Potential on the surface of a solid sphere is x and radius is y. Match the following two columns

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Solution

$\frac{G M}{y} = x$ or $G M = x y$
(a) $E = \frac{G M}{{(2 y)}^{2}} = \frac{x y}{4 y^{2}} = \frac{x}{4 y}$
(b) $| V | = \frac{G M}{y^{3}} (1.5 y^{2} - 0.5 \frac{y^{3}}{4})$
$= (\frac{x y}{y^{3}}) (\frac{11}{8} y^{2}) = \frac{11}{8} x$
(c) $E = \frac{G M}{y^{3}} (\frac{y}{2}) = \frac{x y}{y^{3}} \frac{y}{2} = \frac{x}{2 y}$
(d) $| V | = \frac{G M}{2 y} = \frac{x y}{2 y} = \frac{x}{2}$

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