Question

The $M.I$ of a semi circular ring of mass $M$ and radius ${}^{\prime }{R}^{\prime }$ about an axis lying the plane which is passing through its centre and angle $\theta$ with the line joining its end is:

• A. $\frac{{MR}^2}{2}$ if $\theta =0^o$
• B. $\frac{{MR}^2}{2}$ at $\theta ={60}^o$
• C. $\frac{{MR}^2}{2}$ at $\theta ={120}^o$
• D. $\frac{{MR}^2}{2}$ at $\theta ={180}^o$

Answer 1

The correct option is A $\frac{{MR}^2}{2}$ if $\theta =0^o$

Moment of inertia of ring through an axis perpendicular to its plane through its centre is $M{R}^2$

$I_x+I_y=I_z$

where x,y,z are perpendicular planes

moment of inertia through diameter is $I=\frac{M{R}^2}{2}$

where $\theta =0^0$