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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 ms−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:C: 2.5m/s

Given Data:

mass of bullet, m1=25g=0.025kg

velocity of bullet before firing, u1=0ms1

velocity of bullet after firing, v1=500ms1
mass of gun,m2=5kg
velocity of gun before firing,u2=0ms1
Let velocity of gun after firing be, v2
From law of conservation of momentum,

m1u1+m2u2=m1v1+m2v2

m1×0+m2×0=0.025×500+5×v2

0=12.5+5v2

v2=12.55=2.5ms1

This means gun moves in opposite direction to bullet, which is called recoil.

Thus, recoil velocity of gun is equal to

2.5ms1

Here, the negative(- ve) sign shows that gun moves in the opposite direction of bullet.


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