A bullet from a gun is fired on a rectangular wooden block with velocity \( u \). When bullet travels \( 24\text{ cm} \) 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 :

Using \( v^2 = u^2 + 2as \): For first part, \( (\frac{u}{3})^2 = u^2 + 2a(24) \implies -\frac{8}{9}u^2 = 48a \). For total distance \( L \): \( 0 = u^2 + 2aL \implies u^2 = -2aL \). Dividing the two equations: \( \frac{8}{9} = \frac{48}{L} \implies L = 48 \times \frac{9}{8} = 54\text{ cm}\dots\text{ Wait, let's recalculate:} \frac{u^2}{9} - u^2 = 2a(24) \implies -\frac{8}{9}u^2 = 48a \implies a = -\frac{u^2}{54} \). For rest: \( 0 = (\frac{u}{3})^2 + 2a x' \implies -\frac{u^2}{9} = 2(-\frac{u^2}{54}) x' \implies x' = 3\text{ cm} \). Total length \( L = 24 + 3 = 27\text{ cm} \).