Amachine gun fires 25g bullates at the rate of 600 per minute with aspeed of 400 m/s . Calculate the force required to keep the gun inposition.

Gun fires 600 bullets in 1 minute so,

no.of bullets fired in 1 second=10

now time taken by 1 bullet to get fired=1/10sec=0.1sec

initial velocity u=0m/s

final velocity v=400m/s

v=u+at 

400=0.1a

a=4000m/s²

now,force exerted by the bullet on the gun=force required to keep the gun in position

so,force exerted by 1 bullet f=ma=25*10^-3*4000=100newtons

force exerted by 600 bullets=100*600=60000N                                                                 

The mass of one bullet is 25g=25/1000 kg

velocity of each bullet = 400m/s

therefore the momentum of each bullet=25/1000*400

momentum of 600 bullets(P) =25/1000*400*600

initial momentum of the bullets is zero and the rate of change of momentum=force applied by the bullets on the gun

to balance this force an equal and opposite force is to be applied to keep the gun in position

therefore force=P/60