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:

27 cm

$\text{Let retardation provided by wooden block is uniform and its equal to -a then}$ 

$ (\frac{u}{3})^2 - u^2 = -2a\times 24 \Rightarrow \frac{-8u^2}{9} = -48a \Rightarrow u^2 = 54a$

$ \text{For next part of the block , Final velocity becomes zero}\Rightarrow 0 ^2 - (\frac{u}{3})^2 = -2as$

$ s = \frac{u^2}{18a} = \frac{54a}{18a} = 3cm$

$\text{Total length of the block is } L = 24cm + 3cm = 27cm$