Question
A uniform solid sphere of mass $M$ and radius $R$ is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius $2R$. The value of gravitational potential at a distance $\frac{3}{2}\,R$ from the centgre is
✓
Answer
Due to solid sphere.
Gravitational potential.
$\mathrm{V}_{1}=-\frac{\mathrm{GM}}{(3 \mathrm{R} / 2)}=-\frac{2 \mathrm{GM}}{3 \mathrm{R}}$
Due to spherical shell.
Gravitational potential, $\mathrm{V}_{2}=-\frac{\mathrm{GM}}{2 \mathrm{R}}$
Net Gravitational potential
$=-\frac{2 \mathrm{GM}}{3 \mathrm{R}}-\frac{\mathrm{GM}}{2 \mathrm{R}}=-\frac{7 \mathrm{GM}}{6 \mathrm{R}}$
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