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The value of acceleration due to gravity...

The value of acceleration due to gravity `(g)` at height `h` above the surface of earth is given by
`g^'=(gR^2)/((R+h)^2)`. If `hlt ltR`, then prove that `g^'=g(1-(2h)/(R))`.

Text Solution

Verified by Experts

`g^(')=g ((R)/(R+h))^(2)=g((1)/(1+(h)/(R)))^(2)`
`=(g)/((1+(h)/(R))^(2))=g(1+(h)/(R))^(-2)`
`=g(1-(2h)/(R))`
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