SEE THE SOLUTION WAS GIVEN BY A FRIEND OF MINE TO ME



ets first do it by a simple and short method...































by energy method...































lets work in frame of reference of sphere..































let P be the point where it makes an angle @ with the verticle...































forces acting on particle : pseudo force(=ma); weight(=mg) and normal reaction(=N)































now, K.E at P = Wpseudo force + Wmg + WN































1/2mv2 = maRsin@ + mgR(1-Rcos@) + 0































solve to get v = [2R(asin@ + g -gcos@)]1/2