The correct option is A 5 ms−1
Mass of gun, m1=4 kg.
Let recoil velocity of gun be v1, initial velocity of gun be u1, initial velocity of bullet be u2
Mass of bullet, m2=40 g=0.04 kg
Velocity of bullet after firing be v2=500 ms−1.
Using law conservation of momentum :
m1u1+m2u2=m1v1+m2v2 ...(1)
Total momentum of gun and bullet initially is zero, as the bullet is in rest before firing, i.e initial velocities of bullet and gun are 0 ms−1
⇒(m1+m2)×0 = m1v1+m2v2
v1=−m2v2m1
Here the negative sign suggests that this velocity is in the opposite direction to the motion of bullet.
∴Recoil velocity, v1=m2v2m1=0.04×5004=5 ms−1