Motion under Gravity

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

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

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its mass only.
its radius only.
both its mass and radius.
either its mass or its radius.
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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22. An object is dropped from a height onto the floor. Which one of the fo

An object is dropped from a height onto the floor. Which one of the following remains uniform as it falls ?

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Its acceleration
Its momentum
Its kinetic energy
Its potential energy
This question was previously asked in
UPSC CDS-2 – 2022
Download PDFAttempt Online
When an object is dropped from a height and falls towards the floor, its acceleration remains uniform (assuming negligible air resistance). This is because the acceleration is due to gravity, which is approximately constant near the Earth’s surface.
Acceleration due to gravity (g) is approximately 9.8 m/s² near the Earth’s surface and acts downwards. For a freely falling object (with negligible air resistance), this acceleration is constant.
As the object falls, its velocity increases (due to uniform acceleration), its momentum (mass x velocity) increases, and its kinetic energy (1/2 x mass x velocity²) increases. Its potential energy (mass x gravity x height) decreases as its height decreases. Only the acceleration due to gravity remains constant.

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