Question

A bullet is fired normally towards an immovable wooden block. It loses $25\%$ of its kinetic energy in penetrating through a thickness $x$ of the plank. The total thickness penetrated by the bullet into the block is:

• A. $4x$
• B. $6x$
• C. $8x$
• D. $2x$

Answer 1

Answer: (A)

$4x$

Let's consider the initial KE of the bullet is $K$ and the resistance force experienced by the bullet is $F$.
Now, by using the work-energy theorem for the first case,
Loss in KE = Work done

$\Rightarrow \frac{K}{4}=Fx$
$\Rightarrow K=4Fx$ ---------(1)

We know the bullet will stop when kinetic energy is $0$.

Hence, the change in KE will be $K$. Considering the total thickness penetrated by the bullet to be y.
Then using work-energy theorem,

$K=Fy$ --------------(2)
From equation (1) and (2):
$K=4Fx=Fy$
$\Rightarrow y=4x$
Hence, the correct option is $\left(A\right)$