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Question

What would be the relation between magnitude of velocity of the gun and bullet after firing, if the mass of gun is less than the mass of bullet? Assume no external force is acting on the gun bullet system.


A

Velocity of gun is higher than the velocity of bullet

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B

Velocity of bullet is higher than the velocity of gun

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C

Velocity of gun = velocity of bullet

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D

None of the above

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Solution

The correct option is B

Velocity of gun is higher than the velocity of bullet


The law of conservation of momentum can be applied in this as no external force is applied on the system
m1u1+m2u2=m1v1+m2v2
where
m1 is mass of bullet.
m2 is mass of gun.
u1 is initial velocity of bullet.
u2 is initial velocity of gun.
v1 is final velocity of bullet.
v2 is final velocity of gun.
Initially the bullet is resting in the gun. So initial momentum is zero.
0=m1v1+m2v2
v2v1=m1m2
Negative sign indicates the opposite directions of the velocities.
In this case, the mass of the bullet is higher than the mass of the gun. Thus, the velocity of the gun is higher than the velocity of the bullet.


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