A small bucket of mass `M` is attached to a long inextensible cord of length `L`. The bucket is released from rest when the cord is in a horizontal position. In its lowest position the bucket scoops up m of water, what is the height of the swing above the lowest position?

Options

A. `((M)/(M+m))^(2)L`
B. `((M)/(M+m))L`
C. `((M+m)/(M))^(2)L`
D. `((M+m)/(M))L`

Answer

A

Explanation

Using consevation of energy
`(1)/(2)Mv^(2)=MgLrArrv=sqrt(2gl)`
using conservation of linear momentum
`(M+m)v'=MvrArrv'=(Msqrt(2gl))/(M+m)`
using conservation of energy
`(M+m)gh=(1)/(2)(M+m)v'^(2)`
`rArrh=(v'^(2))/(2g)=((M)/(M+m))^(2)L`