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Gravitational Potential of a Solid Sphere

A sphere of u...

Question

A sphere of uniform density has a spherical cavity inside it, then

A

field inside cavity will be constant.

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B

region of cavity may be equipotential.

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C

region of cavity may not be equipotential.

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D

field inside cavity may be zero.

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Solution

The correct options are
A field inside cavity will be constant.
B region of cavity may be equipotential.
C region of cavity may not be equipotential.
D field inside cavity may be zero.

Field at P = Field due to $S_{1}$ - Field due to $S_{2}$
Field inside a sphere is proportional to distance from the radius.
$∴$ Field at $P = k {\to r}_{1} - k {\to r}_{2}$
$= k ({\to r}_{1} - {\to r}_{2}) = k - -- \to O_{1} O_{2}$
Which is a constant.

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