A solid sphere of mass M and radius R is surrounded by a spherical shell of same mass and radius 2R as shown. A small particle of mass m is relased from rest from a height h`(lt lt R)` above the shell. There is a hole in the shell.
Q. In what time will it enter the hole at A

Options

A. `2sqrt((hR^(2))/(GM))`
B. `sqrt(2hR^(2))/(GM)`
C. `sqrt((hR^(2))/(GM))`
D. None of these

Answer

A

Explanation

`a=(GM)/((2R)^(2))+(GM)/((2R)^(2))=(GM)/(2R^(2))thereforet=sqrt((2xxh)/(a))=sqrt((2xxhxx2R^(2))/(GM))=2sqrt((hR^(2))/(GM))`