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

Answer 1

Answer: (B)

The moment of inertia $I$ of a solid sphere about the axis of rotation through the centre is
$I = \frac{2}{5} MR^{2}$
$\therefore $ Angular momentum $L = I\omega$
$ = \frac{2}{5}MR^{2}\times\frac{2\pi}{T}$
$= \frac{4\pi MR^{2}}{5T}$
where $T = $ time period of rotation.