Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth from the surface of earth, if its weight on the surface of earth is 200 N, will be:
Select the correct option:
A
400 N
B
500 N
C
300 N
D
100 N
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol.
$$
\mathrm{M}=\frac{\mathrm{W}}{\mathrm{~g}}=\frac{200}{10}=20 \mathrm{~kg}
$$
Acc. Due to gravity at a depth $\mathrm{g}^{\prime}=\mathrm{g}\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)$
$$
\begin{aligned}
& d \rightarrow \text { depth from surface } \\
& d=\frac{R}{2} \\
& g^{\prime}=g\left(1-\frac{R / 2}{R}\right)=\frac{g}{2}=5 \mathrm{~m} / \mathrm{s}^2 \\
& \text { weight }=m \times g \\
& \text { at depth } R / 2=20 \times 5=100 \mathrm{~N}
\end{aligned}
$$
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