A bullet of mass ‘m’ is fired with certain velocity from a gun of mass M. Gun, which is attached with one end of the spring compresses by distance ‘d’.  If ‘K’ is the spring constant  K,  velocity of the bullet is

apply law of conservation of linear momentum ∴   MV   =    mu ⇒u=MVm---(1) mass of gun =M; velocity of gun=V;mass of the bullet=m; velocity of bullet be u apply law of conservation of linear momentum, 12 MV2  =   12 Kd2 ⇒V=dKM---(2) K is spring constant; d is distance of compression of the spring substitute eqn(2) in eqn(1) ⇒u=MmdKM ⇒u=dmKM