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Standard XII

Physics

Satellites

A solid spher...

Question

A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2 a$ and mass $2 M$ . The gravitational field at distance $3 a$ from the centre will be:

\frac{2 G M}{9 a^{2}}

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\frac{G M}{3 a^{2}}

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\frac{G M}{9 a^{2}}

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\frac{2 G M}{3 a^{2}}

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Solution

The correct option is B $\frac{G M}{3 a^{2}}$
We use gauss's law for gravitation
$g .4 π r^{2} = 4 π G$ (Mass enclosed)
$g = \frac{3 M 4 π G}{4 π {(3 a)}^{2}} = \frac{M G}{3 a^{2}}$

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The correct option is B $\frac{G M}{3 a^{2}}$
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