A sphere of mass m, moving with velocity V, enters a hanging bag of sand and stops. If the mass of the bag is M and it is raised by height h, then the velocity of the sphere was

By the conservation of linear momentum Initial momentum of sphere = Final momentum of system mV=(m+M)vsys.                           …(i) If the system rises up to height h then by the conservation of energy 12(m+M)vsys.2=(m+M)gh            …(ii)⇒vsys.=2ghSubstituting this value in equation (i) V=m+Mm 2gh