Question

A gun of mass M fires a bullet of mass m with a kinetic energy E.The velocity of recoil of gun is

Answer 1

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)

$v_{1}=\dfrac{m\times(\sqrt{\dfrac{2E}{m}})}{M}$

$v_{1}=\dfrac{\sqrt{2mE}}{M}$

Hence, The recoil velocity of gun is $\dfrac{\sqrt{2mE}}{M}$