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Explain the variation of 'g' with altitude. |
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Answer» SOLUTION :Variation of g with altitude: Consider an object of mass m at a height h from the SURFACE of the Earth. Acceleration experienced by the object due to Earth is `g' = (GM)/((R_(E) + h)^(2))` `R_(E) to` Radius of Earth `g' = (GM)/(R_(E)^(2)(1 + h/(R_E))^(2)) = (GM)/(R_E^2) (1 + h/(R_E))^(-2)` If `h < < R_(E)` We can use Binomial expansion. Taking the terms UPTO first order `g' = (GM)/(R_E^2) (1-2h/(R_E)) = g(1-2 h/(R_E))` We find TAT `g' < g`. This means that as altitude h increases, the acceleration due to gravity g decreases.  .
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