A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2a. Find the gravitational field at a distance a). 3/2 a from the centre , b). 5/2 as from the centre.

Answer

A, B, C, D

Explanation

At distance `(3 a)/(2)` which lies between solid sphere and shell field is only due to solid sphere.
`E = (GM)/(3a//2)^(2) = (4 GM)/(9a^(2))` (towards centre)
(b) At distance `(5a)/(2)` which lies outside the shell. So, field strength is due to both
`:. E = (G(M + M))/(5a//2)^(2) = (8 GM)/(25 a^(2))`(towards centre)