A point of mass m is released from rest at a distance of 3R from the cente of a then walled hollow spehre of radius R and mass M as shown. The hollow sphere is fixed in position and the motion is due to only gravitational attraction of the hollow sphere. There is a very small hole in the hollow sphere through which the point mass falls as shown. Then the velocity of point mas when it passes through point P at distance R/2 from the centre of the sphere is

Options

A. `sqrt((2GM)/(3R))`
B. `sqrt((5GM)/(3R))`
C. `sqrt((25GM)/(24R))`
D. `sqrt((4GM)/(3R))`

Answer

D

Explanation

Inside the spherical shell, v is constant
`(-GMm)/(3R)=(mv^(2))/2-(GM)/R`
`v=sqrt((4GM)/(3R))`