A block of mass M is hanging from a rigid support by an in-extensible light string…..

Q: A block of mass M is hanging from a rigid support by an in-extensible light string. A ball of mass m hits it with a vertical velocity v at its bottom. Find the change in momentum of the ball assuming inelastic collision.

Sol: Let the velocity of combined mass of bullet and block just after collision be v1
Applying COLM,
$\displaystyle m v = (M + m) v_1 $

$\displaystyle v_1 = \frac{m v}{M+m}$
Numerical

Change in the momentum of bullet = Pf – Pi = mv1 – mv

$\displaystyle = \frac{m^2 v}{M+m} – m v $

$\displaystyle = – \frac{M m }{M+m}v $