Circular Motion Exercise PDF

TG: @NEETxNOAH PRE-MEDICAL PHYSICS ENTHUSIAST | LEADER | ACHIEVER EXERCISE Circular Motion ENGLISH MEDIUM  Physics : Circular Motion TG: @NEETxNOAH...

TG: @NEETxNOAH PRE-MEDICAL PHYSICS ENTHUSIAST | LEADER | ACHIEVER EXERCISE Circular Motion ENGLISH MEDIUM  Physics : Circular Motion TG: @NEETxNOAH ® Pre-Medical EXERCISE-I (Conceptual Questions) Build Up Your Understanding KINEMATICS OF CIRCULAR MOTION 5. A particle moves in a circle of the radius 25 cm at 1. A particle of mass 'm' describes a circle of radius two revolutions per second. The acceleration of (r). The centripetal acceleration of the particle is 2 the particle in m/sec is :– 4. The momentum of the particle :– (1) π 2 (2) 8π2 r2 (3) 4 π (4) 2 π 2 2 2m 2m 4m 4m (1) (2) (3) (4) r r r r CR0005 CR0001 6. A particle moves in a circle describing equal angle 2. A particle is moving around a circular path with in equal times, its velocity vector :– ® uniform angular speed (ω). The radius of the (1) remains constant circular path is (r). The acceleration of the particle is :– (2) change in magnitude ω2 ω (3) change in direction (1) (2) (3) vω (4) vr r r (4) changes in magnitude and direction CR0002 CR0006 3. A car moves on a circular road, describing equal 7. A mass of 2 kg is whirled in a horizontal circle by angles about the centre in equal intervals of times. means of a string at an initial speed of 5 r.p.m. Which of the statements about the velocity of car Keeping the radius constant the tension in the is true :– string is doubled. The new speed is nearly :– (1) velocity is constant (1) 7 r.p.m. (2) 14 r.p.m. (2) magnitude of velocity is constant but the direction of velocity change (3) 10 r.p.m. (4) 20 r.p.m. (3) both magnitude and direction of velocity CR0007 change 8. A particle moving along a circular path. The (4) velocity is directed towards the centre of circle angular velocity, linear velocity, angular CR0003 acceleration and centripetal acceleration of the 4. An insect trapped in a circular groove of radius    particle at any instant respectively are ω , v , α , 12 cm moves along the groove steadily and  a c. Which of the following relation is/are completes 7 revolutions in 100 s. What is the correct:– linear speed of the motion :– → → → → → → → → (1) 2.3 cm/s (2) 5.3 cm/s (a) ω ⊥ v (b) ω ⊥ α (c) v ⊥ a c (d) ω ⊥ a c (3) 0.44 cm/s (4) none of these (1) a,b,d (2) b,c,d (3) a,b,c (4) a,c,d CR0004 CR0008 59 ®  TG: @NEETxNOAH Physics : Circular Motion Pre-Medical 9. A particle is acted upon by a force of constant 13. A particle of mass (m) revolving in horizontal magnitude which is always perpendicular to the circle of radius (R) with uniform speed v. When particle goes from one end to other end of velocity of the particle. The motion of the particle diameter, then:- takes place in a plane. It follows, that :– 1 (1) its velocity is constant (1) K.E. changes by mv 2 2 (2) its K.E. is constant (2) K.E. change by mv 2 (3) its acceleration is constant (3) no change in momentum (4) it moves in a straight line (4) change in momentum is 2 mv CR0013 CR0009 14. A stone is tied to one end of string 50 cm long ® 10. If the equation for the displacement of a particle and is whirled in a horizontal circle with constant moving on a circular path is given by speed. If the stone makes 10 revolutions in 20 s, (θ) = 2t3 + 0.5, where θ is in radians and t in then what is the magnitude of acceleration of the seconds, then the angular velocity of the particle stone:- after 2 s from its start is :– (1) 493 cm/s2 (2) 720 cm/s2 (1) 8 rad/s (2) 12 rad/s (3) 860 cm/s2 (4) 990 cm/s2 (3) 24 rad/s (4) 36 rad/s CR0014 CR0010 15. For a particle in a non-uniform accelerated circular motion :– 11. A sphere of mass m is tied to end of string of (1) velocity is radial and acceleration is tangential length  and rotated through the other end along only a horizontal circular path with speed v. The work (2) velocity is tangential and acceleration is radial done in full horizontal circle is :- only (3) velocity is radial and acceleration has both  mv 2  (1) 0 (2) .2π radial and tangential components      (4) velocity is tangential and acceleration has  mv 2  both radial and tangential components (3) mg.2π (4) .      CR0015 CR0011 16. The angular velocity of a particle rotating in a circular orbit 100 times per minute is 12. A body moves with constant angular velocity on (1) 1.66 rad / s a circle. Magnitude of angular acceleration :- (2) 10.47 rad / s (1) rω 2 (2) Constant (3) 10.47 degree / s (3) Zero (4) None of the above (4) 60 degree / s CR0012 CR0016 60  Physics : Circular Motion TG: @NEETxNOAH ® Pre-Medical 17. Two particles having mass 'M' and 'm' are moving 20 22. A particle moves along a circle of radius ( )m in a circular path having radius R and r. If their π time period are same then the ratio of angular with constant tangential acceleration. If the velocity will be :– velocity of the particle is 80 m/s at the end of r R R (1) (2) (3) 1 (4) the second revolution after motion has begun, R r r the tangential acceleration is :– CR0017 18. Angular velocity of minute hand of a clock is :– (1) 40 m/s2 (2) 640 π m/s2 π (3) 160 π m/s 2 (4) 40 π m/s2 (1) rad/s (2) 8π rad/s 30 CR0022 2π π (3) rad/s (4) rad/s ® 1800 1800 23. The angular velocity of a wheel is 70 rad/s. If the CR0018 radius of the wheel is 0.5 m, then linear velocity 19. A car moving with speed 30 m/s on a circular of the wheel is :– path of radius 500 m. Its speed is increasing at (1) 70 m/s (2) 35 m/s the rate of 2m/s2. The acceleration of the car is :– (3) 30 m/s (4) 20 m/s 2 2 (1) 9.8 m/s (2) 1.8 m/s CR0023 2 (3) 2 m/s (4) 2.7 m/s2 24. A stone tied to the end of a string of 1m long is CR0019 whirled in a horizontal circle with a constant 20. If a particle is rotating uniformly in a horizontal circle, then – speed. If the stone makes 22 revolution in (1) no force is acting on particle 44 seconds, what is the magnitude and direction (2) velocity of particle is constant of acceleration of the stone :– (3) particle has no acceleration (1) π2 m/s2 and direction along the tangent to the (4) no work is done circle. CR0020 (2) π m/s and direction along the radius towards 2 2 21. A body of mass 1 kg tied to one end of string is the centre. revolved in a horizontal circle of radius 0.1 m with a speed of 3 revolution/sec, assuming the π2 2 effect of gravity is negligible, then linear velocity, (3) m/s and direction along the radius 4 acceleration and tension in the string will be :– towards the centre. 2 (1) 1.88 m/s, 35.5 m/s , 35.5 N (4) π m/s and direction along the radius away 2 2 (2) 2.88 m/s, 45.5 m/s2, 45.5 N 2 (3) 3.88 m/s, 55.5 m/s , 55.5 N from the centre. (4) None of these CR0024 CR0021 61 ®  TG: @NEETxNOAH Physics : Circular Motion Pre-Medical 25. A fly wheel rotating at 600 rev/min is brought 30. A pendulum is suspended from the roof of a rail under uniform deceleration and stopped after road car. When the car is moving on a circular 2 minutes, then what is angular deceleration in track the pendulum inclines : 2 rad/sec ? (1) Forward π 1 (1) (2) 10 π (3) (4) 300 (2) Backward 6 12 (3) Towards the centre of the path CR0025 (4) Away from the centre of the path 26. The tangential and angular acceleration of a CR0030 particle are 10 m/s2 and 5 rad/s2 respectively. It will be at a distance from the axis of rotation. 31. A string of length 0.1 m cannot bear a tension (1) 50 m (2) m (3) 1 m (4) 2 m more than 100N. It is tied to a body of mass 100g and rotated in a horizontal circle. The CR0026 maximum angular velocity can be - ® (1) 100 rad/s (2) 1000 rad/s DYNAMICS OF HORIZONTAL CIRCULAR (3) 10000 rad/s (4) 0.1 rad/s MOTION CR0031 27. The angular acceleration of particle moving 32. The radius of the circular path of a particle is along a circular path with uniform speed :– doubled but its frequency of rotation is kept (1) uniform but non zero constant. If the initial centripetal force be F, then (2) zero the final value of centripetal force will be :– (3) variable F (1) F (2) (3) 4F (4) 2F 2 (4) as can not be predicted from given information CR0032 CR0027 33. A 0.5 kg ball moves in a circle of radius 0.4 m at a speed of 4 m/s. The centripetal force on the 28. If the speed and radius both are trippled for a body moving on a circular path, then the new ball is :– centripetal force will be :– (1) 10N (2) 20N (3) 40N (4) 80N (1) Doubled of previous value CR0033 (2) Equal to previous value 34. A body is revolving with a constant speed along a (3) Triple of previous value circle. If its direction of motion is reversed but the (4) One third of previous value speed remains the same then :– CR0028 (a) the centripetal force will not suffer any change in magnitude 29. When a body moves with a constant speed along (b) the centripetal force will have its direction a circle :– reversed (1) no acceleration is present in the body (c) the centripetal force will not suffer any (2) no force acts on the body change in direction (3) its velocity remains constant (d) the centripetal force is doubled (4) no work gets done on it (1) a,b (2) b,c (3) c,d (4) a, c CR0029 CR0034 62  Physics : Circular Motion TG: @NEETxNOAH ® Pre-Medical 35. ar and at represent radial and tangential 40. A motor cycle driver doubles its velocity when he acceleration. The motion of a particle will be is taking a turn. The force exerted towards the centre will become :- uniform circular motion, if :– (1) double (2) half (1) ar = 0 and at = 0 1 (3) 4 times (4) times (2) ar = 0 but at ≠ 0 4 (3) ar ≠ 0 but at = 0 CR0040 41. The force required to keep a body in uniform (4) ar ≠ 0 and at ≠ 0 circular motion is :- CR0035 (1) Centripetal force 36. In uniform circular motion, the velocity vector (2) Centrifugal force and acceleration vector are (3) Resistance (4) None of the above ® (1) Perpendicular to each other CR0041 (2) Same direction (3) Opposite direction BANKING OF TRACKS (4) Not related to each other 42. A car moving on a horizontal road may be CR0036 thrown out of the road in taking a turn :– (1) by the gravitational force 37. A string of length 10 cm breaks if its tension (2) due to lack of proper centripetal force exceeds 10 newton. A stone of mass 250 g tied (3) due to rolling friction between the tyres and to this string, is rotated in a horizontal circle. The the Road maximum angular velocity of rotation can be :- (4) due to reaction of the road (1) 20 rad/s (2) 40 rad/s CR0042 (3) 100 rad/s (4) 200 rad/s 43. Radius of the curved road on national highway is R. Width of the road is b. The outer edge of the CR0037 road is raised by h with respect to inner edge so 38. The earth (Me = 6 × 1024 kg) is revolving round that a car with velocity v can pass safely over it. The value of h is :– the sun in an orbit of radius (1.5 × 108) km with –7 angular velocity of (2 × 10 ) rad/s. The force (in v2b v v2R v2b (1) (2) (3) (4) Rg Rgb bg R newton) exerted on the earth by the sun will be :- 21 CR0043 (1) 36 × 10 (2) 16 × 1024 44. A boy holds a pendulum in his hand while (3) 25 × 1016 (4) Zero standing at the edge of a circular platform of CR0038 radius r rotating at an angular speed ω. The pendulum will hang at an angle θ with the 39. A 500 kg car takes a round turn of radius 50 m vertical so that :– (Neglect length of pendulum) with a velocity of 36 km/hr. The centripetal ω2 r 2 (1) tan θ = 0 (2) tan θ = force is :- g (1) 250 N (2) 1000N (3) 750N (4) 1200 N rω2 g (3) tan θ = (4) tan θ = g ω2 r CR0039 CR0044 63 ®  TG: @NEETxNOAH Physics : Circular Motion Pre-Medical VERTICAL CIRCULAR MOTION 49. In a vertical circle of radius (r), at what point in its path a particle may have tension equal to zero :– 45. Let 'θ' denote the angular displacement of a (1) highest point simple pendulum oscillating in a vertical plane. If the mass of the bob is (m), then the tension in (2) lowest point string is mg cosθ :– (3) at any point (1) always (4) at a point horizontal from the centre of radius (2) never CR0049 (3) at the extreme positions 50. A stone attached to one end of a string is whirled in a vertical circle. The tension in the string is (4) at the mean position maximum when :– CR0045 (1) the string is horizontal ® 46. A pendulum bob has a speed 3 m/s while (2) the string is vertical with the stone at highest passing through its lowest position, length of the position pendulum is 0.5 m then its speed when it makes (3) the string is vertical with the stone at the o an angle of 60 with the vertical is :– lowest position (g = 10 m/s2) (4) the string makes an angle of 45° with the vertical (1) 2 m/s (2) 1 m/s (3) 4 m/s (4) 3 m/s CR0050 CR0046 51. A weightless thread can withstand tension upto 47. The mass of the bob of a simple pendulum of 30 N. A stone of mass 0.5 kg is tied to it and is length L is m. If the bob is left from its horizontal revolved in a circular path of radius 2m in a position then the speed of the bob and the vertical plane. If g = 10 m/s2, then the maximum angular velocity of the stone can be :– tension in the thread in the lowest position of the bob will be respectively :– (1) 5 rad/s (2) 30 rad/s L O (3) 60 rad/s (4) 10 rad/s (1) 2gL and 3 mg L CR0051 (2) 3gL and 2 mg 52. A body tied to a string of length L is revolved in a vertical circle with minimum velocity, when the (3) 5gL and 2 mg body reaches the upper most point the string breaks and the body moves under the influence (4) gL and 3 mg of the gravitational field of earth along a parabolic path. The horizontal range AC of the CR0047 body will be :– P v 48. A stone of mass 1 kg is tied to the end of a string (1) x = L L of 1 m length. It is whirled in a vertical circle. If (2) x = 2L m O the velocity of the stone at the top be 4 m/s. (3) x= 2 2L x A C What is the tension in the string (at that instant) ? (4) x= 2L (1) 6 N (2) 16 N (3) 5 N (4) 10 N CR0052 CR0048 64  Physics : Circular Motion TG: @NEETxNOAH ® Pre-Medical 53. A particle is moving in a vertical circle the 58. A frictionless track ABCDE ends in a circular tension in the string when passing through two loop of radius R. A body slides down the track position at angle 30o and 60o from vertical from from point A which is at a height h = 5 cm. lowest position are T1 and T2 respectively then :– Maximum value of R for the body to successfully (1) T1 = T2 (2) T1 > T2 complete the loop is :– (3) T1 < T2 (4) T1 ≥ T2 (1) 5 cm. D A CR0053 (2) 2 cm. h 2R C 54. A body crosses the topmost point of a vertical 10 E circle with critical speed. What will be its (3) cm. 3 B centripetal acceleration when the string is horizontal :– 15 (4) cm. (1) g (2) 2g (3) 3g (4) 6g 4 ® CR0054 CR0058 55. Stone tied at one end of light string is whirled 59. A particle of mass m is performing vertical round a vertical circle. If the difference between circular motion (see figure). If the average speed the maximum and minimum tension experienced of the particle is increased, then at which point by the string wire is 2 kg wt, then the mass of maximum breaking possibility of the string :– the stone must be :– A (1) A (1) 1 kg (2) 6 kg (3) 1/3 kg (4) 2 kg m (2) B CR0055 D O C (3) C 56. A mass tied to a string moves in a vertical circle B with a uniform speed of 5 m/s as shown. At the (4) D point P the string breaks. The mass will reach a CR0059 height above P of nearly (g = 10 m/s2) :– (1) 1 m 60. A stone tide with a string is moving in a vertical (2) 0.5 m 1m circle of radius 'r'. Its minimum velocity at the P O highest point of the circle will be :– (3) 1.75 m (4) 1.25 m gr (1) 3gr (2) 2gr (3) gr (4) 2 CR0056 CR0060 57. If the overbridge is concave instead of being convex, then the reaction on the road at the 61. A stone of mass 0.2 kg is tied to one end of a lowest position will be :- thread of length 0.1 m whirled in a vertical circle. mv 2 mv 2 When the stone is at the lowest point of circle, (1) mg + (2) mg − r r tension in thread is 52N, then velocity of the m2 v 2 g v2g stone will be :– (3) (4) r r (1) 4 m/s (2) 5 m/s (3) 6 m/s (4) 7 m/s CR0057 CR0061 65 ®  TG: @NEETxNOAH Physics : Circular Motion Pre-Medical 62. A suspended simple pendulum of length  is making an angle θ with the vertical. On releasing, its velocity at lowest point will be :- (1) 2g(1 + cos θ) (2) 2g sinθ (3) 2g(1 − cos θ) (4) 2g CR0062 ® EXERCISE-I (Conceptual Questions) ANSWER KEY Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Ans. 2 3 2 2 3 3 1 4 2 3 1 3 4 1 4 Que. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Ans. 2 3 4 4 4 1 1 2 2 1 4 2 3 4 4 Que. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Ans. 1 4 2 4 3 1 1 1 2 3 1 2 1 3 3 Que. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Ans. 1 1 1 1 3 1 2 2 3 3 4 1 2 2 3 Que. 61 62 Ans. 2 3 66  Physics : Circular Motion TG: @NEETxNOAH ® Pre-Medical EXERCISE-II (Previous Year Questions) AIPMT/NEET AIPMT 2006 AIPMT 2011 1. A tube of length L is filled completely with an 5. A particle moves in a circle of radius 5 cm with incompressible liquid of mass M and closed at constant speed and time period 0.2π s. The both the ends. The tube is then rotated in a acceleration of the particle is :- horizontal plane about one of its ends with a (1) 15 m/s2 (2) 25 m/s2 uniform angular velocity ω. The force exerted by (3) 36 m/s2 (4) 5 m/s2 the liquid at the other end is :– CR0067 M L ω2 M L 2ω (1) (2) 2 2 AIPMT (Pre) 2012 M L 2 ω2 6. A car of mass 1000 kg negotiates a banked (3) M L ω 2 (4) 2 curve of radius 90 m on a frictionless road. If the ® CR0063 banking angle is 45°, the speed of the car is :- 2. A car runs at a constant speed on a circular track (1) 5 m/s (2) 10 m/s of radius 100 m, taking 62.8 seconds for every (3) 20 m/s (4) 30 m/s circular lap. The average velocity and average CR0068 speed for each circular lap respectively is :- (1) 0,0 (2) 0, 10 m/s AIPMT (Mains) 2012 (3) 10 m/s, 10 m/s (4) 10 m/s, 0 7. A car of mass m is moving on a level circular CR0064 track of radius R. If µs represents the static AIPMT 2008 friction between the road and tyres of the car, 3. A roller coaster is designed such that riders the maximum speed of the car in circular motion experiece"weightlessness" as they go round the is given by :- top of a hill whose radius of curvature is 20 m. (1) mRg / µs The speed of the car at the top of the hill is between. (g = 10 m/s2) (2) µs Rg (1) 16 m/s and 17 m/s (3) µs mRg (2) 13 m/s and 14 m/s (3) 14 m/s and 15 m/s (4) Rg / µs (4) 15 m/s and 16 m/s CR0069 CR0065 AIPMT (Pre) 2010 Re-AIPMT 2015 8. Two stones of masses m and 2 m are whirled in 4. A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r horizontal circles, the heavier one in a radius r from the centre of the record. The static 2 coefficient of friction is µ. The coin will revolve and the lighter one in radius r. The tangential with the record if :- speed of lighter stone is n times that of the value µg (1) r ≥ (2) r =µgω2 of heavier stone when they experience same ω2 centripetal forces. The value of n is : ω2 µg (3) r < (4) r ≤ 2 (1) 1 (2) 2 (3) 3 (4) 4 µg ω CR0066 CR0070 67 ®  TG: @NEETxNOAH Physics : Circular Motion Pre-Medical  9. The position vector of a particle R as a function NEET-II 2016 of time is given by :- 13. 2 In the given figure, a = 15 m/s represents the  R 4 sin(2πt)iˆ + 4 cos(2πt)ˆj = total acceleration of a particle moving in the Where R is in meters, t is in seconds and î and clockwise direction in a circle of radius R = 2.5 ĵ denote unit vectors along x and y-directions, m at a given instant of time. The speed of the particle is :- respectively. Which one of the following statements is wrong for the motion of particle ? (1) Path of the particle is a circle of radius 4 O a meter  (2) Acceleration vectors is along −R v2 (3) Magnitude of acceleration vector is (1) 5.7 m/s (2) 6.2 m/s R (3) 4.5 m/s (4) 5.0 m/s where v is the velocity of particle. CR0075 ® (4) Magnitude of the velocity of particle is 8 meter/second 14. A particle moves so that its position vector is  CR0071 given by r = cos ωt xˆ + sin ωt yˆ. Where ω is a NEET-I 2016 constant. Which of the following is true ? 10. A particle of mass 10 g moves along a circle of (1) Velocity and acceleration both are radius 6.4 cm with a constant tangential  perpendicular to r. acceleration. What is the magnitude of this (2) Velocity and acceleration both are parallel to acceleration if the kinetic energy of the particle  –4 r becomes equal to 8 × 10 J by the end of the  (3) Velocity is perpendicular to r and second revolution after the beginning of the acceleration is directed towards the origin motion?  2 (4) Velocity is perpendicular to r and (1) 0.1 m/s (2) 0.15 m/s2 acceleration is directed away from the origin (3) 0.18 m/s2 (4) 0.2 m/s2 CR0076 CR0072 NEET(UG) 2017 11. What is the minimum velocity with which a body 15. One end of string of length  is connected to a of mass m must enter a vertical loop of radius R at lowest point so that it can complete the loop ? particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal (1) gR (2) 2gR (3) 3gR (4) 5gR table. If the particle moves in circle with speed 'v' CR0073 the net force on the particle (directed towards 12. A car is negotiating a curved road of radius R. centre) will be (T represents the tension in the The road is banked at an angle θ. the coefficient string) :- of friction between the tyres of the car and the mv 2 road is µ s. The maximum safe velocity on this (1) T +  road is:- mv 2 µ s + tan θ 2 µ + tan θ (2) T − (1) gR (2) gR s  1 − µ s tan θ 1 − µ s tan θ (3) Zero g µ s + tan θ g µ s + tan θ (3) (4) (4) T R 1 − µ s tan θ R2 1 − µ s tan θ CR0078 CR0074 68  Physics : Circular Motion TG: @NEETxNOAH ® Pre-Medical NEET(UG) 2018 NEET(UG) 2019 (Odisha) 16. A body initially at rest and sliding along a 20. A particle starting from rest, moves in a circle of frictionless track from a height h (as shown in the radius 'r'. It attains a velocity of V0 m/s in the nth figure) just completes a vertical circle of diameter round. Its angular acceleration will be :- AB = D. The height h is equal to :- V0 V02 (1) rad / s2 (2) rad / s2 n 2πnr 2 B h V02 V02 (3) rad / s2 (4) rad / s2 4πnr 2 4πnr A CR0103 NEET(UG) 2020 (COVID-19) 3 7 5 (1) D (2) D (3) D (4) D 2 5 4 21. The angular speed of the wheel of a vehicle is increased from 360 rpm to 1200 rpm in CR0079 14 second. Its angular acceleration is NEET(UG) 2019 (1) 2π rad/s2 (2) 28π rad/s2 ® 17. A block of mass 10 kg is in contact against the (3) 120π rad/s2 (4) 1 rad/s2 inner wall of a hollow cylindrical drum of radius CR0104 1 m. The coefficient of friction between the 22. A point mass 'm' is moved in a vertical circle of block and the inner wall of the cylinder is 0.1. radius 'r' with the help of a string. The velocity of The minimum angular velocity needed for the the mass is 7gr at the lowest point. The cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will tension in the string at the lowest point is : be : (1) 6 mg (2) 7 mg (g = 10 m/s ) 2 (3) 8 mg (4) 1 mg CR0105 10 NEET (UG) 2021(Paper-2) (1) 10 rad/s (2) rad/s 2π 23. A ball of mass m is attached to a string of length (3) 10 rad/s (4) 10π rad/s L and given a horizontal velocity 10gL at its CR0100 lowest point as shown. The ratio of tension in the string when it has turned an angle 60° to 18. A mass m is attached to a thin wire and whirled initial tension, i.e. T2/T1 is in a vertical circle. The wire is most likely to O break when : (1) the mass is at the highest point T (2) the wire is horizontal 60° (3) the mass is at the lowest point (4) inclined at an angle of 60° from vertical T1 CR0101 19. Two particles A and B are moving in uniform circular motion in concentric circles of radius rA and rB with speed υA and υB respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be : 17 19 19 17 (1) (2) (3) (4) (1) rA : rB (2) υA : υB 21 21 22 23 (3) rB : rA (4) 1 : 1 CR0106 CR0102 EXERCISE-II (Previous Year Questions) ANSWER KEY Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Ans. 1 2 3 4 4 4 2 2 4 1 4 2 1 3 4 Que. 16 17 18 19 20 21 22 23 Ans. 4 3 3 4 3 1 3 3 69 ®  TG: @NEETxNOAH Physics : Circular Motion Pre-Medical EXERCISE-III (Analytical Questions) Master Your Understanding 1. A wheel has a constant angular acceleration of 4. A mass m is attached to the end of a rod of 3.0 rad/s2, During a certain 4.0 s interval, it length . The mass goes around a verticle turns through an angle of 120 rad. Assuming that at t = 0, angular speed ω0 = 3 rad/s how circular path with the other end hinged at the long, is motion at the start of this 4.0 second centre. What should be the minimum velocity of interval ? mass at the bottom of the circle so that the mass (1) 7 sec. (2) 9 sec. completes the circle ? (3) 4 sec. (4) 10 sec. (1) 4g (2) 3g CR0080 2. Keeping the banking angle of the road constant, (3) 5g (4) g the maximum safe speed of passing vehicles is to CR0083 be increased by 10%. The radius of curvature of 5. A stone is tied to a string of length ‘’ and is the road will have to be changed from 20 m to :- (1) 16 m (2) 18 m whirled in a vertical circle with the other end of ® (3) 24.20 m (4) 30.5 m the string as the centre. At a certain instant of CR0081 time, the stone is at its lowest position and has a 3. Three identical particles are joined together by a speed ‘u’. The magnitude of the change in thread as shown in figure. All the three particles velocity as it reaches a position where the string are moving in a horizontal plane. If the velocity is horizontal (g being acceleration due to gravity) of the outermost particle is v0, then the ratio of is :– tensions in the three sections of the string is :- (1) 3 : 5 : 7 (1) u2 − g (2) u – u2 − 2g (2) 3 : 4 : 5 O A B C (3) 2g (4) 2(u2 − g ) (3) 7 : 11 : 6    CR0084 (4) 3 : 5 : 6 CR0082 EXERCISE-III (Analytical Questions) ANSWER KEY Que. 1 2 3 4 5 Ans. 1 3 4 1 4 70