Question

Two identical bullets are fired on by a light rifle and another by a heavy rifle with the same force.Which rifle will hurt the shoulder more and why?

Answer 1

Let m1 be the mass of light rifle.
let m2 be the mass of heavy rifle.
If they come with same force, that means the initial velocities are equal.
Let initial velocities be u m/s.
Let v1 and V2 be the final velocities for light and heavy rifles
Considering momentum conservation of Light Rifle:
Total momentum before firing= total momentum after firing.
0=mu-mv1
mv1=mu-------(1)
Considering momentum conservation of heavy Rifle:
Total momentum before firing= total momentum after firing.
0=mu-mv2
mv2=mu-----(2)
by equation 1 and 2 we get
both the momentum of guns after firing are same, hence they both will equally the shoulder.