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Standard XII

Physics

Relative Velocity

A machine gun...

Question

A machine gun is mounted on a flat railroad car. The gun is firing bullets at the rate of $10$ bullets per second each of mass $10 g$ . The bullets are fired at velocity $500 {m s}^{- 1}$ relative to the car. Calculate the acceleration and force of car at the instant when its mass is $200 k g$ .

0.25 {m s}^{- 2}, 50 N

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2.5 {m s}^{- 2}, 500 N

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25 {m s}^{- 2}, 50 N

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8 {m s}^{- 2}, 1600 N

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Solution

The correct option is B $0.25 {m s}^{- 2}, 50 N$
Here the reacting force, $F = v e l o c i t y \times t o t a l m a s s o f b u l l e t p e r s e c o n d$ .
$∴ F = 500 \times \frac{10 \times 10}{1000} = 50 N$
Acceleration, $a = \frac{F}{m} = \frac{50}{200} = 0.25 m / s^{2}$

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A machine gun is mounted on a flat railroad car. The gun is firing bullets at the rate of 10 bullets per second each of mass 10g. The bullets are fired at velocity 500ms−1 relative to the car. Calculate the acceleration and force of car at the instant when its mass is 200kg.

The correct option is B 0.25ms−2,50NHere the reacting force, F=velocity×total mass of bullet per second.∴F=500×10×101000=50 NAcceleration, a=Fm=50200=0.25 m/s2

A machine gun is mounted on a flat railroad car. The gun is firing bullets at the rate of $10$ bullets per second each of mass $10 g$ . The bullets are fired at velocity $500 {m s}^{- 1}$ relative to the car. Calculate the acceleration and force of car at the instant when its mass is $200 k g$ .

The correct option is B $0.25 {m s}^{- 2}, 50 N$
Here the reacting force, $F = v e l o c i t y \times t o t a l m a s s o f b u l l e t p e r s e c o n d$ .
$∴ F = 500 \times \frac{10 \times 10}{1000} = 50 N$
Acceleration, $a = \frac{F}{m} = \frac{50}{200} = 0.25 m / s^{2}$