The acceleration due to gravity at the Earth's surface depends on

The acceleration due to gravity at the Earth’s surface depends on

[amp_mcq option1=”its mass only.” option2=”its radius only.” option3=”both its mass and radius.” option4=”either its mass or its radius.” correct=”option3″]

This question was previously asked in

UPSC CDS-2 – 2022

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The correct answer is C) both its mass and radius.

The acceleration due to gravity (g) at the surface of a celestial body like Earth is given by Newton’s Law of Universal Gravitation. The formula for g is g = GM/R², where G is the universal gravitational constant, M is the mass of the Earth, and R is the radius of the Earth. This formula clearly shows that the acceleration due to gravity depends directly on the mass (M) and inversely on the square of the radius (R).

While the formula g = GM/R² gives the ideal value of gravity assuming Earth is a perfect sphere of uniform density, the actual value of ‘g’ varies slightly across Earth’s surface due to factors like Earth’s rotation (centrifugal force reduces effective gravity, more at the equator), Earth’s shape (it’s an oblate spheroid, larger radius at the equator), altitude (g decreases with height above the surface), and local variations in crustal density. However, the fundamental dependence is on the Earth’s total mass and average radius.

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