The acceleration due to gravity varies with which of the following?

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Mass of the planet

Size of the planet

Both 1 and 2

None of these

answer is C.

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Detailed Solution

The acceleration due to gravity varies with the mass of the planet and the size of the planet.
Assume that the body's mass is

m

, the planet’s mass is

M

, and the distance between the body's and the planet's centres 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)

Where

g

represents the gravity on that planet.
Combining the equations (1) and (2), we have:

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

The acceleration due to gravity,

g = GM / r^{2}

From the above expression, the acceleration due to gravity is directly proportional to the mass of the planet. So as the mass of the planet increases, the acceleration due to gravity increases. But the radius of the planet is inversely proportional to gravity. So the value of gravity decreases with an increase in the size of the planet.

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