Question

A wheel comprises of a ring of radius $R$ and mass and three spokes of mass $m$ each. The moment of inertia of the wheel about its axis is

• A. $(M+\frac{m}{4})R^2$
• B. $(M+m)R^2$
• C. $(M+3m)R^2$
• D. $\left(\frac{M+m}{2}\right)R^2$

Answer 1

The correct option is B $(M+m)R^2$

The moment of inertia of the ring is $I_1=M{R}^2$

The moment of inertia of every spoke is $I_2=\frac{1}{3}m{R}^2$ since O is at the end of each spoke.

Total moment of inertia $I=I_1+3I_2$ since there are three spokes.

$⟹I=M{R}^2+m{R}^2$

$⟹I=(M+m)R^2$

Answer-(B)