Question

acceleration due to gravity by earth surface at height H

Answer 1

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Answer 2

here is your answer OK

For this question,

We have the formula, g' = g/(1+h/R)^2

Here g' = acceleration due to gravity at the height

g = 9.8m/s^2

R = radius of earth

h = height

g/g' = (1+h/R)^2

4 = (1+h/R )^2

1+h/R = 2

h/R = 1

h = R

So at the height of 6371 km the value of g is 1/4 th of its original value .

The acceleration due to gravity varies even on the surface of earth at different places.

But, If for approximation we take that earth is a perfect sphere, then it’s quite easy to find out that height.

First take any height “h” above the earth’s surface where the acceleration due to gravity is one-fourth.

Then equate the ratio of the formula that is used for finding the acceleration due to gravity on the earths’s surface and at any height “h” to g/g/4

Solve that equation as many thing will eventually get cancelled out and you will simply get the answer.
P.S.- As per my opinion this is one of the most basic question of gravitation in secondary school, So you should try to solve these trivial problems by yourself only.