Question

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

• A. $\frac{M{R}^{2}T}{2\pi }$
• B. $\frac{4\pi M{R}^2}{5T}$
• C. $\frac{\pi M{R}^{3}T}{T}$
• D. $\frac{2\pi M{R}^2}{T}$

Answer 1

The correct option is B $\frac{4\pi M{R}^2}{5T}$

The moment of inertia $I$ of a solid sphere about the axis of rotation through the centre is $I=\frac{2}{5}M{R}^2$
$\therefore$ Angular momentum, $L=I\omega$
$=\frac{2}{5}M{R}^2\times \frac{2\pi }{T}=\frac{4\pi M{R}^2}{5T}$
where T = Time period of rotation.
Hence, the correct answer is option (b).