Question

A gun weighing 4 kg fires a bullet of 40 g with a velocity of 500 $m{s}^{-1}$. Find the velocity with which the gun recoils.

• A. 5 $m{s}^{-1}$
• B. 10 $m{s}^{-1}$
• C. 20 $m{s}^{-1}$
• D. 4 $m{s}^{-1}$

Answer 1

The correct option is A 5 $m{s}^{-1}$

By the law conservation of momentum:
$m_g$$u_g$ + $m_b$$u_b$ = $m_g$$v_g$ + $m_b$$v_b$
4 × 0 + 0.04 × 0 = 4 × $v_g$ + 0.04 × 500
(The initial velocity of the gun and bullet is zero as they are at rest.)
$v_g$ = $\frac{-0.04\times 500}{4}$
$v_g$ = - 5 $m{s}^{-1}$
Here, the negative sign indicates that the velocity is in the opposite direction to the motion of the bullet.