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(A) The gravitational potential at a point outside a spherical body is given by $V = -\frac{GM}{r}$.Since the point at distance $r = 2.5 a$ is outside

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$\frac{-3 GM}{5 a}$

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(A) The gravitational potential at a point outside a spherical body is given by $V = -\frac{GM}{r}$.Since the point at distance $r = 2.5 a$ is outside both the solid sphere and the spherical shell,both act as point masses at the center.The total mass of the system is $M_{total} = M + 0.5 M = 1.5 M$.The gravitational potential energy $U$ of a unit mass $(m = 1)$ at distance $r = 2.5 a$ is given by $U = V = -\frac{G M_{total}}{r}$.Substituting the values: $U = -\frac{G(1.5 M)}{2.5 a} = -\frac{1.5}{2.5} \frac{GM}{a} = -\frac{3}{5} \frac{GM}{a} = -\frac{3 GM}{5 a}$.

$A$ uniform solid sphere of mass $M$ and radius $a$ is surrounded by a concentric uniform thin spherical shell of mass $0.5 M$ and radius $1.5 a$. The gravitational potential energy of a unit mass kept at a distance of $2.5 a$ from the center is

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