Question

A 50 g bullet moving with a velocity of 10${ms}^{-1}$ gets embedded into a 950$g$ stationary body. The loss in $KE$ of the system will be

• A. 95$\%$
• B. 100$\%$
• C. 5$\%$
• D. 50$\%$

Answer 1

The correct option is A 95$\%$

$Letthespeedofmasswhenitstrucktheblocksisvm/s$

$Thecombinedvelocityoftheblockandthemassaftercollisionis$

$\left(\frac{950+50}{50}\right)v=\frac{v}{20}$

$InitialK.E=\frac{1}{2}\times 50\times {10}^{-3}{v}^2=\frac{v^2}{40}$

$FinalK.E=\frac{1}{2}\times 1\times \frac{v^2}{800}=\frac{v^2}{800}$

$\Delta K.E=\frac{\frac{v^2}{40}-\frac{v^2}{800}}{\frac{v^2}{40}}\times 100=95\%$

Hence,

option $\left(A\right)$ is correct answer.