Question

Find the recoil velocity of a gun having a mass equal to 5 kg, if a bullet of 25 g acquires the velocity of 500 m/s after firing from the gun.

• A. 2.5 m/s
• B. 2.5 m/s
• C. 10 m/s
• D. 5 m/s

Answer 1

The correct option is B

2.5 m/s

Here given,
Mass of bullet $\left(m_1\right)=25g=0.025kg$
Velocity of bullet before firing $\left(u_1\right)=0$
Velocity of bullet after firing $\left(v_1\right)=500m/s$
Mass of gun $\left(m_2\right)=5kg$
Velocity of gun before firing, $\left(u_2\right)=0$
Velocity of gun after firing = ?
We know that,$m_1{u}_1+m_2{u}_2$$=m_1{v}_1+m_2{v}_2$
$0.025kg\times 0+5kg\times 0$$=0.025kg\times 500m/s+5kg\times v_2$
$0=12.5kgm/s+5kg\times v_2$
$5kg\times v_2=-12.5kgm/s$
$v_2=\frac{12.5kgm/s}{5kg}=2.5m/s$
Thus, recoil velocity of gun is equal to 2.5 m/s. Here negative (- ve) sign shows that gun moves in the opposite direction of bullet.