Tiêu đề 04. MOtion in a plane Easy.pdf ✅

1. If the body is moving in a circle of radius r with a constant speed v , its angular velocity is (a) v /r 2 (b) vr (c) v / r (d) r / v 2. Two racing cars of masses m1 and m2 are moving in circles of radii 1 r and 2 r respectively. Their speeds are such that each makes a complete circle in the same duration of time t . The ratio of the angular speed of the first to the second car is (a) 1 2 m : m (b) 1 2 r :r (c) 1 : 1 (d) 1 1 2 2 m r : m r 3. A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is (a) Doubled (b) Quadrupled (c) Halved (d) Unchanged 4. A body of mass m is moving in a circle of radius r with a constant speed v . The force on the body is r mv 2 and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle (a) r r mv   2 (b) Zero (c) 2 2 r mv (d) 2 2 mv r 5. If a particle moves in a circle describing equal angles in equal times, its velocity vector (a) Remains constant (b) Changes in magnitude (c) Changes in direction (d) Changes both in magnitude and direction 6. A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v . If the string is released, the stone flies (a) Radially outward (b) Radially inward (c) Tangentially outward (d)With an acceleration l mv 2 7. A body is moving in a circular path with a constant speed. It has (a) A constant velocity (b)A constant acceleration (c) An acceleration of constant magnitude (d) An acceleration which varies with time 8. A motor cyclist going round in a circular track at constant speed has (a) Constant linear velocity (b)Constant acceleration (c) Constant angular velocity (d) Constant force 9. A particle P is moving in a circle of radius 'a' with a uniform speed v . C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 4 : 1 10. Two particles of equal masses are revolving in circular paths of radii 1 r and 2 r respectively with the same speed. The ratio of their centripetal forces is (a) 1 2 r r (b) 1 2 r r (c) 2 2 1         r r (d) 2 1 2         r r 11. A particle moves with constant angular velocity in a circle. During the motion its (a) Energy is conserved (b) Momentum is conserved (c) Energy and momentum both are conserved (d) None of the above is conserved 12. A stone tied to a string is rotated in a circle. If the string is cut, the stone flies away from the circle because (a) A centrifugal force acts on the stone (b)A centripetal force acts on the stone (c) Of its inertia (d)Reaction of the centripetal force 13. When a body moves with a constant speed along a circle (a) No work is done on it (b) No acceleration is produced in the body (c) No force acts on the body (d) Its velocity remains constant 14. A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant (a) Acceleration (b) Velocity (c) Momentum (d) Kinetic energy 15. On a railway curve, the outside rail is laid higher than the inside one so that resultant force exerted on the wheels of the rail car by the tops of the rails will (a) Have a horizontal inward component (b) Be vertical (c) Equilibriate the centripetal force (d) Be decreased 16. If the over bridge is concave instead of being convex, the thrust on the road at the lowest position will be (a) r mv mg 2 + (b) r mv mg 2 −
(c) r m v g 2 2 (d) r v g 2 17. A cyclist taking turn bends inwards while a car passenger taking same turn is thrown outwards. The reason is (a) Car is heavier than cycle (b) Car has four wheels while cycle has only two (c) Difference in the speed of the two (d) Cyclist has to counteract the centrifugal force while in the case of car only the passenger is thrown by this force 18. A car sometimes overturns while taking a turn. When it overturns, it is (a) The inner wheel which leaves the ground first (b) The outer wheel which leaves the ground first (c) Both the wheels leave the ground simultaneously (d) Either wheel leaves the ground first 19. A tachometer is a device to measure (a) Gravitational pull (b) Speed of rotation (c) Surface tension (d) Tension in a spring 20. Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is (a) R /r (b) r / R (c) 2 2 R /r (d) 2 2 r / R 21. The ratio of angular speeds of minute hand and hour hand of a watch is (a) 1 : 12 (b) 6 : 1 (c) 12 : 1 (d) 1 : 6 22. A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud, as it leaves the ground are thrown (a) Vertically upwards (b) Vertically inwards (c) Towards north (d) Towards south 23. An aircraft executes a horizontal loop with a speed of 150 m/s with its, wings banked at an angle of o 12 . The radius of the loop is ( 10 / ) 2 g = m s (a) 10.6 km (b) 9.6 km (c) 7.4 km (d) 5.8 km 24. A particle is moving in a horizontal circle with constant speed. It has constant (a) Velocity (b) Acceleration (c) Kinetic energy (d) Displacement 25. A motor cyclist moving with a velocity of 72 km/hour on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 meters. The acceleration due to gravity is 10 m/sec2 . In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than (a) tan 6 −1  = (b) tan 2 −1  = (c) tan 25.92 −1  = (d) tan 4 −1  = 26. A train is moving towards north. At one place it turns towards north-east, here we observe that (a) The radius of curvature of outer rail will be greater than that of the inner rail (b) The radius of the inner rail will be greater than that of the outer rail (c) The radius of curvature of one of the rails will be greater (d) The radius of curvature of the outer and inner rails will be the same 27. The angular speed of a fly wheel making 120 revolutions/minute is (a) 2 rad / s (b) 4 rad / s 2  (c)  rad / s (d) 4 rad / s 28. A particle is moving on a circular path with constant speed, then its acceleration will be (a) Zero (b) External radial acceleration (c) Internal radial acceleration (d) Constant acceleration 29. A car is moving on a circular path and takes a turn. If R1 and R2 be the reactions on the inner and outer wheels respectively, then (a) R1 = R2 (b) R1  R2 (c) R1  R2 (d) R1  R2 30. A mass of 100 gm is tied to one end of a string 2 m long. The body is revolving in a horizontal circle making a maximum of 200 revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is (approximately) (a) 8.76 N (b) 8.94 N (c) 89.42 N (d) 87.64 N 31. A road is 10 m wide. Its radius of curvature is 50 m. The outer edge is above the lower edge by a distance of 1.5 m. This road is most suited for the velocity (a) 2.5 m/sec (b) 4.5 m/sec (c) 6.5 m/sec (d) 8.5 m/sec 32. Certain neutron stars are believed to be rotating at about 1rev /sec . If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be (a) 8 2 20 10 m / sec (b) 5 2 8 10 m / sec (c) 5 2 120 10 m /sec (d) 8 2 4 10 m / sec
33. A particle revolves round a circular path. The acceleration of the particle is (a) Along the circumference of the circle (b)Along the tangent (c) Along the radius (d)Zero 34. The length of second's hand in a watch is 1 cm. The change in velocity of its tip in 15 seconds is (a) Zero (b) / sec 30 2 cm  (c) / sec 30 cm  (d) / sec 30 2 cm  35. A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in 2 m / s is (a) 2  (b) 2 8 (c) 2 4 (d) 2 2 36. An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m. The acceleration of a point on the tip of the blade is about (a) 1600 2 m / sec (b) 4740 2 m / sec (c) 2370 2 m / sec (d) 5055 2 m / sec 37. The force required to keep a body in uniform circular motion is (a) Centripetal force (b) Centrifugal force (c) Resistance (d) None of the above 38. Cream gets separated out of milk when it is churned, it is due to (a) Gravitational force (b) Centripetal force (c) Centrifugal force (d) Frictional force 39. A particle of mass m is executing uniform circular motion on a path of radius r . If p is the magnitude of its linear momentum. The radial force acting on the particle is (a) pmr (b) p rm (c) r mp 2 (d) rm p 2 40. A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r' . The speed of the particle is (a) Proportional to 2 r (b) Independent of r (c) Proportional to r (d) Proportional to 1 /r 41. Two masses M and m are attached to a vertical axis by weightless threads of combined length l . They are set in rotational motion in a horizontal plane about this axis with constant angular velocity  . If the tensions in the threads are the same during motion, the distance of M from the axis is (a) M m Ml + (b) M m ml + (c) l M M + m (d) l m M + m 42. A boy on a cycle pedals around a circle of 20 metres radius at a speed of 20 metres / sec. The combined mass of the boy and the cycle is 90 kg. The angle that the cycle makes with the vertical so that it may not fall is ( 9.8 / sec ) 2 g = m (a) o 60 .25 (b) o 63 .90 (c) o 26 .12 (d) o 30 .00 43. The average acceleration vector for a particle having a uniform circular motion is (a) A constant vector of magnitude r v 2 (b) A vector of magnitude r v 2 directed normal to the plane of the given uniform circular motion (c) Equal to the instantaneous acceleration vector at the start of the motion (d) A null vector 44. Radius of the curved road on national highway is R . Width of the road is b . The outer edge of the road is raised by h with respect to inner edge so that a car with velocity v can pass safe over it. The value of h is (a) Rg v b 2 (b) Rgb v (c) g v R 2 (d) R v b 2 45. When a particle moves in a uniform circular motion. It has (a) Radial velocity and radial acceleration (b) Tangential velocity and radial acceleration (c) Tangential velocity and tangential acceleration (d) Radial velocity and tangential acceleration 46. A motorcycle is going on an overbridge of radius R . The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it (a) Increases (b) Decreases (c) Remains the same (d) Fluctuates 47. A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly (a) 14 rpm (b) 10 rpm
(c) 2.25 rpm (d) 7 rpm 48. The magnitude of the centripetal force acting on a body of mass m executing uniform motion in a circle of radius r with speed v is (a) mvr (b) mv /r 2 (c) v r m 2 / (d) v /rm 49. A string breaks if its tension exceeds 10 newtons. A stone of mass 250 gm tied to this string of length 10 cm is rotated in a horizontal circle. The maximum angular velocity of rotation can be (a) 20 rad/s (b) 40 rad/s (c) 100 rad/s (d) 200 rad/s 50. A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is (a) 250 N (b) 750 N (c) 1000 N (d) 1200 N 51. A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved (a) 14 m/s (b) 3 m/s (c) 3.92 m/s (d) 5 m/s 52. A body of mass 5 kg is moving in a circle of radius 1m with an angular velocity of 2 radian/sec. The centripetal force is (a) 10 N (b) 20 N (c) 30 N (d) 40 N 53. If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force ( / ) 2 −k r , the total energy is (a) r k 2 − (b) r k − (c) r 2k − (d) r 4k − 54. A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be (a) 20 −1 ms (b) 16 −1 ms (c) 14 −1 ms (d) 12 −1 ms 55. A circular road of radius 1000 m has banking angle o 45 . The maximum safe speed of a car having mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5 (a) 172 m/s (b) 124 m/s (c) 99 m/s (d) 86 m/s 56. The second's hand of a watch has length 6 cm. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be (a) 6.28 and 0 mm/s (b) 8.88 and 4.44 mm/s (c) 8.88 and 6.28 mm/s (d) 6.28 and 8.88 mm/s 57. A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v . The work done in full horizontal circle is (a) 0 (b) l l mv . 2 2         (c) mg . 2l (d) .( ) 2 l l mv         58. A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point on circular path (a) 10 m/s (b) 2 m/s (c) 20 m/s (d) 2 m/s 59. Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2 (a) 0.14 m/s (b) 140 m/s (c) 1.4 km/s (d) 14 m/s 60. A car when passes through a convex bridge exerts a force on it which is equal to (a) r Mv Mg 2 + (b) r Mv 2 (c) Mg (d) None of these 61. The angular speed of seconds needle in a mechanical watch is (a) 30  rad/s (b) 2 rad/s (c)  rad/s (d)  60 rad/s 62. The angular velocity of a particle rotating in a circular orbit 100 times per minute is (a) 1.66 rad/s (b) 10.47 rad/s (c) 10.47 deg/s (d) 60 deg/s 63. A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is (a) 100 rJ (b) (r / 100 )J (c) (100 / r)J (d) Zero 64. A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is