Question

State the relation between magnitude of velocity of the gun and bullet after firing, if the mass of gun is less than the mass of bullet? Assume no external force is acting on the gun bullet system.

Answer 1

The law of conservation of momentum can be applied in this as no external force is applied on the system $m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
where $m_1$ is mass of bullet.
$m_2$ is mass of gun.
$u_1$ is initial velocity of bullet.
$u_2$ is initial velocity of gun.
$v_1$ is final velocity of bullet.
$v_2$ is final velocity of gun.

Initially the bullet is resting in the gun.
So initial momentum is zero.
$0=m_1{v}_1+m_2{v}_2$ $\frac{v_2}{v_1}=-\frac{m_1}{m_2}$
Negative sign indicates the opposite directions of the velocities.

In this case, the mass of the bullet is higher than the mass of the gun.
Thus, the velocity of the gun is higher than the velocity of the bullet.