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 center , b. `5/2 a` from the center.

Explanation

ure shows the situation. Thepoint `P_1` is at a distance `3/2a` from the cenre and `P_2 is at a distance `5/2a` from the centre. As `P_1` in inside the cavity of the thin spherical shell, the field here due to the shell is zero. the field due to the solid sphere is
`E=(GM)/((3/2a)^2)=(4GM)/(9a^2)`
This is also the resultant field. The direction is twoards the centre. the point `P_2` is outside the sphere as well as teh shell. Both may be replaced by single particles of the same mass at the centre.The field due to eac of them is
`E'=(GM)/((5/2a)^2)=(4GM)/(25a^2)`
The resultasnt field is E=2F=(8GM)/(25a^2)` towards the centre.