A gun of mass M fires a bullet of mass m with a velocity v relative to the gun. The average force required to bring the gun to rest in 1 sec is

$F=\frac{mMv}{\left(M+m\right)t}$  $=\frac{mMv}{1\left(M+m\right)}$ 

Assume that velocity of the bullet is

 $$\begin{gathered} v_{2 }and velocity of the gun is v_{1}then \\ M V_1=m V_2.........\left(1\right) \\ GIVEN V_{REL}=v=V_2+V_1.........\left(2\right) \\ force required to hold the gun =F=\frac{M V_1}{t} given t=1 \\ F=M V_1.........\left(3\right) \\ FROM 1,2 and 3 \\ F= \frac{M m v}{\left(M+m\right)} \end{gathered}$$