Depth at which weight becomes one-fourth – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

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?
\(\frac{R}{4}\)
\(\frac{R}{2}\)
\(\frac{3R}{4}\)
None

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

The acceleration due to gravity at depth \(d\) is \(g' = g \left(1 - \frac{d}{R}\right)\). Setting \(g' = g/4\), we get \(1 - \frac{d}{R} = \frac{1}{4}\) which gives \(d = \frac{3R}{4}\).

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