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MHT CET · Physics · Gravitation

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)

  1. A \(300\ N\)
  2. B \(250\ N\)
  3. C \(200\ N\)
  4. D \(150\ N\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(150\ N\)

Step-by-step Solution

Detailed explanation

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 \(\mathrm{d}_1\)
\(\mathrm{W}_{\mathrm{d}}=\mathrm{mg}_{\mathrm{d}}=300 \times \frac{1}{2}=150 \mathrm{~N}\)