Acceleration due to gravity g for a body of mass m on earth’s surface is proportional (Radius of earth = R, mass of earth = M) to)
Acceleration due to gravity is the rate at which an object accelerates towards Earth, approximately 9.81 m/s² near the surface.
Class 11 Physics
Gravitation
CBSE EXAM 2024-25
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The acceleration due to gravity for a body on the Earth’s surface depends on the mass of the Earth and its radius. It is directly proportional to the Earth’s mass and inversely proportional to the square of its radius. This means that as the mass of the Earth increases, the gravitational pull also increases, making the acceleration due to gravity stronger.
Conversely, if the radius of the Earth increases while keeping its mass constant, the gravitational force weakens, reducing the acceleration due to gravity. This proportional relationship explains how Earth’s mass and size influence gravity experienced at its surface.
g = GM/R² ∴ g ∝ M/R²