Two concentric shells of masses `M_(1)` and `M_(2)` are situated as shown in figure. Find the force on
particle of mass m when the particle is located at (a)r=a (b),r=b and (c) r=c. The distance r measured from tł centre of the shell.

Explanation

We know that attraction at an external point due to a spherical shell of mass M is `(("GM")/(r^(2)))` While at a
intemal point is zero. So :
(a) For r = a, the point is external to both the shells, so
`I_(A)=(G(M_(1)+M_(2)))/(a^(2))`
So , `F_(A)="mI"_(A)=("Gm"(M_(1)+M_(2)))/(a^(2))`
(b) For r=b, the point is external to the shell of mass `M_(2)` and internal to the shell of mass `M_(1)`,so
`I_(B)=("GM"_(2))/(b^(2))+0,i.e., F_(B)="mI"_(a)=(("GM"_(2)m)/(b^(2)))`
(c) For r = c, the point is internal to both the shells, so
`I_(c)=0+0=0,i.e.,F_(c)="mI"_(c)=0`