Question

If earth suddenly contracts to one fourth its present radius keeping its mass constant, what would be the length of the day?

Answer 1

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Answer 2

Given:

Mass of the Earth = M (constant)

Length of the day = 24 hours

Radius contracts to the same = R/2

To Find: The length of the day after radius is reduced T'

Formula Used:

Angular momentum is conserved.

$I\omega = I'\omega '$

Moment of inertia of the sphere, $I = \frac{2}{5}MR^2$

$\omega=\frac{2\pi}{T}$

Calculations:

As mass is constant, $I\propto R^2$

$\frac{R^2}{T}=\frac{R^2}{16T'}\\T'=\frac{T}{16}\\T=\frac{24h}{16}=1.5 h$

Thus, the length of the day would be 1.5 hours i.e. 1 hour 30 minutes.

Learn more about: Conservation of angular momentum

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