Question

Define acceleration due to gravity. Deduce an expression for it in terms of mass of the earth (M) and universal gravitational constant (G).

or

Show that the acceleration due to gravity of an object is independent of its mass.​

Answer 1

Answer:

The acceleration produced in a body due to the gravitational force is called acceleration due to gravity.

Answer 2

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$\huge\bold\purple{Answer:-}$

⏩ Acceleration due to gravity:-

The acceleration produced in the motion of a body falling under the force of gravity is termed as acceleration due to gravity. It is denoted by 'g'.

⏩ Relation between g and G:-

Suppose the earth is a sphere of mass M and radius R, as shown in the attachment above. Consider a body of mass m situated at a distance r from the centre of the earth. According to Newton's law of gravitation, the force of attraction between the earth and the body is given by,

F= GMm/r² .....→ (1)

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

Hence, from Newton's second law,

F= Mass × acceleration = mg ...→(2)

Now, from equations (1) and (2), we get,

mg= GMm/r²

or

g= GM/r² ....→(3)

This equation gives acceleration due to gravity at points far away from the earth.

If body is located on the surface of the earth, then r=R, the radius of the earth. The above equation then becomes,

g surface= GM/R² ....→(4)

This equation gives acceleration due to gravity at the surface of the earth. Clearly, g is independent of the mass m of the body.

And now, as the radius of the earth does not change much over its entire surface, the value of 'g' is almost constant near or on the earth.

→The value of 'g' on earth's surface= 9.8 m/s²

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