Question

if potential at the surface of earth is assigned zero value,then potential at centre of earth

Answer 1

$For\ r \leq R,\ V(r)= \frac{2}{3} \pi G \rho(r^2-3R^2)$

$at\ center,\ V(0)= \frac{2}{3} \pi G \rho(-3R^2)=-2 \pi G \rho R^2\\ \\at\ surface,\ V(R)= \frac{2}{3} \pi G \rho(R^2-3R^2)=- \frac{4}{3} \pi G \rho R^2\\ \\if\ we\ assume\ potential\ at\ surface\ is\ 0,\ or\ V'(R)=0,\ then$

$V'(0)=V(0)-V(R)\\ \\V'(0)= (-2 \pi G \rho R^2)-(- \frac{4}{3} \pi G \rho R^2)\\ \\V'(0)=(\frac{4}{3}-2) \pi G \rho R^2\\ \\V'(0)=\boxed {- \frac{2}{3} \pi G \rho R^2}$

Answer 2

Answer:

Hope this helps!!

Explanation: