Question

What is meant by acceleration due to gravity? Derive an expression for acceleration due to gravity in terms of mass M of earth and its radius R.​

Answer 1

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$\huge\mathfrak\purple{Solution:-}$

⏩ ** The acceleration produced in the motion of a body falling freely under the force of gravity is called the acceleration due to gravity. It is denoted by 'g'.

** Consider the earth to be a sphere of mass M and radius R. Now, suppose a body of mass 'm' situated at distance 'r' from the centre of the earth.

As we know, according to Newton's law of gravitation, the force of attraction between the earth and the body is given by

F= GmM/r² ....→ (i)

This force produces an acceleration 'g', called acceleration due to gravity in the body of mass m.

So, from Newton's second law,

F= mg ....→ (ii)

Now,

From equations (i) and (ii), we get,

mg = GMm/r²

or

g= GM/r² ....→ (iii)

This equation gives acceleration due to gravity at points far away from the earth. Now, if body is located on the surface of the earth, then r= R, i.e., the radius of the earth. Then, the equation (iii) becomes

G surface = GM/R²

This equation gives acceleration due to gravity at the surface of the earth.

The value of 'g' on the earth's surface is 9.8 m/s²

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Hope it helps...:-)

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