Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { At surface: } \mathrm{mg}=300 \mathrm{~N} \ & \mathrm{~m}=\frac{300}{\mathrm{~g}_{\mathrm{s}}} \ & 	ext { At Depth } \frac{\mathrm{R}}{4}: \mathrm{g}_{\mathrm{d}}=\mathrm{g}_{\mathrm{s}}\left[1-\frac{\mathrm{d}}{\mathrm{R}}ight] \ & \mathrm{g}_{\mathrm{d}}=\mathrm{g}_{\mathrm{s}}\left[1-\frac{\mathrm{R}}{4 \mathrm{R}}ight] \ & \mathrm{g}_{\mathrm{d}}=\frac{3 \mathrm{~g}_{\mathrm{s}}}{4}\end{aligned}$ weight at depth $\quad=\mathrm{m} 	imes \mathrm{g}_{\mathrm{d}}$ $\begin{aligned} & =\mathrm{m} 	imes \frac{3 \mathrm{~g}_{\mathrm{s}}}{4} \ & =\frac{3}{4} 	imes 300 \ & =225 \mathrm{~N}\end{aligned}$

Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface…

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