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InterviewSolution
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Calculate the distance from the surface of the earth at which above the surface, acceleration due to gravity is the same. |
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Answer» Correct Answer - `h=(sqrt(5)-1)/(2)R` Let at height or depth h from surface of earth acceleration due to gravity is same. `g_(d)=g_(h)` `g(1-(h)/(R ))=(gR^(2))/((R+h)^(2))rArr ((R-h))/(R )=(R^(2))/((R+h^(2)))` `(R-h)(R+h)^(2)=R^(3)rArr (R-h)(R^(2)+h^(2)+2hR)=R^(3)` `R^(3)+Rh^(2)+2hR^(2)-hR^(2)-h^(3)-2h^(2)R=R^(3)rArr h^(2)+Rh-R^(2)=0` `h = (-R+-sqrt(R^(2)+4R^(2)))/(2) rArr ((sqrt(5)-1)R)/(2)` |
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