The height above the surface of the earth where acceleration due to gravity becomes…

The height above the surface of the earth where acceleration due to gravity becomes $\left(\frac{g}{9}\right)$ is ( $R$ is radius of the earth, $g$ is acceleration due to gravity)
  1. 2R
  2. $\frac{R}{3}$
  3. $\frac{R}{\sqrt{2}}$
  4. $\sqrt{2} R$

Solution

$\begin{aligned} & g^{\prime}=\frac{g}{\left(1+\frac{h}{R}\right)^2} \\ & \frac{g}{9}=\frac{g}{\left(1+\frac{h}{R}\right)^2} \\ & h=2 R\end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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