A gun of mass M fires a bullet of mass m with a kinetic energy E.The v

1.	A gun of mass M fires a bullet of mass m with a kinetic energy E.The velocity of recoil of gun is
Answer» Given that, Mass of gun = M Mass of bullet = m Kinetic ENERGY of bullet = E We need to calculate the velocity of gun Using conservation of MOMENTUM $Mv_{1}=mv_{2}$ $v_{1}=\dfrac{mv_{2}}{M}$ ...(I) We need to calculate the RECOIL velocity of gun Using formula of kinetic energy $K.E=\dfrac{1}{2}mv_{2}^2$ Put the VALUE into the formula $E=\dfrac{1}{2}mv_{2}^2$ $v_{2}=\sqrt{\dfrac{2E}{m}}$ Now, put the value of v₂ in equation (I) $v_{1}=\dfrac{m\times(\sqrt{\dfrac{2E}{m}})}{M}$ $v_{1}=\dfrac{\sqrt{2mE}}{M}$ $\dfrac{\sqrt{2mE}}{M}$ Hence, The recoil velocity of gun is