A body weighs 48 N on the surface of the earth. The gravitational...

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is :

Options

A16 N
B27 N
C32 N
D36 N

Correct answer

B. 27 N

Step-by-step solution

\begin{aligned} & \mathrm{W}^{\prime}=\mathrm{mg}^{\prime}=\mathrm{mg}\left(\frac{\mathrm{R}}{\mathrm{R}+\mathrm{h}}\right)^2 \\ & =48\left(\frac{\mathrm{R}}{\mathrm{R}+\frac{\mathrm{R}}{3}}\right)^2 \\ & =48 \times \frac{9}{16}=27 \mathrm{~N}\end{aligned}

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