A bullet from a gun is fired on a rectangular wooden block with v… - Vidyadip

MCQ

A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels 16 cm through the block along its length horizontally, velocity of bullet become $\frac{2 u}{3}$. 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
28.7cm
B
27.7cm
✓
28.8 cm
D
28.9 cm

✓

Answer

Correct option: C.

28.8 cm

(C)
$\begin{array}{l}\frac{1}{2} m\left(\frac{2 u}{3}\right)^2-\frac{1}{2} m u^2=-F_R \times 160 \\ 0-\frac{1}{2} m u^2=-F_R \times d \\ \frac{\frac{1}{2} m u^2}{\frac{1}{2} m u^2 \times \frac{5}{9}}=\frac{d}{16} \\ d=\frac{16 \times 9}{5}=28.8 cm\end{array}$

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