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At what altitude, the acceleration due t...

At what altitude, the acceleration due to gravity reduces to one fourth of its value as that on the surface of the earth ? Take radius of earth as `6.4 xx 10^(6) m`, g on the surface of the earth as `9.8 ms^(-2)`.

Text Solution

Verified by Experts

We have given that
`g_(h) = g[R/(R+h)]^(2)`
` (g_(h))/g = [R/(R+h)]^(2)`
` :. 1/(sqrt(2)) = [R/(R+h)] `
` :. R + h = sqrt(2)R `
` h = (sqrt(2)-1)R`
` :. h = (1.414-1) 6.4 xx10^(6)`
` :. h = 2.65 xx10^(6)m `
Acceleration due to gravity is reduced to half its value on the earth.s surface at an altitude of `2.65 xx10^(6)` m .
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