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

Hint: 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
${E_K} = \dfrac{1}{2}M{V^2},E = {E_T} + {E_R}$