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

At the lowest position
COLM : `Msqrt(2gL) = (M + m)v` ……(i)
COLM : `(1)/(2) (M + m)v^(2) = (M + m)gh` …..(ii)
`rArr v = sqrt(2gh) = (Msqrt2gL)/((M + m)) rArr h = ((M)/(m + M))^(2) L`