Question

what is meant by accelration due to gravity? derive an equation for it​

Answer 1

Answer:

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Explanation:

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Answer 2

The acceleration of a body when falling freely under the gravitational pull of earth is known as acceleration due to gravity.

It is represented by 'g'.

If we drop a body of mass m from a height, h, to the surface of earth

[mass M and radius R ] its speed will increase as it comes nearer to the surface of earth. Let h be very small as compared to R. The acceleration of the body is the acceleration due to gravity(g). The force on the body :-

∵ F = m×a

∴ F = m×g ---(1)

But, this force on the body is due to gravitational pull of earth.

∴ F = GMm/R² -----(2)

From, equation (1) and (2) :-

=> mg = GMm/R²

=> g = GM/R²

This formula can be used for any other planet :-

=> gₚ = GMₚ/R²ₚ

Where :-

• gₚ is acceleration due to the planet.

• Mₚ is mass of the planet.

• Rₚ is radius of the planet.