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AL-MC-Revision / p.1 1. (88-I-1) 3. (88-I-3) A football player is running at a velocity of 3 ms 1 due north. After a violent collision with another player, he is moving at a velocity of A boy wished to swim across a river with parallel 4 ms 1 due east. Which of the following arrows banks as shown in the diagram above. Assuming the water current is flowing at 0.5 ms 1 , and the swimming speed of the boy is 1 ms1 , along best represents the direction of his change of velocity? which direction should the boy swim if he wishes (1) to reach the opposite bank in the shortest time? (2) to take the shortest route to the opposite bank? (1) shortest time (2) shortest route 4. 2. A. X Y B. X Z C. Y X D. Y Z E. Z Y (88-I-5) (88-I-2) The graph shown is a possible representation of the A smooth block of mass 2 kg slides down a wedge. relation between velocity and time for the motion The wedge, of mass 10 kg, is placed on a of horizontal table, and its inclined plane makes an o angle of 30 with the horizontal. If the wedge remains stationary all the time, the normal reaction (1) of the table acting on the wedge is (2) a mass, attached to a spiral spring, pulled vertically downwards and then released. the spot on the screen of a CRO when a linear time base is operating. A. 15 N. B. 85 N. C. 100 N. D. 115 N. E. 120 N. (3) a ball dropped vertically onto a hard, smooth and horizontal surface, where it undergoes elastic collisions. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only AL-MC-Revision / p.2 5. (89-I-3) 7. (89-I-5) Two ships X and Y travel with equal speeds. X moves North and Y moves East. Which of the following best gives the direction of the velocity of X relative to Y? In the figure above, X and Y are blocks of mass 1 kg and 2 kg respectively. S is a spring balance of negligible mass and P is a smooth pulley fixed at the top of two smooth inclined planes. What is the reading of S when X is held stationary? 8. A. 5N B. 10 N C. 15 N D. 20 N E. 30 N (89-I-6) A ball bounces up and down on the ground in the 6. (89-I-4) vertical direction. Which of the following graphs best describes the variation of its acceleration a with time t? Two objects of weights 2 N and 3 N are suspended from a fixed point by two identical light springs A and B as shown in the diagram. The force constants of the springs are both 1 N cm1 . What are the extensions of springs A and B? Extension of Extension of spring A spring B A. 5 cm 3 cm B. 5 cm 2 cm C. 3 cm 2 cm D. 3 cm 5 cm E. 2 cm 3 cm AL-MC-Revision / p.3 9. 11. (89-I-7) (90-I-2) A man weighs an object with a spring balance in a When a man is running due north, he feels lift. Before the lift moves the scale reads 50 N. The that the wind is blowing towards him from lift goes down and then stops. The reading on the the east. What is the actual direction of the scale is wind? A. 50 N throughout the journey. A. from the east B. More than 50 N when the lift starts, B. from north-east and remains steady until it comes to C. from south-east rest. D. from south-west Less than 50 N when the lift starts, and E. from north-west C. remains steady until it comes to rest. D. E. More than 50 N as the lift starts, and 12. (90-I-3) less than 50 N as it comes to rest. A uniform rope has a length l and a mass m. Less than 50 N as the lift starts, and It is held stationary with 4/5 of the length of more than 50 N as it comes to rest. the rope lying on a smooth horizontal table surface and with the remaining 1/5 hanging 10. freely over the edge. The minimum work (89-I-13) required to pull the whole rope onto the table surface is A. 0.01 mg l B. 0.02 mg l A ball rolls down an inclined plane. The ball is first C. 0.1 mg l released from rest from P and then later from Q. D. 0.2 mg l Which of the following statements is/are correct? E. mg l (1) (2) (3) The ball takes twice as much time to roll 13. (91-I-1) from Q to O as it does to roll from P to O. In which of the following situations is the The acceleration of the ball at Q is twice as magnitude of the normal reaction of the supporting large as the acceleration at P. surface, R, equal to the weight of the body, mg? The ball has twice as much K.E. at O when rolling from Q as it does when rolling from (1) At rest on a rough inclined plane. P. (2) On the floor of a spacecraft in circular orbit around the earth. A. (1), (2) and (3) (3) On the floor of a lift moving upwards with B. (1) and (2) only C. (2) and (3) only D. (1) only A. (1), (2) and (3) E. (3) only B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only uniform velocity. AL-MC-Revision / p.4 14. (91-I-2) An object of mass m slides with constant acceleration a down a plane making an angle B. C. with the horizontal. The frictional force acting on D. the object is E. A. B. C. D. E. 1.6 10 3 rad 5.7 10 3 rad 8.3 10 3 rad 1.6 10 2 rad 8.3 10 2 rad A. mg ma mg ma sin mg sin ma (mg ma) sin (mg ma) sin 17. (92-I-1) Three blocks A, B and C of masses m, 2m and 2m respectively are placed on a smooth horizontal 15. (91-I-3) ground as shown in the figure above. A constant horizontal force is applied to block A so that the three blocks move with the same acceleration towards the right. What is the resultant force acting on block B? A. F/5 B. F/3 A gas atom of mass m moving with a uniform C. 2F/5 speed v makes an elastic collision with the wall of D. 3F/5 the container as shown in the diagram. What is the E. F magnitude of the change in the momentum of the gas atom? 18. (92-I-2) A man in a lift measures his weight with a A. B. C. D. E. 16. 2mv mv sin mv cos 2mv sin 2mv cos compression balance and discovers that his weight is reduced by 10%. The lift is probably (91-I-4) A spacecraft of mass 4.0 10 4 kg was travelling (1) moving upwards and accelerating at g /10. (2) moving upwards and decelerating at g/10. (3) moving downwards and accelerating at g/10. (4) moving downwards and decelerating at g/10. (5) moving downwards with uniform velocity. on its way to the moon with the rocket motors shut A. (1) and (3) only down. At the instant when it was travelling at B. (1) and (4) only 1500 ms 1 , the rocket motors were turned on for 5 C. (2) and (3) only D. (2) and (4) only seconds to make a course correction. If the rocket E. (5) only gave a thrust of 1.0 10 N at right angles to the direction of travel, through what angle would the 5 flight path of the spacecraft be turned? AL-MC-Revision / p.5 19. (92-I-3) 21. (93-I-1) A simple pendulum is swinging in a vertical plane. When it is at the position shown, which of the The resultant of two forces following diagrams best represents the forces acting on the bob? Neglect air friction. F1 and F2 acting at a point can have a minimum value of 1 N and a maximum value of 7 N. When the two forces act at right angles to each other, the magnitude of their resultant is A. 3N B. 5N C. 6N D. E. 22. 50 N 8N (93-I-3) A box moves at a uniform velocity of 2 ms-1 on a 20. (92-I-11) A ball-bearing is dropped into viscous oil. Which frictionless horizontal surface. Sand falls into the of the following correctly describes its motion box with negligible speed at a rate of 90 kg per before the terminal speed is reached? minute. What horizontal force is required to keep the box moving uniformly at 2 ms-1? Velocity Acceleration A. decreases decreases A. 0N B. decreases increases B. 3N C. increases constant C. 6N D. increases decreases D. 90 N E. increases increases E. 180 N AL-MC-Revision / p.6 23. (94-IIA-1) 24. (94-IIA-2) A man of weight W stands on a compression balance placed inside a lift. The velocity-time graph of the lift is shown below (The upward direction is taken to be positive) : The above figure shows a propeller-motor system connected by a light, rigid rod to a fixed point P on Which of the following graphs best shows the the ceiling. The system remains stationary when variation of the reading on the balance, R, with the motor is on. Which of the following diagrams time, t? correctly represents the forces acting on the propeller-motor system? 25. (94-IIA-4) A softball of mass 0.5 kg flies horizontally with a speed of 20 ms-1 towards a player. After being hit by the bat, it flies away at 30 ms-1 perpendicular to its original direction. Find the magnitude of the impulse acting on the softball. A. 5 kg ms-1 B. 18 kg ms-1 C. 20 kg ms-1 D. 25 kg ms-1 E. 36 kg ms-1 AL-MC-Revision / p.7 26. (94-IIA-6) 28. (95-IIA-1) Three bombs are released from a bomber flying When given a slight push, a toy car moves freely horizontally with constant velocity to the right. with constant velocity down a plane inclined at They are released from rest (relative to the bomber) 20 o to the horizontal. If the mass of the car is one by one at one-second intervals. Neglecting air 0.5 kg, find the force parallel to the inclined plane resistance, which of the following diagrams for pulling the car up the plane with constant correctly shows the positions of the bomber and velocity. the three bombs at a certain instant? 29. A. 1.7 N B. 3.4 N C. 4.7 N D. 6.7 N E. 9.4 N (95-IIA-2) Two small spheres A and B of masses 1 kg and 2 kg respectively are released from rest at heights 4h and h above the ground as shown. Which of the following statements is/are correct? (Assume air resistance is negligible) 27. (94-IIA-7) When an object falls freely, its total energy (1) The acceleration of sphere A doubles that of sphere B. A. increases during the fall. (2) The time taken for sphere A to reach the B. decreases during the fall. C. remains constant during the fall. D. is zero at the beginning of the fall. reaching the ground is double that of sphere E. is at a maximum at the end of the ball. B. ground is double that of sphere B. (3) The kinetic energy of sphere A when A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) AL-MC-Revision / p.8 30. (95-IIA-3) 32. (96-IIA-4) An object is thrown vertically upward and experiences an air resistance opposing its motion with magnitude proportional to its speed. Which of the following graphs best represents the variation A trolley travels with constant velocity to the right of the acceleration, a, of the object with time, t, on horizontal ground and collides with a light starting from the moment when the object leaves helical spring attached to a wall fixed to the ground one’s hand up to the time when it returns to the (earth) as shown. At the instant that the trolley ground? (Take downward as positive.) comes momentarily to rest during collision, what has happened to the initial momentum of the trolley? A. It has been transferred to the earth. B. It has been stored in the spring. C. It has been dissipated as sound and heat. D. It has been destroyed by the friction due to the ground. E. It has been lost because the collision was not perfectly elastic. 31. (96-IIA-1) Which of the following pairs of quantities of a moving object must be in the same direction? (1) acceleration and change in momentum (2) displacement and velocity (3) velocity and acceleration A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) AL-MC-Revision / p.9 33. (96-IIA-6) 35. (97-IIA-2) A ball of mass m is projected vertically downwards with speed v from a certain height and rebounds from the ground back to the same height. Which of the following statements is/are correct? (Neglect X, Y and Z are three spheres of the same size but air resistance.) with masses m, m, and 2m respectively, lying on a smooth horizontal track with Y and Z in contact as (1) shown. X is moving to the right with velocity u The collision between the ball and the ground is not perfectly elastic. and makes a head-on collision with Y. If all (2) collisions are perfectly elastic, which of the The loss in energy of the ball in the collision is following gives the possible velocities of the three spheres after all collisions? (3) (Take to the right as positive.) 1 mv 2 . 2 If the ball is projected vertically upwards from the same height with the same speed, it would rebound to a greater height. 34. X Y Z A. 0 0 u/2 A. (1) only B. 0 u/3 u/3 B. (3) only C. -u / 3 0 2u / 3 C. (1) and (2) only D. 0 -u / 3 2u / 3 D. (2) and (3) only E. u/4 u/4 u/4 E. (1), (2) and (3) (97-IIA-1) 36. (97-IIA-6) A nucleus originally at rest splits into two fragments of unequal mass. The fragment with smaller mass has a larger. (1) momentum. Two wooden blocks A and B are connected by a (2) speed string which passes over a smooth, fixed pulley as (3) kinetic energy. shown. The maximum friction between any two surfaces is 2 N. If a horizontal force F is applied to A. (1) only block B, find its minimum value for moving B. B. (3) only C. (1) and (2) only A. 2N D. (2) and (3) only B. 4N E. (1), (2) and (3) C. 6N D. 8N E. 10 N AL-MC-Revision / p.10 37. (98-IIA-1) 39. (98-IIA-3) Two blocks A and B of mass ratio 1 : 2 are placed on a horizontal frictionless surface as shown above. P and Q are horizontal forces acting on A and B Two identical light springs are connected with two respectively ( with P > Q ) so that the blocks move masses of 1.0 kg and 0.5 kg as shown. Which of the to the right with constant acceleration. Find the following statements is/are correct? force acting on B by A. (1) The tension in the upper spring is double that in A. the lower spring. (2) The force acting on the ceiling by the whole B. system is 15N. (3) The tension in the upper spring will remain C. unchanged if the two masses are exchanged in position. D. A. (1) only B. (3) only C. (1) and (2) only E. D. (2) and (3) only E. 38. 40. PQ 3 PQ 3 2( P Q ) 3 2P Q 3 P 2Q 3 (98-IIA-4) (1), (2) and (3) (98-IIA-2) The velocities of the longitudinal and transverse waves produced by an earthquake are 5.0kms 1 1 and 9.0kms respectively. A seismograph records the arrival of the transverse waves 64 s before that of the longitudinal waves. How far away was the earthquake? The initial momentum of an object is 2 Ns in o the direction S 45 E and its final momentum is 1 Ns due east. If this change takes place in 0.5 s, the average force acting on the object during the A. 256 km change is B. 320 km A. 1 N due north C. 576km B. 1 N due south D. 659 km C. 0.5 N due north E. 720 km D. 2 N due south E. 2N due north AL-MC-Revision / p.11 41. (98-IIA-5) Acceleration of A The graph shows the time variation of the net force, F, acting on an object of mass 1 kg. The object is Acceleration of B A. zero F m B. zero zero C. F 2m F m D. F m zero E. F m F m initially at rest and its subsequent motion is along a straight line. Which of the following statements 43. (99-IIA-2) is/are correct? (1) The object is accelerating in the first 5 seconds. (2) The maximum speed of the object is less than 10ms 1 . (3) The final speed of the object is zero. A block of mass 5 kg is placed on the inclined A. (1) only surface of the wedge shown above. All contact B. (3) only surfaces are assumed to be smooth. What is the C. (1) and (2) only magnitude of the horizontal force F exerted on the D. (2) and (3) only wedge so that it remains stationary while the block E. (1), (2) and (3) is sliding down the inclined surface with acceleration ? 42. (99-IIA-1) Two objects A and B of equal mass m are connected by two identical light springs and are placed on a horizontal smooth surface. A horizontal force F is applied to B so that the system is in equilibrium. If the applied force F is suddenly removed, what are the magnitudes of the acceleration of each object at the instant when force F is removed? A. 0N B. 18 N C. 24 N D. 30 N E. 32 N AL-MC-Revision / p.12 44. (99-IIA-3) 46. (00-IIA-1) The above figure shows an open wagon moving Two books A and B are placed on a horizontal table with negligible resistance in vertically falling rain. surface as shown. A horizontal force F is applied to An appreciable amount of rain falls into the wagon A but the system remains stationary. Which of the and accumulates there,. What are the effects of the following statements is/are correct? accumulating rain on the speed, momentum and kinetic energy of the wagon? (Ignore the effects of (1) The frictional force acting on B by the table the rain drops hitting the front of the wagon.) surface is greater than F. (2) The frictional force acting on A by B is towards Speed momentum kinetic energy the left. (3) The system would remain stationary if F is 45. A. decreased unchanged decreased applied to B instead. B. decreased unchanged unchanged C. decreased decreased decreased A. (1) only D. unchanged unchanged unchanged B. (3) only E. unchanged increased increased C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) (99-IIA-5) 47. (00-IIA-2) In which of the following situations is the magnitude of the normal reaction of the supporting surface always equal to the weight of the body? The above graph shows the variation of kinetic energy E with the square of velocity v of a moving (1) mass m. What is the momentum of the mass when it is moving at a speed of 2 ms 1 ? A ball bouncing vertical on a horizontal ground is in contact with the ground. (2) An astronaut in a spacecraft which performs circular motion around the earth. A. 1 Ns (3) A boy standing in a lift which is moving B. 2 Ns C. 4 Ns D. 8 Ns A. (1) only E. 16 Ns B. (3) only vertically upward with a uniform velocity. C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) AL-MC-Revision / p.13 48. (00-IIA-4) 51. (00-IIA-7) A student holds one end of a string to which a block of mass 8 kg is tied at the other end. He raises the block with an acceleration by pulling the string in an upward direction. If the maximum tension that the string can withstand is 120 N, find the maximum acceleration of the block before the string breaks. A. 5.0 ms-2 B. -2 C. D. E. 7.5 ms A light spring is fixed to the bottom of a vertical tube. A ball is released from rest at a height h 10.0 ms -2 above the upper end of the spring as shown. After 12.5 ms -2 rebounding several times the ball eventually comes 15.0 ms -2 to rest and stays on top of the spring. Assume all contact surfaces are smooth and the spring obeys 49. (00-IIA-5) Hooke’s law throughout. Which of the following A trolley of mass 0.5 kg moves with a certain statements is/are correct? acceleration down a runway which is inclined to the horizontal at 15o. If the angle of inclination is (1) o increased to 20 , the acceleration of the trolley would be doubled. Find the average frictional force, proportional to the mass of the ball. (2) assuming the same in both cases, acting on the trolley. The compression of the spring is The compression of the spring is independent of the height h. (3) The gravitational potential energy lost by the ball is equal to the strain energy stored in the 50. A. 0.72 N B. 0.80 N C. 0.88 N A. (1) only D. 0.96 N B. (3) only E. 1.04 N C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) (00-IIA-6) Two objects A and B of masses m and 2m respectively are initially at rest on a smooth, horizontal surface. If each of them is acted upon by the same force for the same period of time, the ratio of the gain in kinetic energy of A to that of B is A. 2:1 B. 1:2 C. 1:1 D. 1:4 E. 4:1 spring. AL-MC-Revision / p.14 52. (01-IIA-1) 54. (01-IIA-8) A block rests on a rough inclined plane. Which of the following diagrams correctly shows the lines of application of all the forces acting on the block? (The dot represents the center of mass of the block.) The figure shows a swinging simple pendulum, starting from a point higher than P. Which of the following forces is/are acting on the pendulum bob when it is at P? (Neglect air resistance) (1) the weight of the bob (2) a force exerted by the string pointing towards O (3) a third force along the direction of motion of the bob 53. (01-IIA-5) An object accelerates uniformly along a straight A. (1) only B. (3) only C. (1) and (2 only D. (2) and (3) only E. (1) , (2) and (3) 55. (02-IIA-1) line from X to Z. It passes X and Z with speed u and Two identical blocks X and Y v respectively. What is its speed when it passes Y, are connected by a light spring which is the mid-point of XZ? and the system is suspended from a fixed support by a light A. u2 v2 2 B. uv cord as shown. The system is in static equilibrium. If the cord is suddenly cut, what is the magnitude of the acceleration of each block at that instant? C. 2uv uv Acceleration of X Acceleration of Y A. g g D. uv 2 B. g 2g C. zero g E. It cannot be found as the distance D. zero 2g between X and Z is not known. 56. (02-IIA-2) AL-MC-Revision / p.15 Two small identical objects P and Q are released from rest from the top of a building 80 m above the ground. Q is released 1 s after P. Neglecting air resistance, what is the maximum vertical separation between P and Q in the air? A. 5m B. 10 m C. 35 m D. 45 m A block of mass m falls from rest at A onto a vertical light spring of force constant k firmly 57. (02-IIA-3) fixed to the ground. When the block reaches The SI unit of length, metre, is defined as n times B, it starts to compress the spring until it the wavelength of a certain orange-red light reaches the lowest position C as shown. emitted from a krypton-86 atom. The number n is Neglecting air resistance and considering the of the order motion of the block from A to C, which of the following statements is/are correct? A. 104 B. 106 C. 10 8 10 10 D. (1) kinetic energy of the block is at a maximum when it is at B (2) The resultant force acting on the block is zero when it sis at C (3) The maximum compression of the mg spring is greater that k 58. (02-IIA-4) 59. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only (02-IIA-5) AL-MC-Revision / p.16 61. (02-IIA-7) The impulse experienced by an object is equal to its change in A bob of mass m is suspended from a fixed A. momentum B. kinetic energy C. velocity D. acceleration support by a light string. A force F is applied to the bob (F is not shown in the figure) so that the 62. (03-IIA-1) string makes an angle with the vertical. What is the minimum value of F required to keep the bob in static equilibrium as shown? A. mgsin B. C. D. 60. mgsin2 A uniform flexible chain of mass m is hung between two fixed supports X and Y at the same horizontal level as shown. The chain makes an angle with the horizontal at each support. Find the tension in the chain at its lowest point. (02-IIA-6) A. B. P, Q and R are three identical spheres moving with the same speed along a smooth horizontal track. C. They undergo head-on elastic collisions with spheres X, Y and Z respectively which are initially at rest. After collision, P continues to move in its original direction, Q becomes stationary while R reverses its motion. After collision, which sphere (X, Y and Z) has the greatest magnitude of (1) momentum (2) kinetic energy (1) (2) A. Y Z B. Y Y C. Z X D. Z Y D. mg 2 mg 2 sin mg 2 cos mg 2 tan AL-MC-Revision / p.17 63. (03-IIA-2) Two wedge shaped blocks, each of mass m, are placed on a smooth horizontal surface as shown. A horizontal force F is applied to one of the blocks so that the two blocks move together to the left with constant acceleration. What is the maximum value of F so that the blocks are moving without relative slipping? (Assume all contact surface are smooth.) A. 2 mg B. 3mg C. 2mg D. 65. (03-IIA-4) The two arms of a beam balance are of slightly different lengths. An unknown mass is weighted first on the left pan and then on the right pan. The two measurements are m1 and m2 respectively. The actual mass is A. B. m1 m 2 2 m1 m 2 2 C. D. 2 2 m1 m 2 66. (03-IIA-5) mg 64. (03-IIA-3) The figure shows part of the stroboscopic picture of a particle initially projected horizontally into the air. The side of each square of the grid is 5cm long. Estimate the frequency of the strobe lamp used. (Neglect air resistance.) A light spring is fixed to a block Q which rests on a horizontal surface as shown. Block P is moving with constant velocity towards Q and makes a head-on elastic collision with Q. After the collision, P reverses its direction of motion, while Q moves to the right. All contact surfaces are smooth. When will the spring be under a state of maximum compression? A. B. C. A. B. C. D. (m 1 m 2 ) 2 5.8 Hz 7.1 Hz 10.0 Hz 12.5 Hz D. When the two blocks move with the same velocity. When block P is momentarily at rest. When block P starts to reserves its direction of motion. When block Q starts to move to the right. AL-MC-Revision / p.18 67. (03-IIA-6) A bullet is shot through a wooden block along the horizontal direction XY. Which of the following graphs shows the variation of the horizontal speed v of the bullet with distance d along XY? (Neglect air resistance.) A. B. C. D.