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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 ms1 after firing from the gun.


  1. 10 ms1
  2. 25 ms1

  3. 2.5 ms1
  4. 5 ms1


Solution

The correct option is C 2.5 ms1

Given, mass of bullet (m1) = 25 g = 0.025 kg
velocity of bullet before firing (u1) = 0
velocity of bullet after firing (v1)=500 ms1
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 ms1

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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