Question

The moment of inertia of a wheel which is having rim of mass $20M$ and twenty spokes each of mass $M$ and length $L$ about its axis is

• A. $\frac{20}{3}M{L}^2$
• B. $\frac{40}{3}M{L}^2$
• C. $\frac{50}{3}M{L}^2$
• D. $\frac{80}{3}M{L}^2$

Answer 1

The correct option is A $\frac{20}{3}M{L}^2$

$\begin{array}{c}\text{Moment of Inertia along one end of}\\ \text{the rod is}\frac{m{d}^2}{3}\text{.}\\ \text{The Moment of inetia of whed along its}\\ \text{axis does not depend on the number of}\\ \text{spokes.}\\ \text{Here spokes are considered as rods}\\ \text{Hence moment of inertia will be}\frac{20M{x}^2}{3}\text{.}\\ \text{Therefore option}\left(A\right)\text{is correct}\end{array}$