Question

A bullet is fired morally towards an immovable wooden block. It loses $25\%$of its kinetic energy in penetrating through a thickness $x$ of the plank the bullet into the block is:
(A) $4x$
(B) $6x$
(C) $8x$
(D) $2x$

Answer 1

We know that kinetic energy is defined as the work needed to accelerate a body to a given mass from nest to its stated velocity on gaming this energy the body maintains until its speed changes.
Loss in kinetic energy $= work{\text{ }}done$

Complete step by step answer:
We can consider the initial kinetic energy of the bullet is k and the resistance force experienced by the resistance the bullet is f now by using the work energy theorem for the first case.
Loss in kinetic energy $= work{\text{ }}done$
$\Rightarrow \dfrac{k}{4} = fx \\\ \Rightarrow 4kx.......(1) \\\$
We know the bullet will stop when kinetic energy is
Hence the change in kinetic energy will be$k$.

Considering the bullet to be $y$
Then using work energy theorem
$k = fy.....(2)$
Form equation $\left( 1 \right)and{\text{ }}\left( 2 \right)$
$k = 4fx = fy \\\ y = 4x \\\$

So, the correct answer is “Option A”.

Note:
In physics the kinetic energy of an object is the energy that it derives due to its motion. Derivation form other quantities is
${E_K} = \dfrac{1}{2}M{V^2},E = {E_T} + {E_R}$