A machine gun fires 360 bullets per minute,each bullet moves with a velocity of 600m/s.If the power of gun is 5.4kW,mass of each bullet is

Power = Work done/ time……(1)Power 5.4 kW = 5400 wattWork done = F.S = mg.sg = 10m/s^2Velocity = ds/dt = 600m/s Putting the values in eq. (1)5400 = 10m * 600m = 5400 ÷ 6000M = .9 kg

Here we take initial velocity as 0 and second equation of motion for finding the distance and acceleration

F = mnv (1)And F = ma (2)Equating 1 and 2mnv = mam gets cancelledn= 360/60 ..... that is 360 bullets per secondHence we can find the acceleration that comes out to be 3600 m/s^2Now from v^2 = u^2 + 2asSupposing u to be zero we get the displacement = 50 mV= u + atU = 0... then time = 1/6 secondsPower = work/timePower = force*displacement/ time5400 = m* 3600* 50* 6(a = 3600.... s=50 ... and time = 1/6)On solving this we get the mass = 5 grams

We know that the change in the kinetic energy is the work done, and also the work done by time is power & the gun gets the recoil velocity, by thisWork done= 360×(1/2)×m×(600)^2Time=60Power=wrk done/ time. =5400Then m=1/200 kg then 5 grms