Question

find the value of 'g' at a height of 800 km above the surface of earth.
Given - Radius of earth= 6400km,
g =9.8ms-2
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Answer 1

Given :

Radius of earth = 6400km

Acc. due to gravity = 9.8m/s²

To Find :

Value of g at a height of 800km above the surface of earth.

Solution :

❖ The acceleration due to gravity decreases both with the increase in height and increase in depth.

• So it is maximum at the surface of the earth and zero at the centre of the earth.

Acceleration due to gravity increases with the increase in latitude of the place$.$

Acceleration due to gravity at a height h above the ground is given by

• g' = g / (1 - h/R)²

Where R denotes radius of the earth.

By substituting the given values;

➙ g' = 9.8 / (1 + 800/6400)²

➙ g' = 9.8 / (1 + 1/8)²

➙ g' = 9.8 / (9/8)²

➙ g' = 9.8 × 64/81

➙ g' = 7.74 m/s²

Answer 2

Given :

Radius of earth = 6400km

Acc. due to gravity = 9.8m/s²

To Find :

Value of g at a height of 800km above the surface of earth.

Solution :

❖ The acceleration due to gravity decreases both with the increase in height and increase in depth.

So it is maximum at the surface of the earth and zero at the centre of the earth.

Acceleration due to gravity increases with the increase in latitude of the place$.$

Acceleration due to gravity at a height h above the ground is given by

g' = g / (1 - h/R)²

Where R denotes radius of the earth.

By substituting the given values;

➙ g' = 9.8 / (1 + 800/6400)²

➙ g' = 9.8 / (1 + 1/8)²

➙ g' = 9.8 / (9/8)²

➙ g' = 9.8 × 64/81

➙ g' = 7.74 m/s²