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Gravitational Potential of a Solid Sphere

A spherical s...

Question

A spherical shell of mass $M / 2$ is enclosing a solid sphere of mass $3 M$ and radius $2 R$ . Then ratio of potential because of the spherical shell and the solid sphere at their common centre is

2 : 27

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1 : 6

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27 : 2

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2 : 3

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Solution

The correct option is A $2 : 27$
Potential due to a spherical shell at the centre is given by

$V_{1} = \frac{- G (\frac{M}{2})}{3 R} = \frac{- G M}{6 R}$

And potential due to the small sphere at the center is

$V_{2} = \frac{- 3}{2} \frac{G (3 M)}{(2 R)} = - \frac{9 G M}{4 R}$

$∴ \frac{V_{1}}{V_{2}} = \frac{- \frac{G M}{6 R}}{- \frac{9 G M}{4 R}} = \frac{2}{27} = 2 : 27$

Hence, option $(a)$ is correct.

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Gravitational Potential of a Solid Sphere

Standard XII Physics

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A spherical shell of mass M/2 is enclosing a solid sphere of mass 3M and radius 2R. Then ratio of potential because of the spherical shell and the solid sphere at their common centre is

The correct option is A 2:27Potential due to a spherical shell at the centre is given by V1=−G(M2)3R=−GM6R And potential due to the small sphere at the center is V2=−32G(3M)(2R)=−9GM4R ∴ V1V2=−GM6R−9GM4R=227=2:27 Hence, option (a) is correct.

A spherical shell of mass $M / 2$ is enclosing a solid sphere of mass $3 M$ and radius $2 R$ . Then ratio of potential because of the spherical shell and the solid sphere at their common centre is