Question

An uniform spherical shell gradually shrinks maintining its shape .The gravitational potential at the centre

Answer 1

AS it is maintaining its shape so its mass will remain constant which implies that if it shrinks then its volume decreases and to keep the mass constant ,its density increases.Also the gravitational potential at the centre of a uniform spherical shell is inversely proportional to the radius of the shell with a negative sign. When a uniform spherical shell gradually shrinks, the gravitational potential at the centre decreases (because of the negative sign in the formula of potential).

Answer 2

Gravitational potential at the centre is always zero no matter what is the size of the object (spherical shell).

Explanation:

Gravitational potential is zero at centre because the distance of centre of object to other object through which we are calculating is zero.

Considering gravitational potential for first.

Gravitational potential,

                                ⇒ Gp = mgh

where, 'Gp' is the gravitational potential and m is the mass of shell and and h is the height of the body above shell. Here 'h' can not be negative. So, this can not be considered.

Considering, Gravitational force,

                                ⇒ F = $\frac{GMm}{r^{2} }$

R is zero in this case, Gravitational force is infinity which is impossible. So, gravitational potential and force is zero at centre because at centre there is no mass for gravity.