Question

A bullet of $25\text{g}$ acquires the velocity of $500{\text{m s}}^{-1}$ after firing from the gun. Find the recoil velocity of a gun having a mass equal to $5\text{kg}$.

• A. $25{\text{m s}}^{-1}$
• B. $2.5{\text{m s}}^{-1}$
• C. $10{\text{m s}}^{-1}$
• D. $5{\text{m s}}^{-1}$

Answer 1

The correct option is B $2.5{\text{m s}}^{-1}$

Given:

Mass of bullet, $\left({\text{m}}_1\right)=25\text{g}=0.025\text{kg}$

Velocity of bullet before firing, $\left({\text{u}}_1\right)=0$

Velocity of bullet after firing, $\left({\text{v}}_1\right)=500{\text{m s}}^{-1}$

Mass of gun, $\left({\text{m}}_1\right)=5\text{kg}$

Velocity of gun before firing, $\left({\text{u}}_2\right)=0$

Velocity of gun after firing = ${\text{v}}_2$

We know that, ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{u}}_2={\text{m}}_1{\text{v}}_1+{\text{m}}_2{\text{v}}_2$

$0.025\times 0+5\times 0$ = $0.025\times 500$ + $5\times {\text{v}}_2$

$0=12.5+5\times {\text{v}}_2$

${\text{v}}_2=\frac{-12.5}{5}=-2.5{\text{m s}}^{-1}$

Thus, recoil velocity of gun is equal to $2.5{\text{m s}}^{-1}$. Here, the negative sign shows that gun moves in the opposite direction of that of the bullet.