First slide

Gravitaional potential at a point

Question

P is a point at a distance r from the centre of a solid sphere of radius a. The gravitational potential at P is V. If V is plotted as a function of r, which is the correct curve ?

Moderate

A
B
C
D

Solution

For a solid sphere gravitational potential is given by
$\large V = -\frac{GM}{2R}(3-\frac{r^2}{a^2})(r\leq a)\\\\\\=V-\frac{GM}{r}(r\geq a)$
Therefore inside a solid sphere V changes parabolically with r and outside the solid V - r graph is a rectangular hyperbolic.
Hence option - (3) is correct.

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