Question

A bullet is fired at a speed of $300m{s}^{-1}$ from a gun of mass $2kg$. If the gun recoils with a speed of $2.4m{s}^{-1}$, find the mass of the bullet.

• A. $16g$
• B. $20g$
• C. $24g$
• D. $28g$

Answer 1

The correct option is A $16g$

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

Given: $v=300m{s}^{-1}$, $M=2kg$, $V=-2.4m{s}^{-1}$. The negative sign indicates that the recoil velocity of gun is opposite to the direction of 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,
$0+(mv+MV)=0\Rightarrow m=\frac{-MV}{v}$
$\Rightarrow m=\frac{-(2\times -2.4)}{300}=0.016kg=0.016\times 1000=16g$
Therefore, the mass of the bullet is $16g$