A machine gun has a mass of `20kg` If fires `25g` bullets at the rate of `600` bullets per minute with a speed of `200ms^(-1)` Calculate (i) recoil velocity of the gun (ii) force required to keep the gun in position .

Answer

`2.5m//s50N` .

Explanation

Mass of machine gun, `M =20kg`
mass of each bullet, `m = 25 g =25 xx 10^(3) kg`
vel of each bullet, `upsilon_(1) = 200m//s`
No of bullets//sec, `n = (600)/(60) = 10`
If `upsilon_(2)` is recoil velocity of gun then
`M upsilon_(2) = n (m upsilon_(1))`
`upsilon_(2) = (n m upsilon_(1))/(M) = (10 xx 25 xx 10^(-3) xx 200)/(20) = 2.5m//s`
Force reqd `= ("Change in momentum")/("time") = (n m upsilon_(1))/(t)`
` =(10 xx 25 xx 10^(-3) xx 200)/(1) = 50 N`.