Question

All sheets are of same mass $\frac{M}{2}$ each but radius $R,\frac{R}{2},\frac{R}{4},\frac{R}{8}$.......There are infinitesheets. What is the moment of inertia about the center?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Moment of inertia, $I=\frac{M{R}^2}{2}+\frac{M}{2}(\frac{R}{4}{)}^2\pm ....$

$I=M{R}^2(\frac{1}{2}+\frac{1}{8}+\frac{1}{32}+....)$

This is a G. P of infinite terms with common ratio, $r=\frac{1}{4}$

$\therefore$ $S_{\propto }=\frac{a}{1-r}=\frac{\frac{1}{2}}{1-\frac{1}{4}}=\frac{2}{3}$

$\therefore I=M{R}^2(\frac{2}{3})=\frac{2}{3}M{R}^2$