Question

Consider the situation where a gun is kept on a frictionless surface and is being operated remotely by a group of engineers. If the mass of the gun is more than that of the bullet, what would be the relation between their velocities?

• A. Velocity of gun is higher than the velocity of bullet
• B. Velocity of bullet is higher than the velocity of gun
• C. Velocity of gun = velocity of bullet
• D. Cannot be determined.

Answer 1

The correct option is B

Velocity of bullet is higher than the velocity of gun

The conservation of momentum can be applied in case of the firing.
If the momentum is constant, then mass is inversely related with the velocity.
i.e $p=mv\Rightarrow v=\frac{p}{m}$
For constant momentum, $v\propto \frac{1}{m}$
In this case, mass of bullet is less than the mass of the gun, so the velocity of the bullet is higher than the velocity of the gun.