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Equipotential Surfaces

Question

Equipotential surfaces are
Surfaces that have same mass on top of it
Surface that have same radius of curvature
Surfaces that have same gravitational field on it
Surfaces that are perpendicular to gravitational fields

A

Surfaces that are perpendicular to gravitational fields

B

Surfaces that have same mass on top of it

C

Surface that have same radius of curvature

D

Surfaces that have same gravitational field on it

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Solution

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Equipotential surfaces are surfaces which have the same value of potential throughout their surface.
For a gravitatiomal field of $E = \frac{G M}{r^{2}}$ ,the potential is $v = - \frac{G M}{r}$
So,at a particular 'r',the potential remains constant at a value of $- \frac{G M}{r}$
So equipotential surfaces are circles for the filed of $E = \frac{G M}{r^{2}}$
Hence,the field is perpendicular to equipotential surface.

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