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A $60 g$ bullet fired from a $5 kg$ gun travels at $500 m / s$ . What would be the recoil velocity of the gun?

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4 m / s

5 m / s

6 m / s

7 m / s

answer is C.

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Detailed Solution

When a

60 g

bullet is fired from a

5 kg

gun that travels at

500 m / s

, the recoil velocity of the gun would be

6 m / s

.
Weight of the bullet (

m_{1})

60 g,

= 60 \times 10^{- 3} kg

= 0.06 kg

Bullet velocity

(v_{1})

is given as

500 m / s

The mass of the gun

m_{2}

5 kg

Let

v_{2}

be the recoil velocity.
According to the law of conservation of momentum
When two objects collide with each other , the sum of their momentum remains conserved when no external force is applied on the bodies. Therefore

m_{1} \times v_{1} = m_{2} \times v_{2}

\Rightarrow 0.06 \times 500 = 5 \times v_{2}

\Rightarrow v_{2} = \frac{0.06 \times 500}{5}

\Rightarrow v_{2} = 6 m / s

Therefore, the recoil speed of the gun is

6 m / s

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