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

(1) 75 N 

(2) 375 N 

(3) 300 N 

(4) 225 N

1 Answer

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Best answer

Correct option is : (4) 225 N

 At surface: \(\mathrm{mg}=300 \mathrm{~N}\)

\( \mathrm{m}=\frac{300}{\mathrm{~g}_{\mathrm{s}}} \)

At Depth \(\frac{\mathrm{R}}{4}: \mathrm{g}_{\mathrm{d}}=\mathrm{g}_{\mathrm{s}}\left[1-\frac{\mathrm{d}}{\mathrm{R}}\right]\)

\(g_{d}=g_{s}\left[1-\frac{R}{4 R}\right]\)

\(\mathrm{g}_{\mathrm{d}}=\frac{3 \mathrm{g}_{\mathrm{s}}}{4}\)

weight at depth

\(\begin{aligned} & =\mathrm{m} \times \mathrm{g}_{\mathrm{d}} \\ \end{aligned}\)    

\(\begin{aligned} =\mathrm{m} \times \frac{3 \mathrm{g}_{\mathrm{s}}}{4} \\ \end{aligned}\)  

\( \begin{aligned} & =\frac{3}{4} \times 300 \\ \end{aligned} \)

\(=225 \mathrm{~N}\)

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