2023 Work, Energy and PowerWork-Energy Theorem Hard Question 3 of 9 in Work-Energy Theorem

A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels $24\ cm$ through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

A 30 cm
B 27 cm
C 24 cm
D 28 cm

The answer is B.

Solution

Work-energy theorem for both stages gives total length $d=24\times\frac{9}{8}=27\ cm$.

$\frac{1}{2}m\left(\frac{u}{3}\right)^2-\frac{1}{2}mu^2=-F_R\times24$ $0-\frac{1}{2}mu^2=-F_R\times d$ $\frac{\frac{1}{2}mu^2}{\frac{1}{2}mu^2\times\frac{8}{9}}=\frac{d}{24}$ $d=24\times\frac{9}{8}=27\ cm$

Concept bullet penetrating a block

Work-Energy Theorem in past papers

9 questions from this chapter have appeared across 9 exam years.