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Motion In Straight Line

Question
CBSEENPH11017513

If acceleration due to gravity at the surface of the earth is g, what will be the acceleration due to gravity at height h? 

Solution
At surface of the earth, the acceleration due to gravity g is given by, 
                          straight g equals GM over straight R squared 
                   
At height h from surface of the earth, it is given by
space space space space space space space straight g subscript straight h equals fraction numerator GM over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction equals GM over straight R squared fraction numerator straight R squared over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction 
      space space space equals straight g fraction numerator straight R squared over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction 
    straight g subscript straight h equals straight g fraction numerator straight R squared over denominator straight R squared open parentheses 1 plus begin display style straight h over straight R end style close parentheses squared end fraction equals straight g open parentheses 1 plus straight h over straight R close parentheses to the power of negative 2 end exponent
 
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#6 {main}</pre>, is the acceleration due to gravity at height h.