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Atoms And Molecules

Question
CBSEENSC9006147

At what height from the surface of the earth, will the value of g be reduced by 36% from the value at the surface ? Radius of the earth = 6400 km.

Solution

Given,
At height h, the value of g reduces by 36%.
i.e., it becomes 64% of that at the surface.
Then,
            straight g subscript straight h space equals space 64 percent sign space o f space straight g space equals space 64 over 100 straight g
But space space space straight g subscript straight h space equals space straight g open parentheses fraction numerator straight R over denominator straight R plus straight h end fraction close parentheses squared
therefore space space space space space space space 64 over 100 straight g space equals space straight g open parentheses fraction numerator straight R over denominator straight R plus straight h end fraction close parentheses squared space space
rightwards double arrow space space space space space space space space space space 8 over 10 space equals space fraction numerator straight R over denominator straight R plus straight h end fraction

rightwards double arrow space space space straight h space equals space straight R over 4 space
space space space space space space space space space space space equals 6400 over 4 space
space space space space space space space space space space space equals space 1600 space km. space space