(A) (B) (C) (D) None of these

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1 Exercise OBJECTIVE PROBLEMS. Action and reaction (A) act on two different objects (C) have opposite directions. Which fiure represents the correct F.B.D. of rod of mass m as shown in fiure : (B) have equal manitude (D) have resultant zero. (A) (B) (C) (D) None of these 3. n which of the followin cases the net force is not zero? (A) A kite skillfully held stationary in the sky (B) A ball freely fallin from a heiht (C) An aeroplane risin upwards at an anle of 45º with the horizontal with a constant speed (D) A cork floatin on the surface of water 4. Two blocks are in contact on a frictionless table. One has mass m and the other m. A force F is applied on m as shown in the fiure. Now the same force F is applied from the riht on m. In the two cases respectively, the ratio force of contact between the two blocks will be : (A) same (B) : (C) : (D) : 3 5. A constant force F is applied in horizontal direction as shown. Contact force between M and m is N and between m and M is N then (A) N or N equal (B) N > N (C) N > N (D) cannot be determined 6. A mass M is suspended by a rope from a riid support at A as shown in fiure. Another rope is tied at the end B, and it is pulled horizontally with a force F. If the rope AB makes an anle with the vertical, then the tension in the strin AB is : (A) F sin (B) F/sin (C) F cos (D) F/cos 7. Two persons are holdin a rope of neliible weiht tihtly at its ends so that it is horizontal. A 5 k weiht is attached to the rope at the mid point which now no loner remains horizontal. The minimum tension required to completely straihten the rope is : 5 (A) 5 k (B) k (C) 5 k (D) nfinitely lare 8. Two masses M and M are attached to the ends of a strin which passes over a pulley attached to the top of a double inclined plane of anles of inclination and. f M > M, the acceleration a of the system is iven by : (A) M sin M M (B) M sin M M M (C) sin M M M sin (D) zero

2 9. Three masses of k, 6 k and 3 k are connected to each other with threads and are placed on table as shown in fiure, What is the acceleration with which the system is movin? Take 0m s. (A) Zero (B) m s (C) m s (D) 3 m s 0. A body of mass 8 k is hanin from another body of mass k. The combination is bein pulled by a strin with an acceleration of. m s. The tension T and T will be respectively : (use 9.8m/s ) (A) 00 N, 80 N (C) 40 N, 96 N (B) 0 N, 90 N (D) 60 N, 96 N k 8k T T a. A fireman wants to slide down a rope. The rope can bear a tension of With what minimum acceleration should the fireman slide down : (A) 3 (B) 6 (C) 4 3 the of the weiht of the man. 4 (D). A particle of small mass m is joined to a very heavy body by a liht strin passin over a liht pulley. Both bodies are free to move. The total downward force on the pulley is (A) m (B) m (C) 4 m (D) >> m 3. Two blocks of masses M and M are connected to each other throuh a liht sprin as shown in fiure. If we push mass M with force F and cause acceleration a in mass M, what will be the acceleration in M? (A) F/M (B) F/(M + M ) (C) a (D) (F M a )/M 4. Two masses of 0 k and 0 k respectively are connected by a massless sprin as shown in fiure. A force of 00 N acts on the 0 k mass at the instant when the 0 k mass has an acceleration of ms, the acceleration of the 0 k mass is : (A) ms (B) 4ms (C) 0ms (D) 0ms 5. In the arranement shown in the Fiure all surfaces are frictionless, the masses of the block are m 0 k and m 30 k. The accelerations of masses m and m will be if F 80 N. (A) a m / s, a m 0 (B) a m / s, m 9 m/s m 9 m 9 (C) am 0, am 9m / s (D) None of these a m m ////////////////////////////////////////////////// 6. Fiure shows a wede of mass k restin on a frictionless floor. A block of mass k is kept on the wede and the wede is iven an acceleration of 5 m/sec towards riht. Then : (A) block will remain stationary w.r.t. wede (B) the block will have an acceleration of m/sec w.r.t. the wede (C) normal reaction on the block is N (D) net force actin on the wede is N 7. A trolley of mass 8 k is standin on a frictionless surface inside which an object of mass k is suspended. A constant force F starts actin on the trolley as a result of which the strin stood at an anle of 37 0 from the vertical. Then : (A) acceleration of the trolley is 40/3 m/sec. (B) force applied in 60 N (C) force applied is 75 N (D) tension in the strin is 5 N F

3 8. A trianular block of mass M rests on a smooth surface as shown in fiure. A cubical block of mass m rests on the inclined surface. If all surfaces are frictionless, the force that must be applied to M so as to keep m stationary relative to M is : (A) M tan 30 (B) m tan 30 (C) (M+m) tan 30 (D) (M+m) cos A trolley is acceleratin down an incline of anle with acceleration sin. Which of the followin is correct. ( is the anle made by the strin with vertical). (A) (B) 0 0 (C) Tension in the strin, T m (D) Tension in the strin, T m sec 0. A flexible chain of weiht W hans between two fixed points A and B at the same level. The inclination of the chain with the horizontal at the two points of support is. What is the tension of the chain at the endpoint. (A) W W cosec (B) sec W (C) W cos (D) sin 3. Two masses m and M are attached with strins as shown. For the system to be in equilibrium we have (A) tan + (C) tan + M m M m (B) tan + (D) tan +. Objects A and B each of mass m are connected by liht inextensible cord. They are constrained to move on a frictionless rin in a vertical plane as shown in fiure. The objects are released from rest at the positions shown. The tension in the cord just after release will be (A) m (B) (C) m (D) m m 4 3. A 50 k person stands on a 5 k platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the fi. The platform moves upwards at a steady rate if the force with which the person pulls the rope is m M m M (A) 500 N (C) 5 N (B) 50 N (D) 50 N 4. A balloon of ross weiht w newton is fallin vertically downward with a constant acceleration a(<). The manitude of the air resistance is : (a) w (B) w a (C) a w (D) a w

4 5. Three blocks A, B and C are suspended as shown in the fiure. Mass of each blocks A and C is m. If system is in equilibrium and mass of B is M, then : (A) M m (C) M > m (B) M < m (D) M m 6. In the system shown in the fiure m > m. System is held at rest by thread BC. Just after the thread BC is burnt : (A) acceleration of m will be upwards (B) m manitude of acceleration of both blocks will be equal to m m m (C) acceleration of m will be equal to zero (D) manitude of acceleration of two blocks will be nonzero and unequal. 7. In the fiure, the blocks A, B and C of mass m each have acceleration a, a and a 3 respectively. F and F are external forces of manitudes m and m respectively. (A) a a a 3 (B) a > a > a 3 (C) a a, a > a 3 (D) a > a, a a 3 8. A strin is wrapped round a lo of wood and it is pulled with a force F as shown in the fiure. (A) (B) tension T in the strin increases with increase in tension T in the strin decreases with increase in (C) tension T > F if > /3 (D) tension T > F if > /4 9. In the fiure the readin of the sprin balance will be : [ 0 m/s ] (A) 6 k f (C) 60 N (B) 5 k f (D) 60 k f 30. Block B moves to the riht with a constant velocity v 0. The velocity of body A relative to B is : (A) (C) v 0, towards left (B) 3v 0, towards left (D) v 0, towards riht 3v 0, towards riht 3. In the arranement shown in fiure, pulleys are massless and frictionless and threads are inextensible. Block of mass m will remain at rest if : (A) m + m3 m (B) 4 m + m3 m (C) m m + m 3 (D) 3 m + m m 3

5 3. Two blocks of masses 0 k and 0 k are connected by a liht sprin as shown. A force of 00 N acts on the 0 k mass as shown. At a certain instant the acceleration of 0 k mass is ms. (A) At that instant the 0 k mass has an acceleration of ms. (B) At that instant the 0 k mass has an acceleration of 4 ms. (C) The stretchin force in the sprin is 0 N. (D) The collective system moves with a common acceleration of 30 ms when the extension in the connectin sprin is the maximum. 33. A block tied between two sprins is in equilibrium. If upper sprin is cut then the acceleration of the block just after cut is 6 m/s downwards. Now, if instead of upper sprin, lower sprin is bein cut then the manitude of acceleration of the block just after the cut will be : (Take 0 m/s ) (A) 6 m/s (B) 4 m/s (C) cannot be determined (D) none of these 34. Readin shown in two sprin balances S and S is 90 k and 30 k respectively and lift is acceleratin upwards with acceleration 0 m/s. The mass is stationary with respect to lift. Then the mass of the block will be : (A) 60 k (B) 30 k (C) 0 k (D) Noneof these 35. Five persons A, B, C, D & E are pullin a cart of mass 00 k on a smooth surface and cart is movin with acceleration 3 m/s in east direction. When person 'A' stops pullin, it moves with acceleration m/s in the west direction. When person 'B' stops pullin, it moves with acceleration 4 m/s in the north direction. The manitude of acceleration of the cart when only A & B pull the cart keepin their directions same as the old directions, is : (A) 6 m/s (B) 3 7 m/s (C) 5 m/s (D) 30 m/s SUBJECTIVE PROBLEMS 36. Which type of forces does a neutron exert on a proton? 37. Which type of forces does a proton exerts on a proton? 38. Two forces of same manitude act on an isolated body in opposite directions to keep it at equilibrium position, is this true accordin to Newton s third law? 39. Accordin to Newton s third law each team pulls the opposite team with equal force in a tu of war. Why then one team wins and the other loses? 40. A body of mass m is placed on a table. The earth is pullin the body with a force m. Takin this force to be the action, what is the reaction? 4. When you hold a pen and write on your notebook, what kind of force is exerted by you on the pen? By the pen on the notebook? 4. Is it true that the reaction of a ravitational force is always ravitational, of an electromanetic force is always electromanetic and so on? 43. Imaine that you are holdin a book weihin 4 N at rest on the palm of your hand. a) A downward force of manitude 4 N is exerted on the book by. b) An upward force of manitude is exerted on the book by the hand. c) Is the upward force (b) the reaction to the downward force (a)? d) The reaction to force (a) is a force of manitude, exerted on by. Its direction is.

6 e) The reaction to force (b) is a force of manitude, exerted on by. Its direction is. f) That the forces (a) and (b) are equal and opposite is an example of Newton s law. ) That forces (b) and (e) are equal and opposite is an example of Newton s law. Suppose now that you exert an upward force of manitude 5 N on the book. h) Does the book remain in equilibrium? i) Is the force exerted on the book by the hand equal and opposite to the force exerted on the book by the earth? j) Is the force exerted on the book by the earth equal and opposite to the force exerted on the earth by the book? k) Is the force exerted on the book by the hand equal and opposite to the force exerted on the hand by the book? Finally, suppose that you snatch your hand away while the book is movin upward. l) How many forces then act on the book? m) Is the book in equilibrium? 44. Two blocks of masses m and m are placed on round as shown in fiure. Two forces of manitude F act on m and m in opposite directions. (i) Draw F.B.D. of masses m and m. (ii) Calculate the contact force between m and m. (iii) What will be the value of action-reaction pair between m and m. (iv) Calculate force exerted by surface on mass m and m 45. A cylinder of weiht w is restin on a V-roove as shown in fiure. (a) Draw its free body diaram. (b) Calculate normal reactions between the cylinder and two inclined walls /////////////////////////// m Smooth 46. The 50 k homoeneous smooth sphere rests on the 30º incline A and bears aainst the smooth vertical wall B. Calculate the contact forces at A and B. 47. A strin is connected between surface and a block of mass k which is pulled by another strin by applyin force F 0 N as shown in fiure. ( 0 m/s ) (i) Calculate tension is strin (). (ii) Calculate tension in strin (). 48. A block of mass k is suspended by a strin of mass k, lenth m as shown in fiure. ( 0 m/s ) Calculate: (a) (b) (c) the tension in strin at its lowest point. the tension in strin at its mid point. force exerted by support on strin.

7 49. In the fiure the tension in the diaonal strin is 60 N. (a) Find the manitude of the horizontal force F and F that must be applied to hold the system in the position shown. (b) What is the weiht of the suspended block? 50. The elevator shown in fiure is descendin with an acceleration of m/s.the mass of the block A is 0.5 k. What force is exerted by the block A on the block B? Solve the problem takin (a) round as the frame (b) lift as the frame. 5. A constant force F m / is applied on the block of mass m as shown in fiure. The strin and the pulley are liht and the surface of the table is smooth. Find the acceleration of m. 5. A chain consistin of five links each with mass 00m is lifted vertically with constant acceleration of m/s. as shown. Find (a) the forces actin between adjacent links (b) the force F exerted on the top link by the aent liftin the chain (c) the net force on each link. 53. A block of mass k connected with a sprin of force constant 00 N/m is suspended to the ceilin of lift movin upward with constant velocity m/s. Calculate the extension produced in sprin. 54. Two blocks A (5 k) & B (3 k) restin on a smooth horizontal plane are connected by a sprin of stiffness 94 N/m. A horizontal force of F N acts on A as shown. At the instant B has an acceleration of 4.9 m/s. Find the acceleration of block A? 55. What will be the readin of sprin balance in the fiure shown in followin situations. ( 0 m/s ) (i) a 0, v 0 (ii) a 0, v m/s (iii) a 0, v m/s (iv) a m/s, v 0 (v) a m/s v 0 (vi) a m/s, v m/s (vii) a m/s, v m/s (vii) a m/s v m/s 56. In the fiure shown, blocks A and B move with velocities v and v alon F horizontal direction. Find the ratio of v v. 57. In the fiure shown, the pulley is movin with velocity u. Calculate the velocity of the block attached with strin.

8 58. The velocity of end A of riid rod placed between two smooth vertical walls moves with velocity u alon vertical direction. Find out the velocity of end B of that rod, rod always remains in contact with the vertical walls. 59. f block A has a velocity of 0.6 m/s of the riht, determine the velocity of cylinder B. 60. A man of mass m standin on a platform of mass m jumps horizontally with an acceleration a. Find the acceleration of platform. 6. Two blocks of masses k and 3 k connected with a sprin are movin on a smooth horizontal surface. Acceleration of mass 3k is m/s alon riht direction. What will be the acceleration of mass k? 6. Man A of mass 60 k pushes the other man B of mass 75 k due to which man B starts movin with acceleration 3 m/s. Calculate the acceleration of man A at that instant. 63. An object of mass k movin with velocity 0 î m/s is seen in a frame movin with velocity 0 î m/s. What will be the value of pseudo force actin on object in this frame. 64. In the adjoinin fiure, a wede is fixed to an elevator movin upwards with an acceleration a. A block of mass m is placed over the wede. Find the acceleration of the block with respect to wede. Nelect friction. 65. A painter of mass M stand on a platform of mass m and pulls himself up by two ropes which han over pulley as shown. He pulls each rope with the force F and moves upward with uniform acceleration a. Find a (nelectin the fact that no one could do this for lon time). 66. Three monkeys A, B and C with masses of 0, 5 & 8 K respectively are climbin up & down the rope suspended from D. At the instant represented, A is descendin the rope with an acceleration of m/s & C is pullin himself up with an acceleration of.5 m/s. Monkeys B is climbin up with a constant speed of 0.8 m/s. Treat the rope and monkeys as a complete system & calculate the tension T in the rope at D. ( 0 m/s )

9 67. The masses of blocks A and B are same and equal to m. Friction is absent everywhere. Find the manitude of normal force with which block B presses on the wall and accelerations of the blocks A and B. 68. A mass M is held in place by an applied force F and a pulley system as shown in fiure. The pulleys are massless and frictionless. (a) Draw a free body diaram for each pulley (b) Find the tension in each section of rope T, T, T 3, T 4 and T 5. (c) Find the manitude of F. 69. A block 'C' of mass m rests on a smooth table. Two blocks A and B each of mass m, are attached to the end of a liht inextensible strin passin over a smooth pulley fixed to C as shown in the fiure. B rests on C and A can move in a frictionless vertical shaft. Find the acceleration of C. 70. In the fiure shown C is a fixed wede. A block B is kept on the inclined surface of the wede C. Another block A is inserted in a slot in the block B as shown in fiure. A liht inextensible strin passes over a liht pulley which is fixed to the block B throuh a liht rod. One end of the strin is fixed and other end of the strin is fixed to A.S is a fixed support on the wede. All the surfaces are smooth. Masses of A and B are same. Find the manitude of acceleration of A and B. (sin 37º 3/5) 7. In the fiure shown all blocks are of equal mass m. All surfaces are smooth. Find the acceleration of all the blocks. 7. A lift L is movin upwards with a constant acceleration a. A small block A of mass ' m ' is kept on a wede B of the same mass ' m '. The heiht of the vertical face of the wede is ' h'. A is released from the top most point of the wede. Find the time taken by A to reach the bottom of B. All surfaces are smooth and B is also free to move. 73. In the arranement shown in the Fi., the block of mass m k lies on the wede of mass M 8 k. Find the initial acceleration of the wede if the surfaces are smooth L ) q A B h a. A mass A ( 0.5 k ) is placed on a smooth table with a strin attached to it. The strin oes over a frictions pulley and is connected to another mass B ( 0. k ). At t 0 the mass A is at a distance m from the end movin with a speed of 0.5 m/s towards the left, what will be its position and speed at t sec? [IIT 975]

10 . A lift is oin up. The total mass of the lift and the passeners is 50 k. The variation in the speed of the lift is iven in the raph. (a) What will be the tension in the rope pullin the lift at t equal to (i) sec (ii) 6 sec and (iii) sec? (b) What is the heiht throuh which the lift takes the passeners? (c) What will be the averae velocity and averae acceleration durin the course of entire motion? [IIT 976] 3. Two masses m and m are connected by a massless strin which passes over a pulley as shown in fi. The masses are held initially with equal lenth of the strin on either side of the pulley. Find the velocity of masses at the instant the lihter mass moves up a distance of 6.54 m. The strin is suddenly cut at that instant. Calculate the time taken by each mass to reach the round. [IIT 977] 4. Two cubes of masses m and m lie on two frictionless slopes of block A which rests on a horizontal table. The cubes are connected by a strin which passes over a pulley as shown in the diaram. To what horizontal acceleration f should the whole system (i.e. block and cubes) be subjected so that the cubes do not slide down the planes? What is the tension in the strin in this situation? 5. A ship of mass 3 x 0 7 k initially at rest is pulled by a force of 5 x 0 4 N throuh a distance of 3m. Assume that the resistance due to water is neliible, the speed of the ship is (A).5 m/s (B) 60 m/s (C) 0. m/s (D) 5 m/s [IIT 980] 6. In the arranement shown in fi. the ends P and Q of an unstretchable strin move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed. (A) U cos (B) U cos (C) U/cos (D) U/cos 7. The pulley arranements of fi. (a) and (b) are indentical. The mass of the rope is neliible. In (a), the mass m is lifted up by attachin a mass m to the other end of the rope. In (b), m is lifted up by pullin the other end of the rope with a constant downward force F m. Find the acceleration of m is the same in both cases: 8. Two blocks of mass.9 k and.9 k are suspended from a riid support S by two inextensible wires each of lenth m. The upper wire has neliible mass and the lower wire has a uniform mass of 0. k/m. The whole system of blocks, wires and support have an upward acceleration of 0. m/s. The acceleration due to ravity is 9.8 m/s. [IIT 989] (i) Find the tension at the midpoint of the lower wire. (ii) Find the tension at the midpoint of the upper wire. 9. Essential characteristic of equilibrium is (A) momentum equal zero (B) acceleration equals zero (C) K.E. equals zero (D) velocity equals zero [REE 989]

11 0. A mass is hun with a liht inextensible strin in fiure. Find the tension of horizontal strin AP. [IIT 990]. What is the tension in a rod of lenth L and mass M at a distance y from F when the rod is acted on two unequal forces F and F (<F ) as shown in the fiure. [IIT 993] A smooth semicircular wire-track of radius R is fixed in a vertical plane shown in fi. One end of a massless sprin of natural lenth (3R/4) is attached to the lower point O of the wire track. A small rin of mass m, which can slide on the track, is attached to the other end of the sprin. The rin is held stationary at point P such that the sprin makes an anle of 60 with the vertical. The sprin constant K m/r. Consider the instant when the rin is released, and (i) draw free body diaram of the rin, (ii) Determine the tanential acceleration of the rin and the normal reaction. [JEE 996, 5 marks] 3. A sprin of force constant K is cut into two pieces such that one piece is double the lenth of the other. Then the lon piece will have a force constant of - (A) /3 K (B*) 3/ K (C) K (D) K [JEE 999] 4. Two blocks of masses m 3 k and m k are connected by a liht inextensible strin which 3 passes over a smooth pe. The blocks rest on the inclined smooth planes of a wede and the pe is fixed to the top of the wede. The planes of the wede supportin m and m are inclined at 30º and 60º, respectively, with the horizontal. Calculate the acceleration of the masses and the tension in the strin. [REE 999] 5. A strin of neliible mass oin over a clamped pulley of mass m supports a block of mass M as shown in the fiure. The force on the pulley by the clamp is iven by - (A) M (B) m (C) (M m) m (D) (M m) M [JEE 00, 3marks ] 6. The pulleys and strins shown in the fiure are smooth and of neliible mass for the system to remain in equilibrium, the anle should be [JEE 00,3 marks] (A) 0º (B) 30º (C) 45º (D) 60º 7. System shown in fiure is in equilibrium and at rest. The sprin and strin are massless Now the strin is cut. The acceleration of mass m and m just after the strin is cut will be : [JEE 006,3 marks] (A) / upwards, downwards (B) upwards, / downwards (C) upwards, downwards (D) upwards, downwards m C O R 60 m m P m

12 EXERCISE #. (A). (C) 3. (B) 4. (B) 5. (B) 6. (B) 7. (D) 8. (C) 9. (C) 0. (C). (C). (C) 3. (D) 4. (B) 5. (A) 6. (C) 7. (C) (D) 8. (C) 9. (A) 0. (A). (A). (B) 3. (B) 4. (C) 5. (B) 6. (A) (C) 7. (B) 8. (A) (C) 9. (A) (C) 30. (B) 3. (B) 3. (B) (C) 33. (B) 34. (B) 35. (C) 36. Gravitational, Nuclear. 37. Gravitational, Electromanetic, Nuclear. 38. No 39. Team who wins, push or apply more force on the earth compare to other team. 40. m actin on earth in opposite direction 4. Electromanetic, Electromanetic 4. Yes 43. (a) Earth (b) 4N (c) No (d) 4N, Earth, book, upward (e) 4N, hand, book, downward (f) nd () rd (h) No (i) No (j) Yes (k) Yes (l) one (m) No 44. (i) (ii) N F (iii) F (iv) m, m. 45. (a) (b) equal manitude w. 46. N A 000 N, NB N (i) zero, (ii) 0 N 48. (a) 0 N, (b) 5 N, (c) 0 N. 49. (a) F F 50. 4N N (b) W N m ( m m ) 5. (a) 4.8 N, 3.6 N,.4N,. N (b) F 6 N (c) 0. N m 54. The acceleration of A is 3 x 0.98 m/s 55. (i) 00 N, (ii) 00 N, (iii) 00 N, (iv) 0 N, (v) 80 N, (vi) 0 N, (vii) 0 N, (viii) 80 N. 56. cos cos 57. u 58. u tan m/s 60. a /, towards left m/s, towards left m/s, opposite direction. 4 4F 63. F ( + a) sin 65. a. M m 66. For the system T 33 m A a A + m B a B + m C a C 0 () + 5 (0) + 8 (3/) T N a ; b ; NBW 5 5 m. 5 M 3M 68. (a) T T T 3, T5 M and T a C a B 7. t 70. a B 3 4 m/s, a A 3 4 sincos ; a 3 sin A sin 3sin h( sin sin.. m;.3 m/s ) 73. a EXERCISE # 4sin ; 3 sin 30 3 m/s. 3 M (b) F m/s.. (a) (i) 7400 N (ii) 4700 N (iii) 000 N (b) 36 m (c) Averae velocity 3 m/s; av. acceleration s ; s 4. (m sin m sin) f (m cos m cos (mm sin( ) T (m cos m cos) 5. C 6. D 7. (a) /3 (b) 8. 0 N, 50 N 9. B 0. 3 M. y y F F L L 5 3, 8 3m 8 C R N kr/4 P 60 O m 3. (B) m / s, N (3 3 ) ( 3 3 ) 5. (D) 6. (C) 7. (A)