Question

A bullet of $4\text{g}$ mass is fired from a gun of mass $4\text{kg}$. If the bullet moves with the muzzle speed of $50{\text{ms}}^{–1}$, the impulse imparted to the gun and velocity of recoil of gun are :

• A. $0.4{\text{kg ms}}^{-1},0.05{\text{ms}}^{-1}$
• B. $0.4{\text{kg ms}}^{-1},0.1{\text{ms}}^{-1}$
• C. $0.2{\text{kg ms}}^{-1},0.1{\text{ms}}^{-1}$
• D. $0.2{\text{kg ms}}^{-1},0.05{\text{ms}}^{-1}$

Answer 1

The correct option is D $0.2{\text{kg ms}}^{-1},0.05{\text{ms}}^{-1}$


$\text{By momentum conservation}$

$4\times {10}^{–3}(50–v)–4v=0$

$\Rightarrow v=\frac{4\times {10}^{-3}\times 50}{4+4\times {10}^{-3}}\approx 0.05{\text{ms}}^{-1}$

$\text{Impulse}J=mv=4\times .05=0.2{\text{kg ms}}^{–1}$

Hence, $\left(B\right)$ is the correct answer.