Q119 / 150 · MHT CET 2022 (07 Aug Shift 2) · Physics

A body weighs ' $W$ ' newton on the surface of the earth its weight at a height equal to half the radius of the earth, will be

  • A
    $\frac{\mathrm{W}}{2}$
  • B
    $\frac{2 \mathrm{~W}}{3}$
  • Correct answer
    C
    $\frac{4 \mathrm{~W}}{9}$
  • D
    $\frac{8 W}{27}$

Solution

The acceleration due to gravity at a distance $r$ from center of the earth is: $\mathrm{g}^{\prime}=\frac{\mathrm{GM}}{\mathrm{r}^2}$ For, $r=\left(R+\frac{R}{2}\right)$ $\begin{aligned} & g^{\prime}=\left(\frac{\mathrm{GM}}{\mathrm{R}^2}\right)\left(\frac{4}{9}\right)=\frac{4}{9} \mathrm{~g}_0 \\ & \therefore \mathrm{W}^{\prime}=\mathrm{mg}=\frac{4}{9}\left(\mathrm{mg}_0\right)=\frac{4}{9} \mathrm{~W}\end{aligned}$

Hence, the correct answer is option: 'C'.

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