A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a. The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points `P_1 and P_2` shown in the figure

Explanation

At `P_(1):`
`E=E_(sphere)+E_(shell)`
`=(Gm)/((4a)^(2))+0=(Gm)/(16a^(2))`
At `P_(2):`
`E=E_(sphere)+E_(shell)`
`=(Gm)/((6a)^(2))+(Gm)/(5a^(2))`
`=(Gm)/(a^(2))(1/36+1/25)`
`=(61Gm)/(900a^(2))`