A uniform solid sphere of mass $M$ and radius ' $a$ ' is surrounded by a concentric uniform thin spherical…
A uniform solid sphere of mass $M$ and radius ' $a$ ' is surrounded by a concentric uniform thin spherical shell of mass $0.5 \mathrm{M}$ and radius $1.5 \mathrm{a}$. The gravitational potential energy of a unit mass kept at a distance of $2.5 \mathrm{a}$ from the center is
$\frac{-3 \mathrm{GM}}{5 \mathrm{a}}$
$\frac{3 \mathrm{GM}}{5 \mathrm{a}}$
$\frac{2 \mathrm{GM}}{5 \mathrm{a}}$
$\frac{-2 \mathrm{GM}}{5 \mathrm{a}}$
Solution
The gravitational potential energy at a distance of $2.5 \mathrm{a}$ is
$\mathrm{U}=-\frac{\mathrm{G}(\mathrm{M}+0.5 \mathrm{~m})}{2.5 \mathrm{a}}=-\frac{1.5 \mathrm{GM}}{2.5 \mathrm{a}}=-\frac{3 \mathrm{GM}}{5 \mathrm{a}}$