A mass m is moving with velocity v collides inelastically with a bob of simple pendulum of mass m and gets embedded into it. The total height to which the masses will rise after collision is

For inelastic collision, linear momentum is conserved   m v =( m+m)v'v'=v2 ⇒h =v'22g=v28g⇒mv1=2m2⇒v2=v12Loss in K.E. = Gain in P.E.                     =12mv12−12(2m)v22=2mgh                      ⇒4mgh=mv12−mv122=mv122=mv22⇒h=v28g