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If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of rotation with time period T is

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$\frac{π M R^{3}}{T}$

$\frac{M R^{2} T}{2 π}$

$\frac{2 π M R^{2}}{T}$

$\frac{4 π M R^{2}}{5 T}$

answer is D.

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Detailed Solution

Radius of earth = R

Mass of earth =M

Angular momentum about the axis of rotation is

$J = \frac{2}{5} M R^{2} \times \frac{2 π}{T} = \frac{4 π M R^{2}}{5 T}$

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