A bullet of mass 10 g is fired from a gun of mass 6 kg with a velocity of 300 m/s. Calculate the recoil velocity of the gun.

Options

A. 0.5 m/s
B. 1 m/s
C. 10 m/s
D. 5 m/s

Answer

A

Explanation

Here, Mass of bullet=10 g
=`10/100` kg
=0.01 kg
Velocity of bullet=300 m/s
Mass of gun=6kg
And, Recoil velocity of gun=? (To be calculated)
Now, putting these values in the relation :
Mass of bullet `xx`Velocity of bullet`xx`=mass of gun `xx`Recoil velocity of gun
We get : `0.01xx300=6xx` Recoil velocity of gun
So, Recoil velocity of gun=`(0.01xx300)/6`
=0.5 m/s
Note. The above prblem can also be solved by calculating the momentum of bullet and the gun separately as follows :
Momentum of bullet=Mass of bullet`xx`Velocity of bullet
`=0.01xx300`
= 3 kg. m/s
Now, suppose the recoil velocity of gun is v m/s.
So, Momentum of gun=Mass`xx`Recoil velocity of gun
`=6xx`v kg m/s
According to the law of conservation of momentum :
So, `3=6xxv`
And, `v=3/6m//s`
Recoil velocity of gun,v=0.5 m/s