A small bucket of mass M kg is attached to a long inextensible cord of length L m. The bucket is released when the cord is in horizontal position. At its lowest point the bucket scoops up m kg of water and swings.up to a height h. The height h is??

Ans) Velocity before scooping=root(2gL)

Applying conservation of momentum,

New velocity= (M/M+m).root(2gL)

The bucket stops when velocity = 0

=>u^2=2gh

=>2gh= [ (M/M+m)^2 ]. 2gL

=> h= [ (M/M+m)^2 ].L