Question 44: 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 :
(1) 28 cm
(2) 30 cm
(3) 27 cm
(4) 24 cm
Answer: Option (3)
Explanation:
The bullet moves through the wooden block under uniform retardation due to resistive force.
Using the equation of motion v^{2}=u^{2}+2as.
After travelling s_{1}=24 \mathrm{~cm}, the velocity becomes v=\frac{u}{3}.
Substituting in the equation,
\left(\frac{u}{3}\right)^{2}=u^{2}+2a(24).
This gives,
\frac{u^{2}}{9}-u^{2}=48a.
-\frac{8u^{2}}{9}=48a.
a=-\frac{u^{2}}{54}.
Now, the bullet finally comes to rest at the other end of the block,
so final velocity v=0. Let the total length of the block be S.
Again using v^{2}=u^{2}+2aS,
0=u^{2}+2\left(-\frac{u^{2}}{54}\right)S.
u^{2}=\frac{2u^{2}S}{54}.
1=\frac{S}{27}.
S=27 \mathrm{~cm}.
Hence, the total length of the block is 27 cm.
Therefore, the correct answer is Option (3).