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Question

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


A
V
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B
32V
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C
23V
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D
zero
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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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