Question

Question #530c6

Answer 1

Ratio of KE of the rifle to that of bullet is inverse ratio of their masses.

Explanation:

Let a bullet of mass `m_b` be fired from a rifle of mass `M_r` with a velocity `vecv` and the rifle recoils with velocity `vecV_`.
As the momentum before firing the bullet is `0`, from Law of conservation of momentum we get
`vec p_b+vec p_r=0`

`=>vec p_b=-p_r` ........(1)

Now KE of the rifle`=vecp_r^2/(2M_r)`
and KE of the bullet`=vecp_b^2/(2m_b)`
`:."KE of the rifle"/"KE of the bullet"=(vecp_r^2/(2M_r))/(vecp_b^2/(2m_b)`
Using equation (1) we get
`"KE of the rifle"/"KE of the bullet"=m_b/M_r`