Question

derive an expression for acceleration due to gravity.​

Answer 1

Answer:

Explanation:

Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.

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Derive an expression for it in terms of mass of the earth and gravitation constant. ... This force of attraction exerted by the earth on a body is called force of gravity and the acceleration possessed by a body moving under the force of gravity is called acceleration due to gravity.

The acceleration of gravity of an object is a measurable quantity. Yet emerging from Newton's universal law of gravitation is a prediction that states that its value is dependent upon the mass of the Earth and the distance the object is from the Earth's center.

Answer 2

Explanation:

Let a body P of mass m be situated at a depth h below the earth's surface.

The gravitational force of attraction on a body inside a spherical shell is always zero. Therefore, the body P experiences gravitational attraction only due to the inner solid sphere. The mass of this sphere is

M′=volume×density=34π(Re−h)3ρ

where ρ is mean density of the earth. Therefore, according to Newton's law of gravitation, the force of attraction on the body P is

(Re−h)2GM′m=G(Re−h)234π(Re−h)3ρm

=34πG(Re−h)ρm

This force must be equal to the weight of the body mg′, where g′ is the acceleration due to gravity at a depth h below the surface of the earth. Thus,

mg′=34πG(Re−h)ρm....(i)

Similarly, if a body be at the surface of the earth (h=0) where acceleration due to gravity is g, then

mg=34πGReρm....(ii)

Dividing eq.(i) by (ii) we have

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