Question

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

A
V
B
32V
C
23V
D
zero

Solution

## The correct option is C $$\dfrac { 3 }{ 2 } V$$At the center its become equal to $$\dfrac{3}{2}$$ times of $$v$$.We know that the gravitational potential at the surface is equal to,$$v=-\dfrac{GM}{R}\rightarrow(1)$$As the earth is solid body, on going down the surface the gravitational potential becomes equal to,$$v_i=-\dfrac{GM}{2R^3}(3R^2-r^2)$$put $$r=0$$$$v_i=-\dfrac{3}{2}\left[\dfrac{GM}{R}\right]$$$$v_i=\dfrac3{2}v$$Physics

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