A particle of mass $m$ is located outside a uniform sphere of mass $M$ at a distance $r$ from its centre. Find the potential energy of gravitational interaction of the particle and the sphere.

\frac{- 2 G M m}{r}

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\frac{- G M m}{r}

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\frac{- G M m}{3 r}

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\frac{- G M m}{2 r}

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Solution

The correct option is C $\frac{- G M m}{r}$
Since for a uniform solid sphere,
$V_{G} = - \frac{G M}{r}$ for $r$
and it is the work done to bring a unit mass from $\infty$ to distance ' $r$ ' from sphere.
For mass ' $m$ '
$V_{G} = - \frac{G M m}{r}$ which is the total potential energy of the system

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A particle of mass m is located outside a uniform sphere of mass M at a distance r from its centre. Find the potential energy of gravitational interaction of the particle and the sphere.

The correct option is C −GMmrSince for a uniform solid sphere,VG=−GMr for r and it is the work done to bring a unit mass from ∞ to distance 'r' from sphere.For mass 'm'VG=−GMmr which is the total potential energy of the system

A particle of mass $m$ is located outside a uniform sphere of mass $M$ at a distance $r$ from its centre. Find the potential energy of gravitational interaction of the particle and the sphere.

The correct option is C $\frac{- G M m}{r}$
Since for a uniform solid sphere,
$V_{G} = - \frac{G M}{r}$ for $r$
and it is the work done to bring a unit mass from $\infty$ to distance ' $r$ ' from sphere.
For mass ' $m$ '
$V_{G} = - \frac{G M m}{r}$ which is the total potential energy of the system