Question

Gravitational potential on the surface of earth is V. Gravitational potential at the centre of earth is THEN :

• A. $V$
• B. $\frac{3}{2}V$
• C. $\frac{2}{3}V$
• D. $zero$

Answer 1

Answer: (B)

$\frac{3}{2}V$

At the center its become equal to $\frac{3}{2}$ times of $v$.

We know that the gravitational potential at the surface is equal to,

$v=-\frac{GM}{R}\to \left(1\right)$

As the earth is solid body, on going down the surface the gravitational potential becomes equal to,

$v_i=-\frac{GM}{2R^3}(3R^2-r^2)$

put $r=0$

$v_i=-\frac{3}{2}\left[\frac{GM}{R}\right]$

$v_i=\frac{3}{2}v$