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MHT CET 2021 (23 Sep, Shift 2) · Acceleration Due to Gravity

Acceleration Due to Gravity question from MHT CET 2021 (23 Sep, Shift 2)

Q100MHT CET 2021 · 23 SEP · SHIFT 2Difficult

Acceleration Due to Gravity

A body of mass 'M' and radius 'R', situated on the surface of the earth becomes weightless at its equator when the rotational kinetic energy of the earth reaches a critical value 'K'. The value of 'K' is given by [Assume the earth as a solid sphere, g = gravitational acceleration on the earth's surfacde]

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Answer: (d)

Here $M$ and $R$ are the earth's mass and radius.
Weightless at equator: $\omega^2 R = g \Rightarrow \omega^2 = \frac{g}{R}$
$K = \frac{1}{2}I\omega^2 = \frac{1}{2} \cdot \frac{2}{5}MR^2 \cdot \frac{g}{R}$
$K = \frac{1}{5}MgR$ , so the answer is (d).

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