Question 345: Gravitation

Question

A body weighs $$500 \mathrm{~N}$$ on the surface of the earth. At what distance below the surface of the earth it weighs $$250 \mathrm{~N}$$ ? (Radius of earth, $$\mathrm{R}=6400 \mathrm{~km}$$ )

Accepted Answer

The value of $$g$$ at a depth $$h$$ below the surface of the earth of radius $$\mathrm{R}$$ is
$$\begin{aligned}
& \mathrm{g}^{\prime}=\mathrm{g}\left[1-\frac{\mathrm{d}}{\mathrm{R}}ight] \
& 	herefore \frac{\mathrm{g}^{\prime}}{\mathrm{g}}=1-\frac{\mathrm{d}}{\mathrm{R}} \quad 	ext{..... (1)}
\end{aligned}$$
It is given that $$\mathrm{mg}=500 \mathrm{~N}$$ and $$\mathrm{mg}^{\prime}=250 \mathrm{~N}$$
$$	herefore \frac{\mathrm{g}^{\prime}}{\mathrm{g}}=\frac{250}{500}=\frac{1}{2}\quad 	ext{..... (2)}$$
$$	herefore$$ From (1) and (2), $$\frac{1}{2}=1-\frac{\mathrm{d}}{\mathrm{R}}$$
$$	herefore \frac{\mathrm{d}}{\mathrm{R}}=\frac{1}{2}$$
$$	herefore \mathrm{d}=\frac{\mathrm{R}}{2}=\frac{6400}{2}=3200 \mathrm{~km}$$

Answer

6400 km

Answer

800 km

Answer

1600 km

Answer

3200 km

Gravitation

A body weighs $500 \mathrm{~N} on the surface of the earth. At what distance below the surface of the earth it weighs 250 \mathrm{~N} ? (Radius of earth, \mathrm{R}=6400 \mathrm{~km}$ )

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