Question:
How much deep inside the earth (radius \(R\)) should a man go, so that his weight becomes one-fourth of that on the earth’s surface?
How much deep inside the earth (radius \(R\)) should a man go, so that his weight becomes one-fourth of that on the earth’s surface?
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Gravity decreases linearly inside Earth.
Updated On: Apr 16, 2026
- \( \frac{R}{2} \)
- \( \frac{3R}{4} \)
- \( \frac{R}{4} \)
- \( \frac{R}{3} \)
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The Correct Option is B
Solution and Explanation
Concept:
Inside earth:
\[
g' = g\left(1 - \frac{d}{R}\right)
\]
Step 1: Given condition.
\[ \frac{g'}{g} = \frac{1}{4} \]
Step 2: Solve.
\[ 1 - \frac{d}{R} = \frac{1}{4} \Rightarrow \frac{d}{R} = \frac{3}{4} \] \[ d = \frac{3R}{4} \]
Step 1: Given condition.
\[ \frac{g'}{g} = \frac{1}{4} \]
Step 2: Solve.
\[ 1 - \frac{d}{R} = \frac{1}{4} \Rightarrow \frac{d}{R} = \frac{3}{4} \] \[ d = \frac{3R}{4} \]
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