﻿ A machine gun fires a bullet of mass 40 g with a velocity 1200 ms−1. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most? | Laws of Motion

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# Laws of Motion

#### Multiple Choice Questions

1.

Out of the following pair, which one does NOT have identical dimensions is

• angular momentum and Planck’s constant

• impulse and momentum

• moment of inertia and moment of a force

• moment of inertia and moment of a force

C.

moment of inertia and moment of a force

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# 2.A machine gun fires a bullet of mass 40 g with a velocity 1200 ms−1. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most? one  Four Two Two

D.

Two

The force exerted by machine gun on man's hand in firing a bullet = change in momentum per second on a bullet or rate of change of momentum

The force exerted by man on machine gun = 144 N Hence, number of bullets fired =144/48 = 3

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3.
A block rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take g = 10 m/s2 )
• 2.0

• 4.0

• 1.6

• 1.6

A.

2.0

Let the mass of block be m.
Frictional force in rest position
F = mg sin 30

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4.

A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3 M and a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

• depends on height of breaking

• does not shift

• body C

• body C

B.

does not shift

No horizontal external force is acting
∴ = acm =0
since vcm= 0
∴∆xcm = 0

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5.

The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

• 2sinφ

• 2cosφ

• 2tanφ
• 2tanφ

C.

2tanφ
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6.

An annular ring with inner and outer radii R1 and R2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1/F2 is

• R1/R2

• (R1/R2)2

• 1

• 1

A.

R1/R2

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7.

A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A.

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8.

A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?

• h/9 metres from the ground

• 7h/9 metres from the ground

• 8h/9 metres from the ground

• 8h/9 metres from the ground

C.

8h/9 metres from the ground

second law of motion
therefore s = h/9 m
Hence, the position of ball from the ground= h- h/9 = 8h/9 m

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9.

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

• 3.0 cm

• 2.0 cm

• 1.5 cm

• 1.5 cm

D.

1.5 cm

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10.

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 cm. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

• 20 m

• 40 m

• 60 m

• 60 m

D.

60 m

Third equation of motion gives
v2 = u2 + 2as ⇒ 2
s ∝ u (since v = 0)
where a = retardation of body in both the cases

therefore,  .... (i)

Here, s1 = 20 m, u1 = 60 km/h, u2 = 120 km/h. Putting the given values in eq. (i), we get

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