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Question
Mon February 14, 2011 By: Arun Iyer

Please explain the accelaration due to gravity below and above the surface of the earth in an easy manner with the derivation ?

Expert Reply
Mon February 14, 2011
Dear student,
 Gravity is a property of matter. All mass exerts a gravitational field. So the further you are away from any mass, the smaller the gravitational field will be.

Consider an object of mass m lying on or near the surface of the Earth. Let Me be the mass of the Earth and Re be its radius i.e., Re is the distance between the object and the centre of the Earth.

According to Newton's law of gravitation, the force of attraction (F) between the Earth and the object is

A Body of Mass m Lying on the Surface of the Earth

According to Newton's second law of motion this force produces an acceleration (g) in the object.

F = ma (a = g)

F = mg

Substituting the value of F in equation (2) we get,

From equation (3) it is very clear that acceleration due to gravity does not depend on the mass m of the object. It only depends on the mass of the Earth (Me) and the distance from the centre of the Earth to the object.

Numerical Value of Acceleration due to Gravity on Earth

Gravitational Constant (G) = 6.6734 x 10-11 Nm2/kg2

Mass of the Earth (Me) = 6 x 1024 kg

Radius of the Earth (Re) = 6.4 x 106 m

Hope this helps.
Team
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