Demonstrate that the gravitational force acting on a particle A inside a uniform spherical layer of matter is equal to zero.

Explanation

(The problem has already a clear hint in the answer sheet of the problem book). Here we adopt a different method.
Let m be the mass of the sperical layer, wich is imagined to be made up of rings. At a point inside the sperical layer at distance r from the centre, the gravitational potential due to a ring element of radius a equals,
`dvarphi=-(gammam)/(2ar)dl`
So, `varphi=intdvarphi=-(gammam)/(2ar)underset(a-r)overset(a+r)intdl=-(gammam)/(a)` (1)
Hence `G_r=-(deltavarphi)/(deltar)=0`.
Hence gravitational fields strength as well as field force becomes zero, inside a thin sperical layer.