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Motion In Straight Line

Question
CBSEENPH11017575

At what height from the surface of the earth the acceleration due to gravity is 1% less than that on the surface of the earth?

Solution
The acceleration due to gravity at the surface of the earth is, 
                straight g equals GM over straight R squared                         ...(1) 
Let at height h from the surface of the earth, the acceleration due to gravity be 1% less than that on the surface of the earth. 
∴           space space space 0.99 straight g equals fraction numerator GM over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction               ...(2) 
From (1) and (2), 
           space space space fraction numerator straight g over denominator 0.99 straight g end fraction equals fraction numerator left parenthesis straight R plus straight h right parenthesis squared over denominator straight R squared end fraction 
rightwards double arrow           fraction numerator straight R plus straight h over denominator straight R end fraction equals 1.005 
rightwards double arrow                  h = 32km, is the height from the surface of the earth.