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HKAL Exercise : Part 1 Mechanics Chapter 2 Newton’s Laws of Motion 2.1 Newton’s Laws and Momentum Centre of mass 1. O O O The above diagram shows a uniform hollow metal cube with a small opening on top. O is the position of the centre of mass of the hollow cube. What will happen to the position of the centre of mass of the system as the cube is being slowly filled with oil from the opening ? A. B. C. D. It will rise gradually and its final position will be above O. It will rise gradually at first and then fall to its original position. It will fall gradually at first and then rise to its original position. It will remain unchanged throughout the process. Momentum 2. Two objects of masses 9 m and m move towards each other along a straight line with kinetic energies E and 9 E respectively. The total linear momentum of both masses taken together is A. 0. B. C. D. 3 2mE . 6 2mE . 9 2mE . 3. m v v m A gas atom of mass m moving with a uniform speed v makes an elastic collision with the wall of the container as shown in the diagram. What is the magnitude of the change in the momentum of the gas atom ? A. 2mv B. mv sinθ C. 2mv sinθ D. 2mv cosθ Equilibrium 4. A smooth block of mass 6 kg slides down a wedge. The wedge, of mass 20 kg, is placed on a horizontal table, and its inclined plane makes an angle of 30∘with the horizontal. If the wedge remains stationary all the time, the normal reaction of the table acting on the wedge is A. 45 N. B. 200 N. C. 245 N. D. 290 N. HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 1/14 5. acceleration A. 31 N. A bob of mass m is suspended from a fixed support by a light string. A force F is applied to the bob (F is not shown in the figure) so that the string makes an angle θ with the vertical. What is the minimum value of F required to keep the bob in static equilibrium as shown ? A. mgsinθcosθ B. C. D. mgcosθ mgsinθ mgsin2θ 46 N. 56 N. 69 N. 7. P rod motor propeller The above figure shows a propeller-motor system connected by a light, rigid rod to a fixed point P on the ceiling. The system remains stationary when the motor is on. Which of the following diagrams correctly represents the force acting on the propeller-motor system ? A. B. 6. F 20 cm B. C. D. horizontal surface A block of mass 10 kg is placed on the inclined surface of the wedge shown above. All contact surfaces are assumed to be smooth. What is the magnitude of the horizontal force F exerted on the wedge so that it remains stationary while the block is sliding down the inclined surface with C. D. Addition of forces 8. F1 F2 The resultant of two forces F1 and F2 acting at a point can have a minimum value of 1 N and a maximum value of 9 N. When the two forces act at right angles to each other, the magnitude of their resultant is A. C. 4N 8N B. D. 41 N 90 N HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 2/14 Newton’s Second Law of Motion 9. Which of the following pairs of quantities of a moving object must be in the same direction ? (1) displacement and velocity (2) momentum and velocity (3) force and change in momentum A. (1) only B. (3) only C. (2) and (3) only D. (1), (2) and (3) 12. F proportional to t . proportional to 1/ t . C Three blocks A, B and C of masses m, 4m and 4m respectively are placed on a smooth horizontal 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/9 B. 4F/9 C. 5F/9 D. F/5 10. A solid of mass starts from rest and travels for a given time t under the action of a given force. The speed which it acquires is A. proportional to t. B. proportional to 1/t. C. D. A B 13. 11. axle P A B Q Two blocks A and B of mass ratio 2 : 5 are placed on a horizontal frictionless surface as shown above. P and Q are horizontal forces acting on A and B respectively (with P > Q) so that the blocks move to the right with constant acceleration. Find the force acting on B by A. A. 5P 2Q 7 B. 2 P 5Q 7 C. PQ 7 D. PQ 7 HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 3 kg 5 kg An object of mass 5 kg is tied to another object of mass 3 kg with a string passing over a fixed smooth pulley. The weight of the pulley is negligible. When the objects move under the action of gravity, the vertical upward force acting on the axle of the pulley is A. zero. B. 20 N. C. 80 N. D. 84 N. 3/14 14. 17. A force F is applied to an initially stationary particle from time t = 0. F 7 kg 30O 2 kg An object of mass 2 kg is placed on a smooth plane inclined at 30 ∘ to the horizontal. It is connected by a light string passing over a frictionless pulley to another object of mass 7 kg, as shown above. Given that g = 10 m/s2, when the system is released, the tension in the string will be varies sinusoidally with time t as shown in the following graph : F 0 Which of the following graphs best represents the variation of the subsequent velocity v of the particle with t ? A. 23 N. B. 28 N. C. 31 N. D. 70 N. 15. A spacecraft of mass 5.0 × 104 kg was A. travelling on its way to the moon with the rocket motors shut down. At the instant when it was travelling at 1700 m/s, the rocket motors were turned on for 6 seconds to make a course correction. If the rocket gave a thrust of 3.0 × 105 N at 0 right angles to the direction of travel, through what angle would the flight path of the spacecraft be turned ? A. 2.1 × 10-3 rad B. 3.5 × 10-3 rad C. 2.1 × 10-2 rad D. 3.5 × 10-2 rad 16. A student holds one end of a string to which a block of mass 4 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 100 N, find the maximum acceleration of the block before the string breaks. A. 12.5 m s-2 B. 15.0 m s-2 C. 20.0 m s-2 D. 25.0 m s-2 HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion t v t B. v 0 t C. v 0 t D. v 0 t 4/14 18. Before the start of a race, the momentum of each competitor is less than his momentum during the race. Which of the following statements is/are correct ? (1) A force acts on each competitor to increase his momentum as he starts to race. (2) The law of conservation of momentum applies only to collisions between two objects. (3) This situation obeys Newton’s law of conservation of momentum. A. (1) only B. (2) only C. (1) and (3) only D. (1), (2) and (3) Feeling of One’s Weight 19. A lift of mass M carries a man of mass m. (5)moving downwards and decelerating at g/10. When the lift is being hauled upward by a A. (1) only rope, the lift rises with an acceleration a. The tension of the rope is A. m (g - a). B. (m + M) (g + a). C. m (g + a) - Ma. D. m (g + a) + Ma. 20. A man weights an object with a spring balance in a lift. Before the lift moves the scale reads 30 N. The lift goes up and then stops. The reading on the scale is A. B. C. D. more than 30 N when the lift starts, and remains steady until it comes to rest. less than 30 N when the lift starts, and remains steady until it comes to rest. more than 30 N as the lift starts, and less than 30 N as it comes to rest. less than 30 N as the lift starts, and more than 30 N as it comes to rest. 21. A man in a lift measures his weight with a compression balance and discovers that his weight is increased by 10%. The lift is probably (1)moving downwards with uniform velocity. (2)moving upwards and accelerating at g/10. (3)moving upwards and decelerating at g/10. (4)moving downwards and accelerating at g/10. B. C. D. 22. 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) : velocity 0 t1 time t2 Which of the following graphs best shows the variation of the reading on the balance, R, with time, t ? A. B. R R W 0 W t 1 t2 t C. 0 t1 t2 t D. R R W 0 HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion (1) and (3) only (1) and (4) only (2) and (5) only W t1 t2 t 0 t 1 t2 t 5/14 2.2 Momentum and Impulse Impulse 23. Steel ball bearings, each of mass m, are fired at the rate of n ball bearings per second towards a fixed vertical steel block with a horizontal speed v. Their horizontal speed become zero after colliding with the wall. The average force exerted on the block is A. zero. B. C. D. 26. A softball of mass 0.5 kg flies horizontally with a speed of 0 m s-1 towards a player. After being hit by the bat, it flies away at 50 m s-1 perpendicular to its original direction. Find the magnitude of the impulse acting on the softball. A. 10 kg m s-1 B. 29 kg m s-1 mnv. 2mnv. 2mgnv. C. D. 40 kg m s-1 58 kg m s-1 27. 24. The work done on a thermally isolated object is equal to its change in A. velocity. B. momentum. C. kinetic energy. D. mechanical energy. 25. final momentum North 60O initial momentum The initial momentum of an object is 3 N s due west and its final momentum is 2 N s in the direction N 60∘W. If this change takes place in 2 s, the average force acting on the object during the change is A. 0.5 N due north. B. 0.5 N due south. C. 1 N due south. D. 1 N due north. HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion F/N 4 0 5 t/s The graph shows the time variation of the net force, F, acting on an object of mass 1 kg. The object is initially at rest and its subsequent motion is along a straight line. Which of the following statements is/are correct ? (1) The object is accelerating in the first 5 seconds. (2) The final speed of the object is zero. (3) The maximum speed of the object is less than 10 m s-1. A. B. C. D. (1) only (3) only (1) and (2) only (1), (2) and (3) 6/14 Principle of Conservation of Momentum 28. A box moves at a uniform velocity of 8 m/s on a frictionless horizontal surface. Sand falls into the box with negligible speed at a rate of 45 kg per minute. What horizontal force is required to keep the box moving uniformly at 8 m/s ? A. 0 N B. 6 N C. 45 N D. 360 N 30. A nucleus originally at rest splits into two fragments of unequal mass. The two fragments have the same (1) kinetic energy. (2) speed. (3) momentum. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only 29. 31. A spaceship burns fuel and moves with constant acceleration in a straight line. Which of the graphs below best represents the variation of its upthrust F with time t? A. B The above figure shows an open wagon moving with negligible resistance in vertically falling rain. An appreciable amount of rain falls into the wagon and accumulates there. What are the effects of A. B. C. D. the accumulating rain on the speed, momentum and kinetic energy of the wagon ? (Ignore the effects of the rain drops hitting the front of the wagon.) kinetic speed momentum energy unchanged unchanged unchanged unchanged increased increased decreased unchanged decreased decreased unchanged unchanged F 0 F t C t D F 0 0 F t 0 t Three types of collision 32. A sphere X of mass m, travelling with speed u, makes a head-on collision with a similar sphere Y which is at rest. After the collision the velocities of X and Y are v1 and v2 respectively. Which one of the following is a possible pair of values for v1 and v2? v1 v2 v1 v2 A. C. u/ 2 2u/3 u/ 2 u/3 B. D. u/2 u/3 HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 3 u/2 2u/3 7/14 33. P X Q Y R Z P, Q and R are three identical spheres moving with the same speed along a smooth horizontal track. 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 or Z) has the greatest magnitude of (1) kinetic energy (2) momentum ? (1) (2) A. X Z B. Y Z C. Z X D. Z Y Elastic Collision 34. In a partially elastic collision between two bodies, and in the absence of external forces, A. kinetic energy and momentum are both conserved. B. kinetic energy is conserved but C. D. momentum is not conserved. kinetic energy is not conserved but momentum is conserved. neither kinetic energy nor momentum is conserved. A. B. C. D. (1) only (1) and (2) only (2) and (3) only (1), (2) and (3) 36. X m u Y m Z 5m C 35. A sphere X moving with velocity u on a smooth horizontal plane makes a head-on collision with another sphere Y of the same mass which is initially at rest. If the X, Y and Z are three spheres of the same size but with masses m, m and 5m respectively, lying on a smooth horizontal track with Y and Z in contact as shown. X is moving to the right with velocity u and makes a head-on collision with Y. If all collisions are perfectly elastic, which of collision is inelastic, which of following statements is/are correct ? (1) Linear momentum is conserved in collision. (2) X and Y stick together and move off the same velocity after the collision. (3) Kinetic energy is conserved in collision. the following gives the possible velocities of the three spheres after all collisions ? (Take to the right as positive.) X Y Z A. -2u/3 0 u/3 B. 0 u/6 u/6 C. 0 -2u/3 u/3 D. u/7 u/7 u/7 the this with this HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 8/14 Collisions in 2-dimension 37. An alpha particle colludes with a stationary helium nucleus ( 24 He ) in a cloud chamber. Which of the following diagrams represents the most probable set of tracks? A. B. 4 2He C. 4 2He D. 4 2He 4 2He 2.3 Friction Static Friction 38. 39. A B F Two wooden blocks A and B are connected by a string which passes over a smooth, fixed pulley as shown. The maximum friction between any two surfaces is 5 N. If a horizontal force F is applied to block B, find its minimum value for moving B. A. 5 N B. C. D. 15 N 20 N 25 N HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion F A B Two blocks A and B are placed on a horizontal table surface as shown. A horizontal force F is applied to A but the system remains stationary. Which of the following statements is/are correct ? (1) The frictional force acting on B by the table surface is equal to F. (2) The system would remain stationary if F is applied to B instead. (3) The frictional force acting on B by A is towards the left. A. (1) only B. (3) only C. (1) and (2) only D. (1), (2) and (3) 9/14 40. 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 centre of mass of the block.) A. B. C. D. Kinetic Friction 41. 43. B P M A horizontal force P is applied to a wooden block at rest on a rough horizontal table. P is increased uniformly from zero. Which of the following graphs best describes the variation of the frictional force acting on the block with P? A. B. F 0 F P 0 C. D. F F 0 P 0 P P 15 m A 40O 40O C A small block M of mass 1 kg is transported across a small hill along the road ABC by an applied force F which is always parallel to the road. The speed of M is kept constant throughout the journal and the kinetic friction between the block and the road is 1.40 N. The total work done by F in transporting M from A to C is A. zero. B. 65 J. C. 300 J. D. 365 J. 44. When given a slight push, a toy car moves freely with constant velocity down a plane inclined at 30∘to the horizontal. If the mass of the car is 2 kg, find the force 42. An object of mass m slides with constant acceleration a down a plane making an angle θ with the horizontal. The frictional force acting on the object is A. mg - ma sinθ B. mg sinθ- ma C. (mg – ma) sinθ D. (ma - mg)sinθ HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion parallel to the inclined plane for pulling the car up the plane with constant velocity. A. 10 N B. 20 N C. 25 N D. 30 N 10/14 45. A trolley of mass 2.0 kg moves with a certain acceleration down a runway which is inclined to the horizontal at 25∘. If the angle of inclination is increased to 30∘, the acceleration of the trolley would be doubled. Find the average frictional force, assuming the same in both cases, acting on the trolley. A. 6.21 N B. 6.90 N C. 7.59 N D. 8.28 N Pulley 46. A builder using a pulley system to lift a bucket of cement of weight 200 N exerts a steady force F and pulls 40 m of rope through the system in order to raise the bucket 15 m. The friction in the system is small but NOT negligible. The value of the force F is most probably A. B. C. D. exactly equal to 75 N. between 75 N and 150 N. between 200 N and 533 N. more than 533 N. 2.4 Spring and Force Constant 47. 48. B A P Y Q Two bodies P and Q are connected by a light string A. The weights of P and Q are 4 N and 12 N respectively. P is connected to the roof by another light string B. If string B is cut and the bodies allowed to fall, the net force acting on Q during free fall is A. B. C. D. 4 N. 8 N. 12 N. 16 N. HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion X Two identical blocks X and Y are connected by a light spring and the system is suspended from a fixed support by a light 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 ? Acceleration Acceleration of X of Y A. zero g B. zero 2g C. g g D. g 2g 11/14 49. 51 spring A 2N A spring B 6N B Two objects of weights 2 N and 6 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/cm. What are the extensions of springs A and B ? A. B. C. D. Extension of spring A 2 cm 8 cm 2 cm 8 cm Extension of spring B 4 cm 4 cm 6 cm 6 cm 50 The figure shows two blocks A and B, of masses m and 4 m respectively, connected by two light springs to a fixed support. Each spring has a force constant k. What is the total extension of the system when it is at static equilibrium ? A. mg/k B. 5mg/(4k) C. 5mg/k D. 9mg/k D 52. h 2.0 kg 1.0 kg Two identical light springs are connected with two masses of 2.0 kg and 1.0 kg as shown. Which of the following statements is/are correct ? (1) The tension in the upper spring is triple that in the lower spring. (2) The force acting on the ceiling by the A light spring is fixed to the bottom of a vertical tube. A ball is released from rest at a height h above the upper end of the spring as shown. After rebounding several times the ball eventually comes to rest and stays on top of the spring. Assume all contact surfaces are smooth and the spring whole system is 10 N. (3) The tension in the upper spring will remain unchanged if the two masses are exchanged in position. A. (1) only B. (1) and (3) only C. (2) and (3) only D. (1), (2) and (3) obeys Hooke’s law throughout. Which of the following statements is/are correct ? (1) The compression of the spring is independent of the height h. (2) The gravitational potential energy lost by the ball is equal to the strain energy stored in the spring. (3) The compression of the spring is HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 12/14 independent of the mass of the ball. A. (1) only B. C. D. 54. (1) and (2) only (2) and (3) only (1), (2) and (3) A trolley travels with constant velocity to the right on horizontal ground and collides with a light helical spring attached to a wall fixed to the ground (earth) as shown. At the instant that the trolley comes momentarily to rest during collision, what has happened to the initial momentum of 53. A B C the trolley ? A. It has been dissipated as sound and heat. B. It has been destroyed by the friction due to the ground. C. It has been lost because the collision was not perfectly elastic. D. It has been transferred to the earth. A block of mass m falls from rest at A onto a vertical light spring of force constant k firmly fixed to the ground. When the block reaches B, it starts to compress the spring until it reaches the lowest position C as shown. Neglecting air resistance and considering the motion of the block from A to C, which of the following statements is/are correct ? (1) The resultant force acting on the block is pointing upward when it is at C. (2) The maximum compression of the mg spring is greater than . k (3) The kinetic energy of the block is at a maximum when it is at B. A. (1) only B. C. D. (3) only (1) and (2) only (2) and (3) only HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 55 P S X Y 30O 30O In the figure above, X and Y are blocks of mass 1 kg and 4 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 ? A. 15 N B. 20 N C. 35 N D. 40 N 13/14 56 A B F 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 ? Acceleration of A Acceleration of B A. zero zero B. zero F m C. F m zero D. F m F m 2.5 Work and Energy Work 57. 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 distance, the ratio of the gain in kinetic energy of A to that of B is A. 1 : 1. B. 1 : 2. C. 1 : 4. D. 2 : 1. Kinetic energy 58. E/J 1 0 1 v/ms The above graph shows the variation of kinetic energy E with the velocity v of a moving mass m. What is the momentum of the mass when it is moving at a speed of 2 m s-1 ? A. 1 N s B. 2 N s C. D. 4Ns 8Ns KEY : 1 – 10 : CACCC, BABCA, 11 – 20 : ABCAC, BBCBC, 21 – 30 : DBBDA, BABCB, 31 – 40 : ADBCB, ABBCA, 41 – 50 : BBBAB, BCBDB, 51 – 56 : DACDB, BAC. HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion 14/14