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

Solution

## The correct option is B $$4x$$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$$\Rightarrow \dfrac {K}{4}=Fx$$$$\Rightarrow K=4Fx$$ ---------(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 $$(A)$$Physics

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