Question

A bullet of 5 $g$ is fired from a pistol of 1.5 kg. If the recoil velocity of a pistol is 1.5 $\frac{m}{s}$. What is the velocity of the bullet?

• A. 450 m/s
• B. 400 m/s
• C. 500 m/s
• D. 600 m/s

Answer 1

The correct option is A

450 m/s

Here we have,
$Massofbullet,m_1=5g=\frac{5}{1000}$ $kg$ = 0.005 $kg$
$Massofpistol,m_2=1.5kg$
$Recoilvelocityofpistol{v}_2=1.5m/s$
$Velocityofbullet{v}_1$= ?
Since, before firing, the bullet and pistol are in rest, thus
Initial velocity of bullet, $u_1=0$
And initial recoil velocity of pistol, $u_2=0$
We know that,
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$(0.005kg\times 0)+(1.5kg\times 0)=(0.005kg\times v_1)+(1.5kg\times 1.5m/s)$
$0=(0.005kg\times v_1)+\left(2.25kgm/s\right)$
$0.005kg\times v_1=-\left(2.25kgm/s\right)$
$v_1=\frac{-2.25kgm/s}{0.005kg}=-450m/s$
Thus, velocity of bullet = 450 $\frac{m}{s}$, here negative sign indicates that bullet moves in the opposite direction of recoiling of the gun.