DPP_NLM-I

NEWTON’S LAWS OF MOTION – I

1 DPP – 1

1.

2.

6N

Two forces of 6N and 3N are acting on the two blocks of masses 2 kg and 1 kg respectively kept on frictionless horizontal floor. The force exerted on 2 kg block by 1 kg block is (a) 1N (b) 2N (c) 4N

2 kg 1 kg

3N

(d) 5N

In the given figure, all the strings are ideal. The ratio of tension T4 and T3 is (a) 1 : 1 (b) 1 : 3 (c) 3 : 1 (d) 2 : 1

60° T5 T4 T2

30° T3 T1 10 kg

3.

A block of weight 9.8 N is placed on a table. The table surface exerts an upward force of 10N on the block. Choose the correct alternative (Assume g = 9.8 m/s2) (a) the block exerts a force of 10N on the table (b) the block exerts a force of 19.8N on the table (c) the block exerts a force of 9.8N on the table (d) the block has downward acceleration.

4.

A block tied between two springs is in equilibrium. If upper spring is cut then the acceleration of the block just after cut is 6 m/s2 downwards. Now, if instead of upper spring, lower spring is being cut then the magnitude of acceleration of the block just after the cut will be (Take g = 10 m/s2) (a) 16 m/s2 (b) 4 m/s2 (c) 8 m/s2

5.

P

The minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane will be  (a) Mg tan   2 Mg cos  (c) 1  sin 

6.

(d) 12 m/s2 

M 

 (b) Mg cot  2

(d) None of these

Two smooth cylindrical bars weighing W N each lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, find the minimum horizontal force (in N) on each lower bar necessary to keep them in contact.(Take W = 20 3 N)

F

F

NEWTON’S LAWS OF MOTION – I

2

7.

A flexible chain of weight 10 N hangs between two fixed points A and B which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is 45°. Find the tension (in N) of the chain at the mid point.

8.

The system shown is in equilibrium. Find the ratio of acceleration of the blocks A and B at the instant when the spring between ceiling and A is cut. All the blocks have equal mass and the springs are ideal.

K A B K C

NEWTON’S LAWS OF MOTION – I

3 DPP – 2

1.

2.

3.

Two blocks A and B of mass 10 kg and 40 kg are connected by an ideal string as shown in the figure. Neglect the masses of the pulleys and effect of friction. Choose the correct alternative 5 ms–2 (a) the acceleration of block A is 2 2 5 (b) the acceleration of block B is ms–2 2 2 (c) the acceleration of block B is 5 ms–2 (d) the acceleration of block A is 10 ms–2 Block A has a velocity of 0.6 m/s to the right. The velocity of block B in m/s is (a) 0.6 (b) 1.8 (c) 1.2 (d) 2 A trolley C shown in the figure is driven with an acceleration a = 3 m/s2. The ratio of acceleration of the bodies A and B of masses 10 kg & 5 kg respectively is (assume pulleys are massless and friction is absent everywhere) (a) 2 : 1 (b) 1 : 3 (c) 1 : 1 (d) 2 : 3

B

A

45°

45°

A B

C

a

B A

4.

A man of mass m slides down along a rope which is connected to the ceiling of an elevator retarding with acceleration a relative to the rope. If elevator is going upwards with an acceleration a relative to the ground then tension in the rope is (a) mg (b) m (g + 2a) (c) m (g + a) (d) m (g + 3a)

5.

A 10 kg object is to be lowered down from a height using a cord with breaking strength of 80N. The object should be (a) lowered very slowly (b) lowered with an acceleration less than 2 m/s2 (c) lowered with an acceleration greater than 2 m/s2 (d) object cannot be lowered down without breaking the cord.

6.

A heavy spherical ball is constrained in a frame as shown in figure. The inclined surface is smooth. The maximum acceleration with which the frame can move without causing the ball to leave the frame is n . Find value of n. 3

30°

a

NEWTON’S LAWS OF MOTION – I

7.

The velocities of A and B are shown in the figure. Find the speed (in m/s) of block C. (Assume that the pulleys and string are ideal)

8.

A 1 kg block B rests on a bracket A of same mass as shown in figure. Constant forces F1 = 20N and F2 = 8N start acting at time t = 0. The distance of block B from pulley is 50 m at t = 0. Determine the time (in s) when block B reaches the pulley.

9.

4

50m

F2

F1 B A

Two men A and B of equal mass are holding the free ends of a massless rope which passes over a frictionless light pulley. Man A climbs up the rope with acceleration 10 m/s2 relative to the rope while man B hangs on without climbing. Find the acceleration (in m/s2) of the man B with respect to ground.

NEWTON’S LAWS OF MOTION – I

5 DPP – 3

1.

2.

Two equal heavy spheres, each of radius r are in equilibrium within a smooth cup of radius 3r. The ratio of normal reaction between the cup and one sphere and that between the spheres is (a) 1 (b) 2 (c) 3 (d) none of these

3r r

In the given figure block of mass M is moving up with acceleration ‘a’. The acceleration of block of mass m is a (a) (b) 15 a 15 a (c) (d) 7 a 7

a m

M

4.

5.

6.

In the figure shown, blocks A and B are moving with velocities v1 and v2 along horizontal direction. The ratio v of 1 at the given moment is v2 cos 1 cos  2 (b) (a) cos  2 cos 1 sin 1 sin  2 (c) (d) sin  2 sin 1

1 A

In the system shown in figure, all the surfaces are smooth. Rod is moved by external agent with acceleration 9 m/s2 vertically downwards. Force exerted on the rod by the wedge will be (a) 120 N (b) 200 N (c) 135/2 N (d) 225/2 N

B

v2

10kg

37°

In the figure shown man is balanced by counter weight of same mass. He starts to climb the rope with an acceleration of 2 m/s2. The time after which he reaches the pulley will be (a) 10 sec (b) 2 5 sec (c) infinity (d) none of these If acceleration of A is 2 m/s2 to left and acceleration of B is 1 m/s2 to left, then acceleration of C will be (a) 1 m/s2 upwards (b) 1 m/s2 downwards (c) 2 m/s2 downwards (d) 2 m/s2 upwards

2

v1

9 m/s2

3.

10m 30kg

B

A

C

NEWTON’S LAWS OF MOTION – I

7.

8.

9.

In the situation given, all surfaces are frictionless. If F = n Mg/2, the ratio of accelerations of blocks A and B is . 5 Find value of n. (Both the blocks have mass M) A block B is kept on an inclined plane. Another block A is inserted in a slot in the block B through a light string. One end of the string is fixed to a support and other end of the string is attached to A. All the surfaces are smooth. Masses of A and B are same. The acceleration of block B is found to be 4/n. Find value of n. (sin37° = 3/5)

6

F A

x y

B

S A B 37°

Starting from rest, the cable is wound onto the drum of the motor at a rate of vA = (24t2)m/s, where t in seconds. Determine the time (in s) needed to lift the load by a distance of 27m.

NEWTON’S LAWS OF MOTION – I

7 DPP – 4

1.

2.

In the figure at the free end of the light string, a force F is applied to keep the suspended mass of 18 kg at rest. Assuming pulleys to be light, the force exerted by the ceiling on the system is (a) 200 N (b) 120 N (c) 180 N (d) 240 N

18 kg

A steel ball is suspended from the ceiling of an accelerating carriage by means of two cords A and B. The acceleration a of the carriage which will cause the tension in A to be twice that in B will be (a)

g

(b)

3 3 g (c) 3 2

3.

F

60° 60° B

a

A

g

2 3 g (d) 3

Two containers of sand S and H are arranged in figure I. The containers alone have negligible mass. The sand in them has a total mass Mtot. The sand in the hanging container H has mass m. The magnitude a of the acceleration of the system in a series of experiments is to be measured where m varies from experiment to experiment but Mtot does not, that is m is taken on the x-axis for sand is to be shifted between the containers before each trial. M tot all the plots and acceleration and tension in the string are taken on the y-axis.

The plot which gives the variation of acceleration magnitude of the containers (taken on yaxis) is y y y y

(a) 0

m M tot

1.0 (b) 0

m M tot

1.0 (c) 0

m M tot

1.0 (d) 0

m M tot

1.0

NEWTON’S LAWS OF MOTION – I

4.

In the above problem, the plot which gives variation of tension in the connecting string (taken on y-axis) is y y y y

(a) 0

m

1.0 (b) 0

M tot

5.

(a) 0

1.0 (c) 0

m

M tot

y

m M tot

7.

m

1.0 (d) 0

m

M tot

1.0

M tot

In the above problem, if net force on container H is taken on the y-axis, the plot which gives the variation of magnitude of net force, on container H is

y

6.

8

1.0 (b) 0

y

m

y

1.0 (c) 0

m

M tot

A 20 kg block B is suspended from an ideal string attached to a 40 kg block A. The ratio of the acceleration of the block B in cases (i) and (ii) shown in figure immediately after the system is released 3n . Find value of n. from rest is 2 2 (Neglect friction)

1.0 (d) 0

m

M tot

B

A

Case (i)

1.0

M tot

A B Case (ii)

In figure shown, pulleys are ideal. Initially the system is in equilibrium and the string connecting m2 to rigid support is cut. Find the initial acceleration (in m/s2) of m2. (Take m1 = 15 kg, m2 = 5 kg) m2 m1

8.

In the given figure, find the velocity (in cm/s) and acceleration (in m/s2) of B, if velocity and acceleration of A are as shown.