Question

# Calculate the recoil velocity of a gun having mass equal to 5 kg, if a bullet of 25 g acquires the velocity of 500 msâˆ’1 after firing from the gun.

A

25 ms1

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B
2.5 ms1
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C
10 ms1
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D
5 ms1
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Solution

## The correct option is B 2.5 ms−1Given, mass of bullet (m1) = 25 g = 0.025 kg velocity of bullet before firing (u1) = 0 velocity of bullet after firing (v1)=500 ms−1 mass of gun (m2) = 5 kg velocity of gun before firing (u2) = 0 Let velocity of gun after firing be v2 From law of conservation of momentum, m1u1+m2u2 = m1v1+m2v2 ⇒ (0.025×0)+(5×0)=(0.025×500)+(5×v2) ⇒0=12.5+(5×v2) ⇒5×v2=−12.5 ⇒ v2=−12.55=−2.5 ms−1 Thus, recoil velocity of gun is equal to 2.5ms−1. Here, the negative(- ve) sign shows that gun moves in the opposite direction of bullet.

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