Question

A bullet of $5g$ is fired from a pistol of $1.5kg$. If the recoil speed of pistol is $1.5m{s}^{-1}$, find the velocity of bullet.

• A. $450m{s}^{-1}$
• B. $400m{s}^{-1}$
• C. $500m{s}^{-1}$
• D. $600m{s}^{-1}$

Answer 1

The correct option is A

$450m{s}^{-1}$

Given:
Mass of the bullet:
$m_1=5g=5\times {10}^{-3}kg$
Mass of the pistol, $m_2=1.5kg$
Recoil speed of the pistol, $v_2=1.5m{s}^{-1}$

Let the velocity of the bullet be $v_1$

Before firing, the bullet and pistol are in rest. Hence,
Initial speed of bullet, $u_1$=0
Initial speed of pistol, $u_2$ = 0

From law of conservation of momentum, initial and final momentums are equal.
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$0=(5\times {10}^{-3}\times v_1)+(1.5\times 1.5)$
$v_1=-450m{s}^{-1}$

Thus, speed of the bullet is $450m{s}^{-1}$.
Negative sign shows that bullet moves in the direction opposite to the direction of recoiling of the gun.