A particle of mass m moving with velocity V0 strikes a simple pendulum of mass m and sticks to it. The maximum height attained by the pendulum will be

Initial momentum of particle = mV0Final momentum of system (particle + pendulum) = 2mvBy the law of conservation of momentum ⇒mV0=2mv⇒Initial velocity of system v=V02∴ Initial K.E. of the system = 12(2m)v2=12(2m)V022If the system rises up to height h then P.E. =  2mghBy the law of conservation of energy 12(2m)V022=2mgh⇒h=V028g