Is it true that acceleration due to gravity depends on the mass of the body?

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True

False

answer is A.

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Detailed Solution

The above statement is False
An object's gravitational force is determined by its mass multiplied by the mass of the other body.

F = \frac{(G  ✕ M_{1} ✕ M_{2})}{R^{2}}

… (1)
Where,

M_{1} =

mass of the earth.

M_{2} =

mass of the object.

R =

radius of the earth.
The speed is calculated by dividing the force by the mass.

g = \frac{F}{M_{1}}

… (2)
From equations (1) and (2), we get,

g = \frac{(G ✕ M_{1} ✕ M_{2} / R^{2})}{M_{1}}

⇒

g = \frac{G ✕ M_{2}}{R^{2}}

Therefore, since a body's mass cancels out, the acceleration it feels due to its gravitational interaction with another body solely relies on the other body's mass.
We can see from the equation clearly that the gravitational acceleration is affected by the mass of the earth, the gravitational constant, and the separation between an item and the earth's centre.

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