Sphere of mass `M` and radius `R` is surrounded by a spherical shell of mass `2M` and radius `2R` as shown. A small particle of mass `m` is released from rest from a height `h(ltltR)` above the shell. There is hole in the shell.
With what approximate speed will it collide at `B`?

Options

A. `sqrt((2GM)/R)`
B. `sqrt((GM)/(2R))`
C. `sqrt((3GM)/(2R))`
D. `sqrt((GM)/R)`

Answer

D

Explanation

`r_(1)=a-ae=a(1-e)`
`r_(2)=a+ae=a(1+e)....(i)`
`V_(2)=(V_(1)r_(1))/(r_(1))rArr V_(2)sqrt((GM)/a((1-e)/(1+e)))`