Question

A uniform wire of length l and mass M bented in the shape of semicircle of radius r as shown in figure.Calculate moment of inertia about XX'

• A. $\frac{M{l}^2}{2{\pi }^2}$
• B. $\frac{4M{l}^2}{{\pi }^2}$
• C. $\frac{4M{l}^2}{4{\pi }^2}$
• D. None of the above

Answer 1

The correct option is D None of the above

So, $l=\pi r+2rl=r(\pi +2)r=\left(\frac{l}{\pi +r}\right)$

Now, $I_{ring}$ about diameter

$\frac{M{R}^2}{2}\Rightarrow M(\frac{l}{\pi +2}{)}^2$

No option is correct.