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Q.

A 10 g bullet travelling at 200 m/s strikes and embeds itself in a 2 kg target that is initially at rest but is free to move. At what speed does the target move away?


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a

4 m/s

b

3 m/s

c

1 m/s

d

6 m/s 

answer is C.

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Detailed Solution

When a 10 g bullet travelling at 200 m/s strikes and embeds itself in a 2 kg target that is initially at rest, the target moves away at a rate of 1 m/s
Weight of the bullet (m1) is 10g, =10×10-3 kg
= 0.01 kg
Bullet velocity (v1) is given as 200 m/s
The mass of the target m2 is 2 kg
Let v2 be the velocity of the target after being hit by the bullet.
According to the law of conservation of momentum:
When two objects collide with each other, the sum of their momentum remains conserved when no external force is applied on the bodies. Therefore,
m1×v1=m2×v2
⇒0.01×200=2×v2
⇒v2=0.01×2002
⇒v2=1 m/s
Therefore, the final velocity of the target is 1 m/s
 
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A 10 g bullet travelling at 200 m/s strikes and embeds itself in a 2 kg target that is initially at rest but is free to move. At what speed does the target move away?