A bullet of mass m leaves a gun of mass M kept on a smooth horizontal surface. If the speed of the bullet relative to the gun is v , the magnitude of recoil speed of the gun will be

Question

A bullet of mass m leaves a gun of mass M kept on a smooth horizontal surface. If the speed of the bullet relative to the gun is v , the magnitude of recoil speed of the gun will be, m M v, m M + m v, m M - m v, M m v

MARKS App · Accepted Answer

Speed of the bullet relative to ground v → b = v → + v → r , where v r is recoil velocity of gun. Now for gun-bullet system applying the conservation law of momentum, we get m v → b + M v → r = 0 or m v → + v → r + M v → r = 0 ⇒ v → r = - m v → m + M or v r = m v m + M

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