Question

A rifle of mass M is initially at rest. A bullet of mass m is fired from the rifle with a velocity v relative to the ground. Which one of the following expressions gives the velocity of the rifle relative to the ground after the bullet is fired?

A) −mv

B) mv

C) Mv/m

D) mv/M

Answer 1

According to law of conservation of momentum, total momentum of the system should remain conserved.

Initially the rifle is at rest and so does the bullet, hence total momentum p of rifle and bullet before shooting is given by

p = M*0 + m*0 = 0+0 = 0

Further, when the bullet is fired from the rifle, both the bullet and the rifle come in motion. According to the question, the velocity of rifle is V and that of bullet is v.

Hence total momentum p' of the system after shooting would be

p' =MV + mv

According to law of conservation of momentum,

p' = p

i.e MV + mv = 0

MV = -mv

or V = -mv/M  

The negative sign indicates that rifle would move in a direction opposite to that in which the bullet is fired. Since the bullet is fired in forward direction, hence the rifle would give a sudden jerk in backward direction.

In magnitude, we can simply write V = mv/M

Hence, option D is the correct answer.