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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
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B
6x
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C
8x
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D
2x
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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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