Question

A bullet weighing $30g$ is fired at a speed of $120m{s}^{-1}$. If the gun recoils with a speed of $4m{s}^{-1}$, find the mass of the gun.

• A. $360g$
• B. $480g$
• C. $640g$
• D. $900g$

Answer 1

The correct option is D $900g$

Let $M$ and $V$ be the mass and velocity of the gun respectively.
Let $m$ and $v$ be the mass and velocity of the bullet respectively.

Given: $v=120m{s}^{-1}$, $m=30g=0.03kg$, $V=-4m{s}^{-1}$. The negative sign indicates that the recoil velocity is opposite to the direction of the bullet velocity.

Initial momentum of the system = $0$ (as both gun and bullet are at rest)
Final momentum of the system = $MV+mv$

Using the law of conservation of momentum:
When no external force is applied to the gun-bullet system,
Initial momentum + Final momentum = 0,
$0+(MV+mv)=0$
$\Rightarrow M=-\frac{mv}{V}=-\left(\frac{0.03\times 120}{-4}\right)$
$\Rightarrow M=900g$
Therefore, the mass of the gun is $900g$