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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
Explanation
Work-energy theorem for both stages gives total length $d=24\times\frac{9}{8}=27\ cm$.
Detailed Solution
$\frac{1}{2}m\left(\frac{u}{3}\right)^2-\frac{1}{2}mu^2=-F_R\times24$
$0-\frac{1}{2}mu^2=-F_R\times d$
$\frac{\frac{1}{2}mu^2}{\frac{1}{2}mu^2\times\frac{8}{9}}=\frac{d}{24}$
$d=24\times\frac{9}{8}=27\ cm$