At what height above the surface of the earth, the acceleration due to gravity will be of the same as in a mine, 100 km deep?

Solution

Let, the acceleration due to gravity at height h be the same as that at a depth, d, deep into the earth.
We have, d = 100 km
Therefore,
g' = g $open parentheses 1 space minus fraction numerator 2 straight h over denominator straight R end fraction close parentheses space equals space straight g space open parentheses 1 space minus straight d over straight R close parentheses$
$rightwards double arrow space space space space space space space space fraction numerator 2 straight h over denominator straight R end fraction space equals space straight d over straight R rightwards double arrow space space space space space space space space space space space space space straight h space equals space straight d over 2 space equals space 100 over 2 space equals space 50 space km space$

Some More Questions From Motion in Straight Line Chapter

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Motion In Straight Line

At what height above the surface of the earth, the acceleration due to gravity will be of the same as in a mine, 100 km deep?

Some More Questions From Motion in Straight Line Chapter

What is rest?

What is motion?

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

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