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Question

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s¯¹, what is the recoil speed of the gun ?

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Solution

Given: The mass of shell is 0.020 kg, mass of gun is 100 kg and the muzzle speed of the shell is 80 ms 1 .

Initially, both the gun and the shell are at rest therefore, the initial momentum of the system is zero.

The final momentum of the system is given as,

p f =mv+MV

Where, m is the mass of shell, M is the mass of gun, v is the velocity of shell and V is the recoil velocity of gun.

From the conservation of momentum,

p f = p i mv+MV=0

By substituting the given values in the above equation, we get

0.020×80+100×V=0 V= 0.020×80 100 =0.016 ms 1 =1.6 cms 1

Thus, the recoil velocity of gun is 1.6 cms 1 .


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