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Which is the mathematical expression for acceleration due to gravity on the surface of any planet?

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\frac{GM}{r}

\frac{GM}{r^{2}}

{GMr}^{2}

\frac{GM}{r^{3}}

answer is B.

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Detailed Solution

The mathematical expression for acceleration due to gravity on the surface of any planet is

\frac{GM}{r^{2}}

.
Assume that the body's mass is

m

, the Earth's mass is

M

, and the distance between the body's and the Earth's centers is

r

.
Now, in accordance with Newton's law of gravity,

F = \frac{GMm}{r^{2}} \dots (1)

Where,

F

is the gravitational force of attraction and

G

is the universal gravitational constant.
From Newton’s second law of motion,

F = mg \dots (2)

Combining the equations (1) and (2), we have:

mg = \frac{GMm}{r^{2}}

The acceleration due to gravity,

g = G \frac{M}{r^{2}}

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