A shell of mass 20 ~g is fired by a gun of mass 100 ~kg . If the shell leaves the gun with a speed of 80 ~ms ⁻¹ , then the speed of recoil of the gun is

Step-by-step solution

Given, mass of shell, m_ s =20 ~g =0.02 ~kg Mass of gun, m_ g =100 ~kg Speed of shell, v_ s =80 ~m / s Let v_ g be the speed of the recoil of gun, then according to law of conservation of linear momentum. Total initial momentum = Total final momentum array ll & 0=m_ s v_ s +m_ g v_ g & 0=0.02 80+100 v_ g & 0=1.6+100 v_ g array aligned v_ g &= -1.6 100 &=-1.6 10⁻² ~m / s =-1.6 ~cm / s aligned Negative sign indicates that gun moves in opposite direction to that of shell. Speed of recoil of g u n=1: 6 ~cm / s