A point mass `m` is released from rest at a distance of `3R` from the centre of a thin-walled hollow sphere of radius `R` and mass `M` as shown. The hollow sphere is fixed in position and the only force on the point mass is the gravitational attraction of the hollow sphere. There is a very small hole in the hollow sphere through which the point mass falls as shown. The velocity of a point mass when it passes through point `P` at a distance `R//2` from the centre of the sphere is

Options

A. `sqrt((2GM)/(3R))`
B. `sqrt((5GM)/(3R))`
C. `sqrt((25GM)/(24R))`
D. none of these

Answer

D

Explanation

Inside the sphereicla shell, `V` is constant, so from energy conservation.
`(-GMm)/(3R)=(mv^(2))/2-(GMm)/R`
`(v^(2))/2=(GM)/R[1-1/3]=(GM)/Rxx2/3` or `v=sqrt((4GM)/(34R))`