Q 11-02-007NEETNEET 2023Top questionMedium
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 $\dfrac{u}{3}$. 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 :
Answer: (A) $27$ cm
Assume uniform retardation $a$.
First $24$ cm: $\left(\dfrac{u}{3}\right)^2 = u^2 - 2a(24)$, so $48a = \dfrac{8u^2}{9}$.
Whole length $L$ (from $u$ to rest): $u^2 = 2aL$.
Dividing:
$$\frac{2aL}{48a} = \frac{u^2}{8u^2/9} = \frac{9}{8} \;\Rightarrow\; L = 24 \times \frac{9}{8} = 27\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics