Physics

Problem

Which one of the following gives the gravitational potential

V

at a distance

r

from an isolated point mass

M

? a)

-\dfrac{2GM}{r}

+\dfrac{GM}{r}

-\dfrac{GM}{r}

-\dfrac{GM}{2r}

Intuitive explanation

Gravitational potential measures the energy per unit mass needed to bring a test mass from infinity to distance $r$ . The key insight is that potential is a scalar (not a vector like field), and it's always negative for an attractive force—the farther away you are, the less negative (higher) it becomes. You're looking for an expression that's inversely proportional to $r$ , includes the mass $M$ , and has the right sign and constants.

Intuitive explanation

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