Variation of Weight with Distance from Earth’s Centre – Rankers Physics
Topic: Gravitation
Subtopic: Acceleration Due to Gravity and its variation

Variation of Weight with Distance from Earth’s Centre

The weight of a body at a distance \(r\) (\(r > R\)) from the centre of earth is \(W\). The weight at a distance \(2r\) from the centre of earth is : (\(R \rightarrow\) Radius of earth)
\(\frac{W}{3}\)
\(\frac{W}{4}\)
\(\frac{W}{2}\)
\(\frac{W}{6}\)

Solution:

Outside the earth, weight \(W \propto \frac{1}{r^2}\). When distance is doubled to \(2r\), the weight becomes \(\frac{1}{2^2} = \frac{1}{4}\) of its initial value, i.e., \(\frac{W}{4}\).

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