Relative Acceleration of Earth and a Superdense Mass – Rankers Physics

Gravitational Field: Practice Problem & Solution

A body of superdense material with mass twice the mass of earth but size very small compared to the size of earth starts from rest from \(h \ll R\) above the earth's surface. It reaches earth in time \(t\). Then:
\(t = \sqrt{\frac{h}{g}}\)
\(t = \sqrt{\frac{2h}{g}}\)
\(t = \sqrt{\frac{2h}{3g}}\)
\(t = \sqrt{\frac{4h}{3g}}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Gravitational Field. Understanding the underlying formula is key to arriving at the correct answer below:

The acceleration of the earth towards the body is \(a_E = 2g\) and the body towards the earth is \(a_B = g\). The relative acceleration is \(a_{rel} = 3g\). Using \(h = \frac{1}{2} a_{rel} t^2\), we get \(t = \sqrt{\frac{2h}{3g}}\).

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