply a couple to the lid. D. Moment of a couple depends on the point about which we take the moment. Answer: D Watch Video Solution 5. Which of the following relations is correct? A. Mechanical advantage = Effort/Load B. Load arm × Effort = Effort arm × Load C. Load arm × Load = Effort arm × Effort D. None of these Answer: c Watch Video Solution 6. A rigid rod of length 2L is acted upon by some forces. All forces labelled F have the same magnitude. Which cases have a non-zero net torque acting on the rod about its centre ?. A. I and II only B. II and III only C. I and III only D. The net torque is zero in all cases. Answer: A Watch Video Solution 7. (1) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts, (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius, (3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.., (4) The radius of gyration of any body rotating about ab axis is the length of the perpendicular dropped from the C.G. the body to the axis. which one of the following pairs of statements is correct ? A. (1) and (4) B. (1) and (2) C. (2) and (3) D. (3) and (4) Answer: A Watch Video Solution 8. A non-uniform bar of weight W and length L is suspended by two strings of negligible weight as shown in figure. The angles made by the strings with the vertical are θ1 and θ2 respectively. The distance d of the centre of gravity of the bar from left end is.. tan θ2 A. L(tan θ 1 + ) tan θ1 tan θ1 B. L( tan θ2 ) tan θ1 + tan θ2 C. L( tan θ2 ) tan θ1 + tan θ2 D. L(tan θ 1 + ) tan θ2 Answer: B Watch Video Solution 9. A uniform rod of length 1m mass 4kg is supports on tow knife-edges placed10cm from each end. A 60N weight is suspended at 30cm from one end. The reactions at the knife edges is. A. 60 N, 40 N B. 75 N, 25 N C. 65 N, 35 N D. 55 N, 45 N Answer: C Watch Video Solution 10. A car weighs 1800kg. The distance between its front and back axles is 1.8m. Its centre of gravity is 1.05m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel. A. 4000 N on each front wheel, 5000 N on each back wheel B. 5000 N on each front wheel, 4000 N an each back wheel C. 4500 N on each wheel, 4500 N on each back wheel D. 3000 N on each front wheel, 6000 N on each back wheel Answer: A Watch Video Solution 11. A 3m along ladder weighing 20kg leans on a frictionless wall. Its feet rest on the floor 1m from the wall. Find the reaction forces of the wall and the floor. A. 25√2 N, 203 N B. 50√2 N, 230 N C. 203 N, 25√2 N D. 230N , 50√2 N Answer: A Watch Video Solution 12. A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on of the other at the 12cm mark, the stick is found to balanced at 45cm. The mass of the metre stick is. A. 56 g B. 66 g C. 76 g D. 86 g Answer: B Watch Video Solution 13. A uniform cube of mass m and side a is placed on a frictionless horizontal surface. A vertical force F is applied to the edge as shown in Fig. Match the following (most appropriate choice) : (a)mg / 4 < F < mg / 2 (p) Cube will move up. (b) F > mg / 2 (q) Cube will not exhibit motion. (c ) F > mg (r) Cube will begin to rotate and slip at A. (d) F = mg / 4 (s) Normal reaction effectively at a / 3 from A, no motion. A. A-p, B-q, C-s, D-r B. A-r, B-s, C-q, D-p C. A-q, B-r, C-p, D-s D. A-s, B-p, C-r, D-q Answer: C Watch Video Solution Moment Of Inertia 1. Analogue of mass in rotational motion is. A. moment of inertia B. torque C. radius of gyration D. angular momentum Answer: A Watch Video Solution 2. Moment of inertia of body depends upon A. mass of the body B. axis of rotation of the body C. shape and size of the body D. all of these Answer: D Watch Video Solution 3. Which of the following has the highest moment of inertia when each of them has the same mass and the same radius ? A. A ring about any of its diameter. B. A disc about any of its diameter. C. A hollow sphere about any of its diameter. D. A solid sphere about any of its diameter. Answer: C Watch Video Solution 4. A person is standing on a rotating table with metal spheres in his hands. If he withdraws his hands to his chest, then the effect on his angular velocity will be. A. increase B. decrease C. remain same D. can't say Answer: A Watch Video Solution 5. A solid cylinder of mass M and radius R rotates about its axis with angular speed ω. Its rotational kinetic energy is 1 A. MR ω 2 2 2 B. M R 2 2 ω 1 C. MR ω 2 2 4 1 D. MR ω 2 2 8 Answer: C Watch Video Solution 6. Match the Column I and Column II.,B A. A-p, B-q, C-r, D-s B. A-q, B-r, C-s. D-p C. A-r, B-q, C-p, D-p D. A-r, B-s, C-p, D-q Answer: d Watch Video Solution 7. The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is. l A. √2 l B. 3 l C. √3 l D. 2 Answer: C Watch Video Solution Theorems Of Perpendicular And Parallel Axes 1. Two masses each of mass M are attached to the end of a rigid massless rod of length L. The moment of inertia of the system about an axis passing centre of mass and perpendicular to its length is. A. M L /42 B. M L /22 C. M L 2 D. 2M L 2 Answer: B Watch Video Solution 2. From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is A. 4M R 2 40 B. MR 2 9 C. 40M R 2 37 D. MR 2 9 Answer: A View Text Solution 3. A uniform square plate S(sidec) and a uniform rectangular plate R(sideb, a) have identical areas and mass [Fig.] Show that (i) , IxR / IxS < 1 (ii) IyR / IyS > 1, (iii) IzR / IzS > 1. A. (i) only B. (ii) only C. Both (i) and (ii) D. Neither (i) nor (ii) Answer: C Watch Video Solution 4. Find the moment of inertia of a sphere about a tangent to the sphere, while the mass of the sphere is M and the radius of the sphere is R. 2 A. MR 2 5 6 B. MR 2 5 4 C. MR 2 5 7 D. MR 2 5 Answer: D Watch Video Solution 5. With reference to Fig. of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.) A. The moment of inertia of cube about z ′ 2 ma is I z ′ = Iz + 2 B. The moment of inertia of cube about z ' ' 2 ma is I z ' ' = Iz + 2 C. I x = Iy D. None of these Answer: B Watch Video Solution Kinematics Of Rotational Motion About A Fixed Axis 1. An athlete throws a discus from rest to a final angular velocity of 15rads −1 in 0.270s before releasing it. During acceleration, discuss moves a circular arc of radius 0.810m. Acceleration of discus before it is released is. A. 45ms −2 B. 182ms −2 C. 187ms −2 D. 192ms −2 Answer: a Watch Video Solution 2. A flywheel rotating at 420r ± slows down at a constant rate of 2rads −2 The time required to stop the flywheel is. A. 22 s B. 11 s C. 44 s D. 12 s Answer: A Watch Video Solution 3. The angular speed of a motor wheel is increased from 120 rpm to 3120 rpm in 16 seconds. The angular acceleration of the motor wheel is A. 2πrads −2 B. 4πrads −2 C. 6πrads −2 D. 8πrads −2 Answer: B Watch Video Solution Dynamics Of Rotational Motion About A Fixed Axis 1. An automobile engine develops 100 kilo − watt, when rotating at a speed of 1800rev / min. Find the torque developed by it. 2 10 A. π Nm 6 4 10 B. π Nm 6 6 10 C. π Nm 6 8 10 D. π Nm 6 Answer: b Watch Video Solution 2. A grindstone of moment of inertia 6kgm 2 is found to have a speed of 150 rpm. 10 sec, after starting from rest, torque applied is A. 3π N m B. 3 N π C. Nm 3 D. 4π N m Answer: A Watch Video Solution 3. The instantaneous angular position of a point on a rotating wheel is given by the equation 3 2 θ(t) = 2t − 6t The torque on the wheel becomes zero at A. t = 1 s B. t = 0.5 s C. t = 0.25 s D. t = 2 s Answer: A Watch Video Solution 4. A rope is wound round a hollow cylinder of mass 3kg and radius40cm. If the rope is pulled with a force of 30N , what is the angular acceleration of the cylinder ? A. 15rads −2 B. 20rads −2 C. 25rads −2 D. 30rads −2 Answer: C Watch Video Solution 5. In the question number 62, the linear acceleration of the rope is A. 5ms −2 B. 10ms −2 C. 15ms −2 D. 20ms −2 Answer: b View Text Solution 6. A hollow cylinder of mass M and radius R is rotating about its axis of symmetry and a solid sphere of same mass and radius is rotating about an axis passing through its centre. It torques of equal magnitude are applied to them, then the ratio of angular accelerations produced is A. 2 : 5 B. 3 : 5 C. 5 : 2 D. 2 : 3 Answer: A Watch Video Solution 7. Too maintain a rotor at a uniform angular speed of 100rads −1 , an engine needs to transmit torque of 100 N m. The power of the engine is A. 10 kW B. 100 kW C. 10 MW D. 100 MW Answer: a Watch Video Solution 8. A cord of negligible mass is wound round the rin of a flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord. The work done by the pull when 2 m of the cord is unwound is A. 20 J B. 25 J C. 45 J D. 50 J Answer: d Watch Video Solution 9. In the question number 66, if wheel starts from rest, what is the kinetic energy of the wheel when 2 m of the cord is unwound? A. 20 J B. 25 J C. 45 J D. 50 J Answer: d View Text Solution 10. A uniform disc of radius R , is resting on a table on its rim. The coefficient of friction between disc and table is μ Fig. Now the disc is pulled with a force F as shown in the Fig. What is the maximum value of F for which the disc rolls without slipping ? A. μMg B. 2μMg C. 3μMg D. 4μMg Answer: c Watch Video Solution Angular Momentum In Case Of Rotations About A Fixed Axis 1. Which of the following principles a circus acrobat employs in his performance? A. Conservation of energy B. Conservation of linear momentum C. Conservation of mass D. Conservation of angular momentum Answer: d Watch Video Solution 2. Total angular momentum of a rotating body remains constant, if the net torque acting on the body is A. zero B. maximum C. minimum D. unity Answer: A Watch Video Solution 3. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along. A. the radius B. the tangent the orbit C. the line at angle of 45 ∘ to the plane of rotation D. the axis of rotation Answer: D Watch Video Solution 4. Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions → with same speed V along parallel lines. At a particular instant, and are their → → r 1 r 2 respective position vectors drawn from point A which is in the plane of the parallel lines. Which of the following is the correct statement ?. → A. Angular momentum L 1 of a particle 1 → about A is → L 1 = mv r 1 ⊙ → B. Angular momentum L 2 of particle 2 → about A is → L 2 = mv r 2 ⊙ C. Total angular momentum of the system → about A is → → L = mv r 1 + r 2 ⊙ D. Total angular momentum of the system → about A is L = mv(d 2 − d 1 ) ⊗ ⊗ represents a unit vector going into the page, ⊙ represent a unit vector coming out of the page? Answer: D Watch Video Solution 5. An solid cylinder of mass 20kg and radius 20cm rotates about its axis with a angular speed 100rads −1. The angular momentum of the cylinder about its axis is. A. 40 J s B. 400 J s C. 20 J s D. 200 J s Answer: A Watch Video Solution 6. Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio. 1 A. 2 B. √2 C. 1 : √2 2 D. 1 Answer: C Watch Video Solution 7. A child is standing with his two arms outstretched at the centre of a turntable that is rotating about its central axis with an angular speed ω0. Now, the child folds his hands back so that moment of inertia becomes 3 times the initial value. The new angular speed is. A. 3ω o B. ω /3 o C. 6ω o D. ω /6 o Answer: B Watch Video Solution 8. A circular platform is mounted on a vertical frictionless axle. Its radius is r = 2m and its moment of inertiaI = 200kgm 2. It is initially at rest. A 70kg man stands on the edge of the platform and begins to walk along the edge at speed v0 = 1ms −1 relative to the ground. The angular velocity of the platform is. A. 1.2rads −1 B. 0.4rads −1 C. 0.7rads −1 D. 2rads −1 Answer: C Watch Video Solution 9. A man stands on a rotating platform with his arms stretched holding a 5kg weight in each hand. The angular speed of the platform is 1.2revs −1. The moment of inertia of the man together with the platform may be taken to be constant and equal to 6kgm. If the man 2 brings his arms close to his chest with the distance n each weight from the axis changing from 100cm to20cm. The new angular speed of the platform is. A. 2revs −1 B. 3revs −1 C. 5revs −1 D. 6revs −1 Answer: B Watch Video Solution 10. Two discs of moments of inertia I1 and I2 about their respective axes , rotating with angular frequencies ω and ω respectively, are 1 2 brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be I1 ω2 A. I 1 ω1 + + I2 I1 I1 ω2 B. I 2 ω1 + + I2 I1 I2 ω2 C. I 1 ω1 − − I2 I1 I1 ω2 D. I 2 ω1 − − I2 I1 Answer: A View Text Solution 11. A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with angular velocity of 20rad / s. When the stretches her arms fully, the spinning speed decrease in 10rad / s. If I is the initial moment of inertia of the dancer, the new moment of inertia is. A. 2I B. 3I I C. 2 I D. 3 Answer: A Watch Video Solution 12. Angular momentum L and rotational kinetic energy K of a body are related to each other R by the relation. (I = moment of inertia) A. K = 2IL R 2 L B. KR = I 2 2I C. KR = L 2 L D. KR = I Answer: b Watch Video Solution 13. A person with outstretched arms, is spinning on a rotating stool. He suddenly brings his arms down to his sides. Which of the following is true about his kinetic energy K and angular momentum L? A. Both K and L increase B. Both K and L remain unchanged C. K remains constant, L increases D. K increases but L remains constant Answer: D Watch Video Solution 14. A child is standing with folded hands at the center of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is A. K/4 B. K/2 C. 2 K D. 4 K Answer: b Watch Video Solution 15. A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic emergies of rotation (Esphere / Ecylinder ) will be. A. 0.085416666666667 B. 0.045138888888889 C. 0.044444444444444 D. 0.12569444444444 Answer: b Watch Video Solution 16. Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed ω1 and ω2 are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process? 2 (ω1 − ω2 ) A. I1 I2 (I1 + I2 ) 2 2 (ω1 − ω2 ) B. I1 I2 I1 + I2 2 (ω1 + ω2 ) C. I1 I2 I1 − I2 2 (ω1 + ω2 ) D. I1 I2 (I1 − I2 ) 2 Answer: A Watch Video Solution Rolling Motion 1. A solid sphere rolls down two different inclined planes of the same height but of different inclinations A. the speed and time of descend will be same. B. the speed will be same but time of descend will be different. C. the speed will be different but time are descend will be same. D. speed and time of descend both are different.. Answer: B Watch Video Solution 2. Which of the following statements is correct? A. Torque is the rotational analogue of force. B. Rolling motion of cylinder down an inclined plane is combination of translation and rotational motion. C. If the effort arm is larger than the load arm, the mechanical advantage is lesser than one. D. For the extended body, the centre of mass and centre of gravity do not coincide. Answer: C Watch Video Solution 3. Which of the following statements is not correct? A. During rolling, the instantaneous speed of the point of contact is zero B. During rolling, the instantaneous acceleration of the point of contact is zero. C. For perfect rolling motion, work done against friction is zero. D. A wheel moving down a perfectly frictionless inclined plane will slip but not roll on the plane. Answer: B Watch Video Solution 4. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is k. If radius of the ball be R , then the fraction of total energy associated with its rotation will be. 2 2 k + R A. 2 R 2 k B. 2 R 2 k C. 2 2 k + R 2 R D. 2 2 k + R Answer: C Watch Video Solution 5. A solid cylinder of mass M and radius R rolls without slipping down an inclined plane making an angle θ with the horizontal. Then its acceleration is. A. 1/3 g sinθ B. 2/3 g sinθ C. 2/5 g sinθ D. 2/7 g sinθ Answer: B Watch Video Solution 6. In the question number 89, the force of friction acting on the cylinder is A. 2/3 Mg sinθ B. 1/3 Mg sinθ C. 2/5 Mg sinθ D. 2/7 Mg sinθ Answer: b View Text Solution 7. A solid cylinder rolls up an inclined plane of inclination θ with an initial velocity v. How far does the cylinder go up the plane ? 2 3v A. 2g sin θ 2 v B. 4g sin θ 2 3v C. g sin θ 2 3v D. 4g sin θ Answer: D Watch Video Solution 8. A cylinder of radius R and mass M rolls without slipping down a plane inclined at an angle θ. Coefficient of friction between the cylinder and the plane is μ. For what maximum inclination θ , the cylinder rolls without slipping ? A. tanθ gt 3μ s B. tanθ ≤ 3μs C. tanθ lt 3μ s D. None of these Answer: B Watch Video Solution 9. A ring of radius R is rotating with an angular speed ω0 about a horizontal axis. It is placed on a rough horizontal table. The coefficient of kinetic friction is μk. The time after it starts rolling is. ωo μk R A. g 2 ωo g B. μk R 2 2ωo R C. g μk ωo R D. μk g 2 Answer: D Watch Video Solution 10. When a solid sphere rolls without slipping down an inclined plane making an angle θ with the horizontal, the acceleration of its centre of mass is a. If the same sphere slides without friction, its acceleration is: 7 A. a 2 5 B. a 7 7 C. a 5 5 D. a 2 Answer: C Watch Video Solution 11. A uniform sphere of mass m and radius R is placed on a rough horizontal surface [Fig.] The sphere is struck horizontally at a hight h from the floor. Match the following : (A) h = R /2 (p) Sphere rolls without slipping with a constant velocity and no loss of energy. (B) h = R (q) Sphere spins clockwise, loses energy by friction. (C ) h = 3R / 2 (r) Sphere spins anti-clockwise, loses energy by friction. (D) h = 7R / 5 (s) Sphere has only a translational motion, looses energy by friction. A. A -r, B - s, C - q, D - p B. A - s, b - p, C - r, D - q C. A - q, B - r, C - p, D - s D. A - p, B - q, C - s, D - r Answer: A Watch Video Solution 12. The moments of inertia of two rotating bodies A and are I and A IB (IA > IB ). If their angular momenta are equal then. A. Kinetic energy of A = Kinetic energy of B B. Kinetic energy of A > Kinetic energy of B C. Kinetic energy of A < Kinetic energy of B D. Kinetic energy of the two bodies cannot be compared with the given data Answer: C Watch Video Solution 13. A body is rolling down an inclined plane. If kinetic energy of rotation is 40 % of kinetic energy in translatory start then the body is a. A. ring B. cylinder C. hollow ball D. solid ball Answer: d Watch Video Solution 14. A wheel of mass 5kg and radius 0.40m is rolling on a road without sliding with angular velocity 10rads −1. The moment of inertia of the wheel about the axis of rotation is 0.65kgm 2. The percentage of kinetic energy of rotate in the total kinetic energy of the wheel is. A. 22.4 % B. 11.2 % C. 88.8 % D. 44.8 % Answer: D Watch Video Solution 15. Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity ? A. Ring B. Solid cylinder C. Solid sphere D. All reach the ground with same velocity Answer: C Watch Video Solution 16. A hoop of radius 2m weight 100kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20cms −1. How much work has to be done to stop it ? A. 2 J B. 4 J C. 6 J D. 8 J Answer: B Watch Video Solution Higher Order Thinking Skills 1. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. Determine the force exerted by the liquid at the other end. L A. M ω 2 2 B. M ω 2 L L C. M ω 2 4 2 L D. M ω 2 2 Answer: a Watch Video Solution 2. Let l be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to A. I B. I sin 2 θ C. I cos 2 θ θ D. I cos 2 (. ) 2 Answer: A Watch Video Solution 3. A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing though O and P is IO and IP respectively. Both these axes are perpendicular to the plane of the lamina. The IP ratio to the nearest integer is IO A. 13 / 37 B. 37 / 13 C. 73 / 31 D. 8 / 13 Answer: B Watch Video Solution 4. A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3m / s 2. The coeffecient of friction between the ground and the ring is large enough that rolling always occur and the coefficient of friction between the stick and the ring A. 0.4 B. 0.8 C. 0.2 D. 0.5 Answer: a View Text Solution 5. A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping. A. Acceleration of disc = 2F/3m B. Friction force between disc and surface = 2F/3 C. Acceleration of disc = 6F/5m D. Friction force between disc and surface is F/3 Answer: D Watch Video Solution 6. A stone of mass m tied to the end of a string, is whirled around in a horizontal circle. (Neglect the force due to gravity). The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T = Ar n where A is a constant, r is the instantaneous radius of the circle and n=.... A. -3 B. 3 C. 2 D. -4 Answer: a Watch Video Solution 7. A rod of weight w is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is.. And on B is...... d A. − x d x B. d − d x C. d − x x D. − x d Answer: c Watch Video Solution 8. A particle is projected at time t=0 from a point P on the ground with a speed v0 , at an angle of 45 ∘ to the horizontal. Find the magnitude and direction of the angular momentum of the particle about P at tiem t = v0 / g 3 mv A. 0 2√2g 3 mv B. 0 √2g 3 3mv C. 0 √2g 3 √2mv D. 0 g Answer: a Watch Video Solution Ncert Exemplar 1. For which of the following does the centre of mass lie outside the body ? A. A pencil B. A shotput C. A dice D. A bangle Answer: d Watch Video Solution 2. Which of the following points is the likely position of the centre of mass of the system shown in Fig. A. A B. B C. C D. D Answer: C Watch Video Solution 3. A particle of mass m is moving in YZ-plane with a uniform velocity v with its trajectory running parallel to + ve Y-axis and intersecting Z-axis at z = a in figure. The change in its angular momentum about the origin as it bounces elastically form a wall at y=constant is Watch Video Solution 4. When a disc rotates with uniform angular velocity, which of the following is not true ? A. The sense of rotation remains same. B. The orientation of the axis of rotation remains same. C. The speed of rotation is non-zero and remains same. D. The angular acceleration is non-zero and remains same. Answer: D Watch Video Solution 5. A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind [Fig.] The moment of inertia about the z-axis is than A. increased B. decreased C. the same D. changed in unpredicted manner Answer: B Watch Video Solution 6. In problem 5, theCM of the plate is now in the following quadrant of x − y plane. A. I B. II C. III D. IV Answer: c Watch Video Solution 7. The density of a non-uniform rod of length 1m is given by ρ(x) 2 = a(1 + bx ) where a and b are constants and 0. ≤ x ≤ 1 The centre of mass of the rod will be at 3(2 + b) A. (3 + b) 4 4(2 + b) B. (3 + b) 3 3(3 + b) C. (2 + b) 4 4(3 + b) D. (2 + b) 3 Answer: a Watch Video Solution 8. A Merry -go-round, made of a ring-like platform of radius R and massM , is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as see from the round). The speed of the round after wards is A. 2ω B. ω C. ω/2 D. 0 Answer: A Watch Video Solution Assertion And Reason 1. Assertion: No real body is truly rigid. Reason: A rigid body is a body with a perfectly definite and unchanging shape. The distances between different pairs of particles of such a body do not change. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: A Watch Video Solution 2. The position of centre of mass does not depend upon the reference frame. Centre of mass depends only upon the mass of the body. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: C Watch Video Solution 3. Statement-1 : The centre of mass of a body may lie where there is no mass. Statement-2 : The centre of mass has nothing to do with the mass. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: C Watch Video Solution 4. To determine the motion of the centre of mass of a system, knowledge of internal forces of the system is required. `For this purpose we need not to know the external forces on the system. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: D Watch Video Solution 5. Assertion: If there are no external forces, the center of mass of a double star moves like a free particle. Reason: If we go to the center of mass frame, then we find that the two stars are moving in a circle about the center of mass, which is at rest. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: B Watch Video Solution 6. A girl sits on a rolling chair, when she stretch her arms horizontally, her speed is reduced. Principle of conservation of angular momentum is applicable in this situation. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: a Watch Video Solution 7. Assertion : The moment of inertia of a rigid body reduces to its minimum value, when the axis of rotation passes through its centre of gravity. Reason : The weight of a rigid body always acts through its centre of gravity. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: A Watch Video Solution 8. Assertion: The centre of gravity of a body coincides with its centre of mass only if the gravitational field does not vary form one part of the body to the other. Reason: Centre of gravity is independent of the gravitational field. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: C Watch Video Solution 9. Assertion: The moment of inertia of rigid body depends only on the mass of the body, its shape and size. Reason: Moment of inertia I = MR 2 where M is the mass of the body and R is the radius vector. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: D Watch Video Solution 10. Value of radius of gyration of a body depends on axis of rotation. Radius of gyration is root mean square distance of particle of the body from the axis of rotation. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: a Watch Video Solution 11. Assertion: A boiled egg can be easily distinguished from a raw unboiled egg by spinning. Reason: The hard boiled egg has a moment of inertia which is more than that of the raw egg. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: c Watch Video Solution 12. A rigid body not fixed in some way can have either pure translation or a combination of translation and rotation. In rotation about a fixed axis, every particle of the rigid body moves in a circle which lies in a plane perpendicular to the axis and has its centre on the axis. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: b Watch Video Solution 13. Assertion: The motion of a ceiling fan is rotational only. Reason: The motion of a rigid body which is pivoted fixed of rotation. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: A Watch Video Solution 14. Assertion: If the head of a right handed screw rotates with the body, the screw advances in the direction of the angular velocty. Reason: For rotation about a fixed axis, the angular velocity vector lies along the axis of rotation. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: a Watch Video Solution 15. Assertion: A sphere cannot roll on a smooth inclined surface. Reason: The motion of a rigid body which is pivoted or fixed in some way is rotation. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion C. If assertion is true but reason is false. D. If both assertion and reason are false. Answer: B Watch Video Solution

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