At a height ' $R$ ' above the earth's surface the gravitational acceleration is ( $\mathrm{R}$ = radius of…

At a height ' $R$ ' above the earth's surface the gravitational acceleration is ( $\mathrm{R}$ = radius of earth, $\mathrm{g}$ = acceleration due to gravity on earth's surface)
  1. g
  2. $\frac{\mathrm{g}}{8}$
  3. $\frac{\mathrm{g}}{4}$
  4. $\frac{\mathrm{g}}{2}$

Solution

Acceleration due to gravity is given by $\begin{aligned} & \mathrm{g}^{\prime}=\frac{\mathrm{GM}}{\mathrm{r}^2}=\frac{\mathrm{GM}}{(\mathrm{R}+\mathrm{h})^2}=\frac{\mathrm{GM}}{(2 \mathrm{R})^2} \\ & =\frac{\mathrm{GM}}{4 \mathrm{R}^2}=\frac{\mathrm{g}}{4} \end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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