Exercise 1OBJECTIVE PROBLEMS1. Action and reaction

(A) act on two different objects (B) have equal magnitude(C) have opposite directions (D) have resultant zero.

2. Which figure represents the correct F.B.D. of rod of massm as shown in figure :

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

3. n which of the following cases the net force is not zero ?(A) A kite skillfully held stationary in the sky(B) A ball freely falling from a height(C) An aeroplane rising upwards at an angle of 45º with the horizontal with a constant speed(D) A cork floating on the surface of water

4. Two blocks are in contact on a frictionless table. One has mass m and the other 2m. A force F isapplied on 2m as shown in the figure. Now the same force F is applied from the right on m. In the twocases respectively, the ratio force of contact between the two blocks will be :

(A) same (B) 1 : 2 (C) 2 : 1 (D) 1 : 3

5. A constant force F is applied in horizontal direction asshown. 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 rigid support at A asshown in figure. Another rope is tied at the end B, and it ispulled horizontally with a force F. If the rope AB makes anangle with the vertical, then the tension in the string AB is :(A) F sin (B) F/sin (C) F cos (D) F/cos

7. Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kgweight is attached to the rope at the mid point which now no longer remains horizontal. The minimumtension required to completely straighten the rope is :

(A) 15 kg (B)2

15kg (C) 5 kg (D) nfinitely large

8. Two masses M1 and M2 are attached to the ends of a string which passes overa pulley attached to the top of a double inclined plane of angles of inclination

and . f M2 > M1, the acceleration a of the system is given by :

(A)

21

2

MMsingM

(B)

21

1

MMsingM

(C)

21

12

MMsinM–sinM

g (D) zero

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9. Three masses of 1 kg , 6 kg and 3 kg are connected to eachother with threads and are placed on table as shown in figure,What is the acceleration with which the system is moving ?Take g = 10m s–2 .(A) Zero (B) 1 m s–2

(C) 2 m s–2 (D) 3 m s–2

10. A body of mass 8 kg is hanging from another body of mass 12 kg. The combination isbeing pulled by a string with an acceleration of 2.2 m s–2. The tension T1 and T2 will berespectively :(use g = 9.8m/s2 )

12kg

8kg

T2

T1

a

(A) 200 N, 80 N (B) 220 N, 90 N(C) 240 N, 96 N (D) 260 N, 96 N

11. A fireman wants to slide down a rope. The rope can bear a tension of43

the of the weight of the man.

With what minimum acceleration should the fireman slide down :

(A) 3g

(B) 6g

(C)4g

(D)2g

12. A particle of small mass m is joined to a very heavy body by a light string passing over a light pulley.Both bodies are free to move. The total downward force on the pulley is(A) mg (B) 2 mg (C) 4 mg (D) >> mg

13. Two blocks of masses M1 and M2 are connected to each other througha light spring as shown in figure. If we push mass M1 with force F andcause acceleration a1 in mass M1, what will be the acceleration in M2 ?(A) F/M2 (B) F/(M1 + M2) (C) a1 (D) (F – M1a1)/M2

14. Two masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure.A force of 200 N acts on the 20 kg mass at the instant when the 10 kg mass has an acceleration of 12ms–2 , the acceleration of the 20 kg mass is :(A) 2 ms–2 (B) 4ms–2

(C) 10ms–2 (D) 20ms–2

15. In the arrangement shown in the Figure all surfaces are frictionless, the massesof the block are m1 = 20 kg and m2 = 30 kg. The accelerations of masses m1and m2 will be if F = 180 N.

//////////////////////////////////////////////////

m1

m2 F

(A) a m sm19 2 / ,am2 0 (B) a m sm1

9 2 / , 9a2m m/s2

(C) 0a1m , 2

m s/m9a2 (D) None of these

16. Figure shows a wedge of mass 2kg resting on a frictionless floor. A block of mass 1 kg is kept on thewedge and the wedge is given an acceleration of 5 m/sec2 towards right. Then :

(A) block will remain stationary w.r.t. wedge(B) the block will have an acceleration of 1 m/sec2 w.r.t. the wedge(C) normal reaction on the block is 11 N(D) net force acting on the wedge is 2 N

17. A trolley of mass 8 kg is standing on a frictionless surface inside which an object of mass2 kg is suspended. A constant force F starts acting on the trolley as a result of which the string stoodat an angle of 370 from the vertical. Then :

(A) acceleration of the trolley is 40/3 m/sec2.(B) force applied in 60 N(C) force applied is 75 N(D) tension in the string is 25 N

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18. A triangular block of mass M rests on a smooth surface as shown in figure.A cubical block of mass m rests on the inclined surface. If all surfaces arefrictionless, the force that must be applied to M so as to keep m stationaryrelative to M is :(A) Mg tan 30 (B) mg tan 30(C) (M+m)g tan 30 (D) (M+m)g cos 30

19. A trolley is accelerating down an incline of angle withacceleration gsin. Which of the following is correct. ( is theangle made by the string with vertical).(A) = (B) = 00

(C) Tension in the string, T = mg(D) Tension in the string, T = mg sec

20. A flexible chain of weight W hangs between two fixed points A and B at the same level. The inclinationof the chain with the horizontal at the two points of support is . What is the tension of the chain at theendpoint.

(A)2W

cosec (B)2W

sec

(C) W cos (D) 3W

sin

21. Two masses m and M are attached with strings as shown. For the system to be in equilibriumwe have

(A) tan = 1 +mM2

(B) tan = 1 +Mm2

(C) tan = 1 +m2M

(D) tan = 1 +M2

m

22. Objects A and B each of mass m are connected by light inextensible cord. They are constrained tomove on a frictionless ring in a vertical plane as shown in figure. The objects are released from rest atthe positions shown. The tension in the cord just after release will be

(A) mg 2 (B) 2mg

(C)2

mg(D)

4mg

23. A 50 kg person stands on a 25 kg platform. He pulls on the rope which is attachedto the platform via the frictionless pulleys as shown in the fig. The platform movesupwards at a steady rate if the force with which the person pulls the rope is

(A) 500 N (B) 250 N(C) 25 N (D) 50 N

24. A balloon of gross weight w newton is falling vertically downward with a constant acceleration a(<g).The magnitude of the air resistance is :

(a) w (B)

ga1w (C)

ga1w (D) g

aw

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25. Three blocks A , B and C are suspended as shown in the figure. Mass of eachblocks A and C is m. If system is in equilibrium and mass of B is M , then :

(A) M = 2 m (B) M < 2 m(C) M > 2 m (D) M = m

26. In the system shown in the figure m1 > m2 . System is held at rest bythread BC . Just after the thread BC is burnt :(A) acceleration of m2 will be upwards

(B) magnitude of acceleration of both blocks will be equal to

2121

mmmm

g

(C) acceleration of m1 will be equal to zero(D) magnitude of acceleration of two blocks will be nonzero and unequal.

27. In the figure , the blocks A , B and C of mass m each have acceleration a1 , a2 and a3 respectively. F1and F2 are external forces of magnitudes 2 mg and mg respectively .

(A) a1 = a2 = a3 (B) a1 > a2 > a3(C) a1 = a2 , a2 > a3 (D) a1 > a2 , a2 = a3

28. A string is wrapped round a log of wood and it is pulled with a force F as shown in the figure .

(A) tension T in the string increases with increase in (B) tension T in the string decreases with increase in (C) tension T > F if > /3(D) tension T > F if > /4

29. In the figure the reading of the spring balancewill be : [ g = 10 m/s2 ]

(A) 6 kg f (B) 5 kg f(C) 60 N (D) 60 kg f

30. Block B moves to the right with a constant velocity v0. The velocity of body A relative to B is :

(A)2v0 , towards left (B)

2v0 , towards right

(C)2v3 0 , towards left (D)

2v3 0 , towards right

31. In the arrangement shown in figure , pulleys are massless andfrictionless and threads are inextensible. Block of mass m1will remain at rest if :

(A)1m

1 =

2m1

+3m

1(B)

1m4

=2m

1 +

3m1

(C) m1 = m2 + m3 (D)3m

1 =

2m2

+1m

3

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32. Two blocks of masses 10 kg and 20 kg are connected by a light spring as shown. A force of 200 N actson the 20 kg mass as shown. At a certain instant the acceleration of 10 kg mass is 12 ms–2.

(A) At that instant the 20 kg mass has an acceleration of 12 ms–2.(B) At that instant the 20 kg mass has an acceleration of 4 ms–2 .(C) The stretching force in the spring is 120 N.(D) The collective system moves with a common acceleration of 30 ms–2 when the extension in the

connecting spring is the maximum.

33. A block tied between two springs is in equilibrium. If upper spring is cut then theacceleration of the block just after cut is 6 m/s2 downwards. Now, if instead of upperspring, lower spring is being cut then the magnitude of acceleration of the block justafter the cut will be : (Take g = 10 m/s2)(A) 16 m/s2 (B) 4 m/s2

(C) cannot be determined (D) none of these

34. Reading shown in two spring balances S1 and S2 is 90 kg and 30 kg respectivelyand lift is accelerating upwards with acceleration 10 m/s2. The mass is stationarywith respect to lift. Then the mass of the block will be :(A) 60 kg (B) 30 kg

(C) 120 kg (D) Noneof these

35. Five persons A, B, C, D & E are pulling a cart of mass 100 kg on a smooth surface and cart is movingwith acceleration 3 m/s2 in east direction. When person 'A' stops pulling, it moves with acceleration1m/s2 in the west direction. When person 'B' stops pulling, it moves with acceleration 24 m/s2 in thenorth direction. The magnitude of acceleration of the cart when only A & B pull the cart keeping theirdirections same as the old directions, is :

(A) 26 m/s2 (B) 713 m/s2 (C) 25 m/s2 (D) 30 m/s2

SUBJECTIVE PROBLEMS36. 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 magnitude act on an isolated body in opposite directions to keep it at equilibriumposition, is this true according to Newton’s third law ?

39. According to Newton’s third law each team pulls the opposite team with equal force in a tug 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 pulling the body with a force mg. Taking this forceto be the action , what is the reaction?

41. When you hold a pen and write on your notebook, what kind of force is exerted by you on the pen? Bythe pen on the notebook?

42. Is it true that the reaction of a gravitational force is always gravitational, of an electromagnetic force isalways electromagnetic and so on ?

43. Imagine that you are holding a book weighing 4 N at rest on the palm of your hand.a) A downward force of magnitude 4 N is exerted on the book by ________.

b) An upward force of magnitude ———————— 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 magnitude________, exerted on ________ by________.Its direction is ________.

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e) The reaction to force (b) is a force of magnitude________, exerted on ________ by________.Its direction is ________.

f) That the forces (a) and (b) are equal and opposite is an example of Newton’s ________ law.

g) 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 magnitude 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 thebook by the earth ?

j) Is the force exerted on the book by the earth equal and opposite to the force exerted on theearth by the book ?

k) Is the force exerted on the book by the hand equal and opposite to the force exerted on thehand by the book ?

Finally, suppose that you snatch your hand away while the book is moving upward.l) How many forces then act on the book?

m) Is the book in equilibrium?

44. Two blocks of masses m1 and m2 are placed on ground as shown in figure. Two forces of magnitude Fact on m1 and m2 in opposite directions.

(i) Draw F.B.D. of masses m1 and m2.(ii) Calculate the contact force between m1 and m2.(iii) What will be the value of action-reaction pair between m1 and m2 .(iv) Calculate force exerted by surface on mass m1 and m2

45. A cylinder of weight w is resting on a V-groove as shown in figure.(a) Draw its free body diagram.(b) Calculate normal reactions between the cylinder and

///////////////////////////

600

600600

mg

Smooth

two inclined walls.

46. The 50 kg homogeneous smooth sphere rests on the 30º incline A and bears against the smoothvertical wall B. Calculate the contact forces at A and B.

47. A string is connected between surface and a block of mass 1kg which is pulled by another string by applying force F = 10 Nas shown in figure. (g = 10 m/s2)(i) Calculate tension is string (1).(ii) Calculate tension in string (2).

48. A block of mass 1 kg is suspended by a string of mass 1 kg, length 1m as shown infigure. (g = 10 m/s2) Calculate:

(a) the tension in string at its lowest point.(b) the tension in string at its mid–point.(c) force exerted by support on string.

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49. In the figure the tension in the diagonal string is 60 N.

(a) Find the magnitude of the horizontal force 1F

and 2F

that must be applied to hold the systemin the position shown.

(b) What is the weight of the suspended block ?

50. The elevator shown in figure is descending with an acceleration of2 m/s2.The mass of the block A is 0.5 kg. What force is exerted by theblock A on the block B ? Solve the problem taking (a) ground as theframe (b) lift as the frame.

51. A constant force F = m2g / 2 is applied on the block ofmass m1 as shown in figure. The string and the pulleyare light and the surface of the table is smooth. Findthe acceleration of m1.

52. A chain consisting of five links each with mass 100gm is lifted vertically withconstant acceleration of 2m/s2. as shown. Find(a) the forces acting between adjacent links

F

(b) the force F exerted on the top link by the agent lifting the chain(c) the net force on each link.

53. A block of mass 1 kg connected with a spring of force constant 100 N/m is suspended to the ceiling oflift moving upward with constant velocity 2 m/s. Calculate the extension produced in spring.

54. Two blocks A (5 kg) & B (3 kg) resting on a smoothhorizontal plane are connected by a spring of stiffness294 N/m. A horizontal force of F = 3 9.8 N acts on Aas shown. At the instant B has an acceleration of4.9 m/s2. Find the acceleration of block A ?

55. What will be the reading of spring balance in the figure shown in following situations. (g = 10 m/s2)(i) a = 0, v = 0(ii) a = 0, v = 2 m/s(iii) a = 0, v = – 2m/s(iv) a = 2m/s2, v = 0(v) a = – 2 m/s2 v = 0(vi) a = 2 m/s2, v = 2 m/s(vii) a = 2 m/s2, v = – 2 m/s(vii) a = – 2 m/s2 v = – 2 m/s

56. In the figure shown, blocks A and B move with velocities v1 and v2 along

horizontal direction. Find the ratio of2

1

vv

.

57. In the figure shown, the pulley is moving with velocity u. Calculate thevelocity of the block attached with string.

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58. The velocity of end ‘A’ of rigid rod placed between two smooth verticalwalls moves with velocity ‘u’ along vertical direction. Find out the velocityof end ‘B’ of that rod, rod always remains in contact with the verticalwalls.

59. f block A has a velocity of 0.6 m/s of the right, determine the velocity of cylinder B.

60. A man of mass m standing on a platform of mass ’2m’ jumps horizontallywith an acceleration ‘a’. Find the acceleration of platform.

61. Two blocks of masses 2 kg and 3 kg connected with aspring are moving on a smooth horizontal surface.Acceleration of mass 3kg is 2m/s2 along right direction.What will be the acceleration of mass 2 kg ?

62. Man ‘A’ of mass 60 kg pushes the other man ‘B’ ofmass 75 kg due to which man ‘B’ starts moving withacceleration 3 m/s2. Calculate the acceleration of

man ‘A’ at that instant.

63. An object of mass 2 kg moving with velocity i10 m/s is seen in a frame moving with velocity i10 m/s.What will be the value of ‘pseudo force’ acting on object in this frame.

64. In the adjoining figure, a wedge is fixed to an elevator moving upwards with anacceleration ‘a’. A block of mass ‘m’ is placed over the wedge. Find the acceleration

of the block with respect to wedge. Neglect friction.

65. A painter of mass M stand on a platform of mass m and pulls himselfup by two ropes which hang over pulley as shown. He pulls eachrope with the force F and moves upward with uniform acceleration‘a’. Find ‘a’ (neglecting the fact that no one could do this for longtime).

66. Three monkeys A, B and C with masses of 10 , 15 & 8 Kg respectively are climbing up& down the rope suspended from D . At the instant represented , A is descending therope with an acceleration of 2 m/s2 & C is pulling himself up with an acceleration of 1.5m/s2 . Monkeys B is climbing up with a constant speed of 0.8 m/s . Treat the rope andmonkeys as a complete system & calculate the tension T in the rope at D .

( g = 10 m/s2 )

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67. The masses of blocks A and B are same and equal to m. Friction is absenteverywhere. Find the magnitude 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 infigure. The pulleys are massless and frictionless.(a) Draw a free body diagram for each pulley(b) Find the tension in each section of rope T1, T2, T3, T4 and T5.

(c) Find the magnitude of F.

69. A block 'C' of mass m rests on a smooth table . Two blocks A and B eachof mass m, are attached to the end of a light inextensible string passingover a smooth pulley fixed to C as shown in the figure. B rests on C and A

can move in a frictionless vertical shaft. Find the acceleration of C.

70. In the figure shown C is a fixed wedge. A block B is kept on the inclinedsurface of the wedge C. Another block A is inserted in a slot in the block B asshown in figure. A light inextensible string passes over a light pulley which isfixed to the block B through a light rod. One end of the string is fixed andother end of the string is fixed to A.S is a fixed support on the wedge. All thesurfaces are smooth. Masses of A and B are same. Find the magnitude ofacceleration of A and B. (sin 37º = 3/5)

71. In the figure shown all blocks are of equal mass ‘m’. All surfaces are smooth. Find theacceleration of all the blocks.

72. A lift L is moving upwards with a constant acceleration a = g. A small block A ofmass 'm ' is kept on a wedge B of the same mass ' m '. The height of the vertical faceof the wedge is ' h'. A is released from the top most point of the wedge. Find the timetaken by A to reach the bottom of B. All surfaces are smooth and B is also free tomove. q

A

B)

a

hL

73. In the arrangement shown in the Fig., the block of mass m = 2 kg lies on thewedge of mass M = 8 kg. Find the initial acceleration of the wedge if thesurfaces are smooth

1. A mass A ( 0.5 kg ) is placed on a smooth table with a stringattached to it. The string goes over a frictions pulley and isconnected to another mass B ( 0.2 kg ). At t = 0 the mass A is ata distance 2m from the end moving with a speed of 0.5 m/s towardsthe left, what will be its position and speed att = 1 sec? [IIT 1975]

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2. A lift is going up. The total mass of the lift and thepassengers is 150 kg. The variation in the speed of the liftis given in the graph.

(a) What will be the tension in the rope pulling the lift at t equal to(i) 1 sec (ii) 6 sec and (iii) 11 sec ?

(b) What is the height through which the lift takes the passengers ?(c) What will be the average velocity and average acceleration during the course of entire motion?[IIT 1976]

3. Two masses m and 2m are connected by a massless string which passes over apulley as shown in fig. The masses are held initially with equal length of the stringon either side of the pulley. Find the velocity of masses at the instant the lightermass moves up a distance of 6.54 m. The string is suddenly cut at that instant.Calculate the time taken by each mass to reach the ground.[IIT 1977]

4. Two cubes of masses m1 and m2 lie on two frictionless slopes ofblock A which rests on a horizontal table. The cubes are connectedby a string which passes over a pulley as shown in the diagram. Towhat horizontal acceleration f should the whole system (i.e. blockand cubes) be subjected so that the cubes do not slide down theplanes? What is the tension in the string in this situation?

5. A ship of mass 3 x 107 kg initially at rest is pulled by a force of 5 x 104 N through a distance of 3m. Assumethat the resistance due to water is negligible, the speed of the ship is(A) 1.5 m/s (B) 60 m/s (C) 0.1 m/s (D) 5 m/s [IIT 1980]

6. In the arrangement shown in fig. the ends P and Q of anunstretchable string move downwards with uniform speed U.Pulleys A and B are fixed. Mass M moves upwards with a speed.(A) 2 U cos (B) U cos (C) 2 U/cos (D) U/cos

7. The pulley arrangements of fig. (a) and (b) are indentical. The massof the rope is negligible. In (a), the mass m is lifted up by attachinga mass 2m to the other end of the rope. In (b), m is lifted up bypulling the other end of the rope with a constant downward forceF = 2 mg. Find the acceleration of m is the same in both cases:

8. Two blocks of mass 2.9 kg and 1.9 kg are suspended from a rigid supportS by two inextensible wires each of length 1 m. The upper wire hasnegligible mass and the lower wire has a uniform mass of 0.2 kg/m. Thewhole system of blocks, wires and support have an upward acceleration of0.2 m/s2. The acceleration due to gravity is 9.8 m/s2.[IIT 1989](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 1989]

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10. A mass is hung with a light inextensible string in figure. Findthe tension of horizontal string AP. [IIT 1990]

11. What is the tension in a rod of length L and mass M at a distance y from F1 when the rod is acted on twounequal forces F1 and F2 (<F1) as shown in the figure . [IIT 1993]

12 A smooth semicircular wire-track of radius R is fixed in a vertical plane shown infig. One end of a massless spring of natural length (3R/4) is attached to the lowerpoint O of the wire track. A small ring of mass m, which can slide on the track, isattached to the other end of the spring. The ring is held stationary at point P suchthat the spring makes an angle of 60° with the vertical. The spring constant K =mg/R. Consider the instant when the ring is released, and (i) draw free body diagramof the ring, (ii) Determine the tangential acceleration of the ring and the normal

60°

mP

O

C R

reaction. [JEE 1996, 5 marks]

13. A spring of force constant K is cut into two pieces such that one piece is double the length of the other.Then the long piece will have a force constant of -(A) 2/3 K (B*) 3/2 K (C) K (D) 2K [JEE 1999]

14. Two blocks of masses m1 = 3 kg and m2 = 31

kg are connected by a light inextensible string which

passes over a smooth peg. The blocks rest on the inclined smooth planes of a wedge and the peg isfixed to the top of the wedge. The planes of the wedge supporting m1 and m2 are inclined at 30º and 60º,respectively, with the horizontal. Calculate the acceleration of the masses and the tension in thestring. [REE 1999]

15. A string of negligible mass going over a clamped pulley of mass m supports ablock of mass M as shown in the figure. The force on the pulley by the clampis given by -

(A) 2 Mg (B) 2 mg (C) gm)mM( 22

(D) gM)mM( 22

[JEE 2001, 3marks ]

16. The pulleys and strings shown in the figure are smooth and of negligiblemass for the system to remain in equilibrium, the angle should be[JEE 2002,3 marks]

(A) 0º (B) 30º

m

2m

m(C) 45º (D) 60º

17. System shown in figure is in equilibrium and at rest. The spring and string aremassless Now the string is cut. The acceleration of mass 2m and m just afterthe string is cut will be : [JEE 2006,3 marks](A) g/2 upwards , g downwards (B) g upwards, g/ 2 downwards(C) g upwards , 2g downwards (D) 2g upwards , g downwards

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EXERCISE # 11. (A) 2. (C) 3. (B) 4. (B) 5. (B) 6. (B) 7. (D)8. (C) 9. (C) 10. (C) 11. (C) 12. (C) 13. (D)14. (B) 15. (A) 16. (C) 17. (C) (D) 18. (C)19. (A) 20. (A) 21. (A) 22. (B) 23. (B) 24. (C)25. (B) 26. (A) (C) 27. (B) 28. (A) (C)29. (A) (C) 30. (B) 31. (B) 32. (B) (C)33. (B) 34. (B) 35. (C)36. Gravitational, Nuclear.37. Gravitational, Electromagnetic, Nuclear.38. No39. Team who wins, push or apply more force on

the earth compare to other team.40. ‘mg’ acting on earth in opposite direction41. Electromagnetic, Electromagnetic42. Yes43. (a) Earth (b) 4N (c) No

(d) 4N , Earth, book , upward(e) 4N , hand , book , downward(f) nd (g) rd (h) No (i) No(j) Yes (k) Yes (l) one (m) No

44. (i)

(ii) N = F (iii) F (iv) m1g, m2g.

45. (a) (b) equal magnitude w .

46. NA = 31000

N, NB = 3500

N

47. (i) zero, (ii) 10 N48. (a) 10 N, (b) 15 N, (c) 20 N.

49. (a) | 1F

| = | 2F

| = 260

N (b) W = 260

N

50. 4N. 51.)( 21

2

mm2gm

52. (a) 4.8 N, 3.6 N, 2.4N, 1.2 N(b) F = 6 N (c) 0.2 N

53. 0.1 m54. The acceleration of A is 3 x 0.98 m/s2

55. (i) 100 N, (ii) 100 N, (iii) 100 N, (iv) 120 N,(v) 80 N, (vi) 120 N, (vii) 120 N, (viii) 80 N.

56.1

2

coscos

57. 2u

58. u tan . 59. 1.8 m/s60. a / 2, towards left. 61. 3 m/s2, towards left.

62.4

15m/s2 , opposite direction.

63. F = 0 64. (g + a) sin 65. a =mM

F4

– g.66. For the system

T 33 g = mAaA + mBaB + mCaC

= 10 (2) + 15 (0) + 8 (3/2) T = 33 g 8 = 322 N

67. a = 25g12

; b = 25g9

; NBW = 25mg12

.

68. (a) T1 = T2 = T3 = 2Mg , T5 = Mg and T4 = 2

Mg3 (b) F =2

Mg

69. 5g

70. aB = 34

m/s2 , aA = 34

2 m/s2.

71. aC =

2sin31

cossing2; aA =

2

2

sin31sing4

;

aB =

2sin31

sing2

72. t =

2

2

sing2)sin1(h

73. a =23

330m/s2 .

EXERCISE # 21. 1.1 m; 2.3 m/s

2. (a) (i) 17400 N (ii) 14700 N (iii) 12000 N (b) 36 m(c) Average velocity = 3 m/s; av. acceleration = 0

3. 2.78s ; 0.665 s

4.)cosmcosm(

)sin(gmm(Tcosmcosm(

g)sinmsinm(f21

21

21

21

5. C 6. D 7. (a) g/3 (b) g 8. 20 N, 50 N

9. B 10. Mg3 11.

LyF

Ly1F 21

12 g8

35, 8

mg3

60°

mg

P

O

C RN

kR/4

13. (B)

14. N

)133(1315,s/m

)133(310 2

15. (D) 16. (C) 17. (A)

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