Question

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

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

Answer 1

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

$\begin{array}{cc}\text{Given}-& \ast \text{Mass of earth}=M\\ & \ast \text{Radius of earth}=R\\ & \ast \text{Time period of Rotation}=T\end{array}$

$\begin{array}{c}\text{we have time period}=T\\ \text{Therefore the angular velocity w}\\ w=\frac{2\pi }{T}\end{array}$

$\begin{array}{c}\text{we know that moment of Inertia(I) of a Sphere-}\\ I=\frac{2}{5}M{R}^2\\ \text{Theretore angular mo mentum will be (L)}\\ L=I\omega =\frac{2}{5}M{R}^2\cdot \left(\frac{2\pi }{T}\right)\\ \text{Hence, option (A) is correct.}\end{array}$