Question

What is the M.I. of a wheel of mass m and radius having two spokes each of mass am about an axis perpendicular to the plane and passing through it center?

• A. $\frac{2}{3}m{r}^2$
• B. $\frac{5}{3}m{r}^2$
• C. $\frac{m{r}^2}{2}$
• D. $m{r}^2$

Answer 1

The correct option is B $\frac{5}{3}m{r}^2$

$\begin{array}{c}\text{Given, mass and radius of wheel (Pereferably ring) are}\\ m\text{and}r\text{respectively.}\\ \text{Also, mass and length on two spokes OA and OB Each are}\\ m\text{and}r\text{.}\\ \text{Here, spokes can be considered as rotating rod.}\end{array}$

$\begin{array}{c}\text{Thus, required moment of inertia}=I_{\text{wheel}}+I_{\text{spokes}}\\ =\left(m{r}^2\right)+2\times \left[\frac{m{r}^2}{3}\right]\\ =\frac{5}{3}m{r}^2\end{array}$