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Question

A bullet fired into a fixed target looses half of its velocity in penetrating $$15 \;cm$$. Before coming to rest, it can penetrate a further distance of:


A
5cm
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B
15cm
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C
7.5cm
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D
10cm
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Solution

The correct option is A $$5 cm$$
Assuming that the bullet has only Kinetic Energy ($$KE$$ ) initially.
Let initial velocity be $$v$$.

So, final  velocity  is $$v/2$$.

Energy  lost is  $$\dfrac{1}{2}mv^{2} - \dfrac{1}{2}m(v/2)^{2} = \dfrac{1}{2} m (\dfrac{3}{4}v^{2})$$
                                                                 
 $$= \dfrac{3}{4}(\dfrac{1}{2} mv^{2})$$

Remaining energy $$= \dfrac{1}{4} (1/2 mv^{2}).$$

Since,  $$\dfrac {3}{4} KE$$ is lost  in $$15 cm$$ penetration,

Hence $$\dfrac{1}{4} KE$$ would penetrate to $$\dfrac{15}{3} = 5 cm$$ 

 So, the distance further travelled by the bullet before coming to rest $$= 5 cm.$$

Physics

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