A body weighs $300 \mathrm{~N}$ on the surface of the earth. How much will it weigh at a distance…
A body weighs $300 \mathrm{~N}$ on the surface of the earth. How much will it weigh at a distance $\frac{R}{2}$ below the surface of earth? ( $\mathrm{R} \rightarrow$ Radius of earth)
$300\ N$
$250\ N$
$200\ N$
$150\ N$
Solution
Acceleration due to gravity at depth $\mathrm{d}$,
$\begin{aligned}
\mathrm{g}_{\mathrm{d}} & =\mathrm{g}\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right) \\
& =\mathrm{g}\left(1-\frac{1}{2}\right) \quad \because \mathrm{d}=\frac{\mathrm{R}}{2} \\
& =\frac{\mathrm{g}}{2}
\end{aligned}$
$\therefore \quad$ Weight of the body at depth $\mathrm{d}_1$
$\mathrm{W}_{\mathrm{d}}=\mathrm{mg}_{\mathrm{d}}=300 \times \frac{1}{2}=150 \mathrm{~N}$