A uniform metal sphere of radius `R` and mass `m` is surrounded by a thin uniform spherical shell of same mass and radius `4R`. The centre of the shell `C` falls on the surface of the inner sphere. Find the gravitational fields at points `A` and `B`.

Options

A. `(21GM)/(900a^(2))`
B. `(61GM)/(450a^(2))`
C. `(61GM)/(900a^(2))`
D. `(61GM)/(1800a^(2))`

Answer

C

Explanation

`E_(P)=(GM)/((4a)^(2))=(GM)/(16a^(2))` and `E_(P^(2)) =(GM)/((6a)^(2))+(GM)/(5a^(2))=(61GM)/(900a^(2))`