Newton's Laws of Motion - From asif

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NEWTON’S LAWS OF MOTION

1. An inclined plane makes an angle 300 with the horizontal. A groove OA = 5 m cut in the plane makes an angle 300 with OX. A short smooth cylinder is free to slide down due to the influence of gravity. The time taken by the cylinder to reach from A to O is: (Take g = 10 m/s2)a) b) 4 s c) 2 s d) 1 s

2. With what force must a man pull on the rope to hold the plank in position if the man weights 60 kg? Neglect the wt. of the plank, rope and pulley. (Take g = 10 m/s2)a) 100 N b) 150 N c) 125 N d) None of these

3. In the situation shown in figure the magnitude of total external force acting on the block A is (all the surface are smooth):a) 21 N b) 14 N c) 7 N d) zero

4. In the figure a rope of mass m and length l is such that its one end is fixed to a rigid wall and the other is applied with a horizontal force F as shown below, then tension at the middle of the string is:a) F b) 2 F c) zero d) F /2

5. Figure shows a light spring balance connected to two blocks of mass 20 kg each. The graduations in the balance measure the tension in the spring. The reading of the balance is:a) 40 kg b) zero kg

c) 20 kg d) Depends on mass of spring balance

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6. A block of mass 10 kg is suspended through two light spring balances as shown below:

a) Both the scales will read 5 kgb) The upper scale will read 10 kg & the lower zeroc) Both the scales will read 10 kg d) The readings may be anything but their sum will be

10 kg.

7. Three blocks A, B and C are suspended as shown below. Mass of each of block A and B is m. If system is in equilibrium, and mass of C is M then:a) M < 2m b) M > 2m c) M = 2m d)

8. A light spring is compressed and placed horizontally between a vertical fixed wall and a block, free to slide over a smooth horizontal table top as shown in the figure below. If the system is released from rest, which of the graphs below represents the relation between the acceleration ‘a’ of the block and the distance ‘x’ traveled by it?

9. In the arrangement, shown below pulleys are mass less and frictionless and threads are in – extensible, block of mass will remain at rest if:

a) b)

b) c)



10. In the arrangement as shown below , Pulleys are mass – less &

strings are light. For what value of M the mass m1

moves with constant velocity (Neglect friction)?a) 4 kg b) 8 kg c) 6 kg d) 10 kg

11. A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statement is / are wrong?

a) b) T = N + W

c) d) N = W tan

12. A boy of mass m with his mass centered at height H is standing in a train moving with constant acceleration a. If this legs are wide spread with a distance 2d and he is not taking the help of any support then normal reactions at his feet are given by:

a) b)

c) d)

13. Blocks A & C starts from rest & moves to the right with acceleration . Here ‘t’ is in seconds. The time when block B again comes to rest is:

a) 1 s b) c) 2 s d)

14. A ball is held at rest in position A by two light cords. The horizontal cord is now cut and the ball swings to the position B. What is the ratio of the tension I the cord in position B to that in position A?a) ¾ b) ½ c)3 d) 1

15. In the shown figure two beads slide along a smooth horizontal rod as shown in figure. The relation between in the shown position will be:

a) b)

c) d)



16. Two masses each equal to m are constrained to move only along x – axis. Initially they are at (-a, 0) and (+a, 0). They are connected by a light string. A force F is applied at at the origin along y – axis resulting into motion of masses towards each other. The acceleration of each mass when position of masses at any instant becomes (-x, 0) and (+x, 0) is given by:

a) b) c) d)

17. All surfaces shown in figure are smooth. System is released with the spring unstretched. In equilibrium, compression in the spring will be:

a) b)

c) d)

18. Find the maximum compression in the spring, if the lower block is shifted to rightwards with acceleration ‘a’. All the surfaces are smooth:

a) b) c) d)

19. A block of mass M is sliding down the plane. Coefficient of static friction is and kinetic friction is

. Then friction force acting on the block is:

a) (F + Mg) sin b)

c) d)

20. The displacement time curve of a particle is shown in the figure. The external force acting on the particles is:a) Acting at the beginning part of motionb) Zeroc) Not zerod) None of these

21. Figure shows a heavy block kept on a frictionless surfaces and being pulled by two ropes of equal mass m. At t = 0, the force on the left rope is withdrawn but the force on the right end continues to act. Let be the magnitudes of he forces acting on the block by the right rope and the left rope on the block respectively, then:



a)

b)

c)

d)

22. In the arrangement shown pulley and thread are mass less. Mass of plate is 20 kg and that of boy is 30 kg. Then:

a) If normal reaction on the boy is equal to weight of the boy then the

force applied on the rope by the boy is (150g/7) Newtonb) If the boy applies no force on the string then the normal reaction

on him is 30 g.c) If the system is in equilibrium then the boy is applying 125

newton force on the roped) None of the above is correct

23. A smooth ring of mass m can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley B and carries a block C of mass 2m as shown below. As the ring starts sliding:

a) The acceleration of the ring is

b) The acceleration of the block is

c) The tension in the string is

d) If the block descends with velocity then the ring slides with

velocity .

24. A block of mass m is kept on an inclined plane of mass 2m and inclination to horizontal. If the whole system is accelerated such that the block does not slip on the wedge then:a) The normal reaction acting on 2m due to m is mg sec b) For the block m to remain at rest with respect to wedge a force

F = 3mg tan must be applied on 2m.c) The normal reaction acting on 2m due to m is mg sec



d) Pseudo force acting on m with respect to ground is mg tan

towards west

25. The car in the given figure moves with constant velocity . When x = 0 ends A and B were coincident at C. Then which of the following sentences is/are correct:

a) The velocity of the block is

b) Acceleration of the block is

c) Acceleration of block A is zerod) Velocity of the block is .

26. Two men of unequal masses hold on to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible?a) The heavier man is stationary while the lighter man moves with some accelerationb) The lighter man is stationary while the heavier man moves with some accelerationc) The lighter man is stationary while the heavier man move with some accelerationd) The two men move with acceleration of the same magnitude in opposite directions

27. In the situation shown in figure F = 500 newton applied on the pulley. and pulley and strings are massless and frictionless. Then the acceleration of the pulley is:

a) b) c) d)

28. In the figure, the pulley P moves to the right with a constant speed u. The downward speed of A is , and the speed of B to the right is :a) b) c) c) The two blocks have acceleration of the same magnitude



29. A box of mass of 10 kg carries a block of mass 2 kg as shown below. The normal reaction acting on 2 kg block is:

a) b) 0 N c) d) 20 N

30. A trolley C can run on a smooth horizontal table. Two, much smaller but equal masses A and B are hung by strings which pass over smooth pulleys. The string are long enough that when C is in equilibrium. A and B both are just on the ground. The trolley is pulled slow to one side and released as shown below. The graph of its velocity against ‘t’ will be as:

31. In the system shown in figure . System is held at rest by thread BP. Just after the thread BP is burnt:a) Magnitude of acceleration of both blocks will be

equal to

b) Acceleration of will be equal to zeroc) Acceleration of will be upwardsd) Magnitude of acceleration of two blocks will be non – zero and unequal

32. A particle is resting over a smooth horizontal floor. At t = 0, a horizontal force starts acting on it. Magnitude of the force increases with time according to law F = at, where ‘a’ is a constant. For figure which of the following statement is / are correct?

a) Curve B indicates velocity against timeb) Curve B indicates velocity against accelerationc) Curve A indicates acceleration against timed) None of these

33. Two particles A & B each of mass m are in equilibrium in a vertical plane under action of a horizontal force F = mg on particle B, as shown in figure. Then:



a) b)

c) d) None of these

34. A body starts to slide from A, down an inclined smooth plane AO having inclination with horizontal and then ascends smooth plane OB. If impact at O is neglected,a) b) c) d) h’ = h e)

35. Figure shows two blocks, each of mass m. The system is released from rest at the position, shown in figure. If initial acceleration of blocks A & B are

respectively and during the motions velocities of A & B are respectively, then:

a) b)

c) d)

36. The magnitude of difference in acceleration of block of mass m in both the cases shown below is:

a) g b) c) zero d) g /31’

37. The block B moves to the right with a constant velocity as shown in the figure. The relative velocity of body A with respect to body B is:(Assume all pulleys and string to be ideal)

a) towards left b) towards

right

c) towards right d) towards

left

38. A particle is observed from two frames . The graph of relative velocity of S1 with respect to S2 is shown in figure. Let be the pseudo forces on the particle when seen from respectively. Which one of the following is not possible?

a) b) c)

d)



39. In the figure the block A, Band C of mass m each, have accelerations

respectively. are external forces of magnitude 2 mg and mg respectively:a) b) c) d)

40. A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown below. Indicate the correct statements: (assume both the friends apply equal forces of equal magnitude)

a) The force exerted by both the friends decreases as the man move up

b) The force applied by each friend is when the man is at

depth of hc) The force exerted by both the friends increases as the man move up

d) The force applied by each friend is

41. Figure shows the displacement of a particle going along the x – axis as a function of time. The force acting on the particle is zero in the region:a) BC b) CD c) AB d) DE

42. In the figure shown pulley is ideal. At t = 0, both masses touches the ground and string is taut. A force F = 2t is applied to pulley (t is in second) then (g = 10 m/s2):a) m2 is lifted off the ground at t = 20 secb) acceleration of pulley when m2 is about to lift off is 5 m/s2 c) m1 is lifted off the ground at t = 10 secd) both blocks are lifted off simultaneously

43. In arrangement shown below, the thread pulley and spring are all massless and there is no friction anywhere. The system is in equilibrium. If thread connecting m4 is cut than just after thread is cut:



a) acceleration of m4 = 0b) acceleration of m1 = c) acceleration of m1 =

d) acceleration of m4 =

44. In the following figure all surfaces are smooth. The system is released from rest, then:a) acceleration of wedge is greater then g sin

b) acceleration of m is

c) acceleration of m is gd) acceleration of wedge is g sin

45. In above question the time taken by m to touch the inclined plane will be:

a) b) c) d) None of these

46. In above question, the normal force acting between:a) wedge and incline plane is Mg cos b) m and wedge is mg cosc) m and wedge is zero d) m and wedge is mg sin

47. In the shown figure, the trolley move with constant acceleration ‘a’ and the string connecting the masses

make constant angles

then:

a) b) tension in the string is mg

c) d) force applied by strings on pulley is

48. In above question if then, acceleration of blocks are:

a) unequal, ground

b) unequal, ground

c) equal, given by w.r.t. trolley

d) equal and acts in a direction making angle with vertical w.r.t.

trolley



SOLUTIONS

1. [C]Component of ‘g’ along the inclined plane = 10 sin 300

= 5 m/sNow component of g sin 300 along the

groove

Now

t = 2 sec



2. [B]For equilibrium

N = T’ + TN = 2T + TN = 3T …(i)N = 600 – T …(ii)

3. [C]Both blocks will moves together

21 = 3 X aa = 7 m/s2

T = 1 X 7 = 7NNet external force on block A = 7 N

4. [A]Tension at all points will be F

rope is not moving, acceleration will be OF – T = 0 F = T

5. [C]Reading in spring balance = T/gT tension in thread connected to springHere system is in equilibrium and T = 20 X g

6. [C]Tension T = 10 X gAlso T’ = T = 10 X g

reading in both spring

7. [A]T = mg …(i)Mg = 2T cos …(ii)

From (i) and (ii)Mg = 2mg cos M = 2m cos M < 2m (as cos < 1)



8. [B]kx = ma

It is a straight line. Here X is the compression in block.In our question X = X0 – xSince X is decreasing with x i.e., spring is coming to natural from and X0 is initial compression.

9. [A]T’ = m1g

… (i)

… (ii)

From (i) and (ii)

Putting value of a

10. [B]Let pulley 2 moves downward with acceleration a’ m1 moves with constant velocity

T = m1 g … (i)

As acceleration of m1 = 0 (a = a’)… (ii)

2T = Ma’2T = Ma … (iii)

[ from (i) and (ii)]

2g – g = 2 X 2a

Put value of T and a in (iii)



M = 8 kg

11. [b]System is in equilibrium

Also, are at right angles

Also

N = W

12. [C]… (i)

Taking torque about O.… (ii)

From (i) and (ii)

13. [D]Block B will come to rest when velocity of block A = velocity of block B

14. [A]



15. [A]As shown in figure

16. [B]2T

For any mass

17. [D]

18. [B]

19. [B]

20. [B]Slope of displacement – time graph gives velocity which is constant here

= constant

21. [C]For t < 0 system is in

equilibrium



For t > 0 system accelerates

22. [A, C]For equilibrium

N + T = 30 g

T = 125 N

23. [A, C]

From (i), (ii) and (iii)



24. [A, B, C]When block does not slip

Mg = N cos N = mg sec

Since block m does not slip on block 2mboth can be taken as one system

N’ = 3mgNormal reaction on 2m by ground = 3 mgAlso from figure 1

And from figure 2 F = 3ma

F = 3mg

25. [A, B]

Differentiating

Differentiating (i) again,

Given

26. [A, C, D]27. [B]

Let acceleration of pulley is aT – 50 = 5 (a + a’)

… (i)T – 100 = 10 (a’ – a)

… (ii)2T = 500 … (iii)

From (i), (ii) and (iii)

28. [A, D]Clearly if B is stationary and pulley moves then block will rise.



29. [C]12g – T + 12a

30. [C]At first B will move downward and C towards right with a constant acceleration and . The moment when B touches ground A will lift up. Now as C is moving toward right A will rise and string between BC will become loose. Therefore block C decelerates with a constant deceleration due to the tension generated in string between A and C. At a certain moment (After this A moves downward). C again accelerates in the opposite direction upto the moment A reaches the ground.

31. [B, C]Just after BP is cutFor block A no force has changed

acceleration of m1 = 0For m2 downward force is being reduced

m2 will move upwards

32. [A, B, C]

Acceleration

i.e., a straight line passing through origin

Parabola

33. [B, C]



From (i) and (ii)

From (iii), (iv) and (v)

34. [D, E]Energy will be conserved

considering horizontal plane as reference line

(P.E. = 0) at A velocity of particle = 0

Also at B

h = h’Clearly MO > ON (from figure)

as h = h’

Similarly

Similarly

As

35. [B]



36. [B, C]In 1st case:

Ma = 2mg – mga = g

In 2nd case:T – mg = ma’

37. [C]Let when A is moved x distance forward then ‘2x’ length string become loose. Also let B then moves y distance forward as clear from figure B requires ‘3y’ length string.

for string to be tight

Relative velocity forward

38. [D]This question is similar to question No.6 this graph has

constant slope

relative acceleration of the two frames is constant

Now proceed similar to A. No.6

39. [A]In 1st case:

In 2nd case:

In 3rd case:



40. [B, C]

As man moves slowly 2T

As man moves upward becomes smalldecreases

T increases

41. [B, C]When ever displacement time graph is a straight line, the velocity is

constant i.e., = constant

42. [A, B, C]2t – 2T = 0 X a

From m1 to lift off T = mg = 10So t = 10 secSimilarly for 2 kg block at t = 20 sec



43. [C, D]In equilibriumAcceleration of each block is zero in

equilibrium

Just after the string is burnt onlyT = 0 and no other force is changed

And acceleration of

44. [C, D]The acceleration of mass ‘m’ and ‘M’ along the inclined plane is g sin so contact for the between them is zero.So mass ‘m’ will fall freely with acceleration g and acceleration of wedge will be g sin .

45. [B]Acceleration of m = g

46. [A, B]As discussed in question No. 33 contact force between ‘m’ and ‘M’ will be zero. So connect for between wedge and inclined wedge will be Mg cos

47. [A, D]Shown:

And

48. [A, C, D]Similarly



Making angle with vertical

If acceleration of each w.r.t. trolley is a’, then as shown in figure.

So



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Newton's Laws of Motion - From asif