JEE Main 2022 — Rotational Motion Question with Solution

For solid sphere

$I_0=I_{\mathrm{com} }+M{R}^2$  (Using parallel axis theorem)

$I_0=\frac{2}{5}M{R}^2+M{R}^2$

$I_0=\frac{7}{5}M{R}^2$$\Rightarrow A\to II$

For hollow sphere

$I=I_{\mathrm{com}}+M{R}^2\Rightarrow I=\frac{5}{3}M{R}^2\Rightarrow B\to I$

For Circular ring

$I_1+I_2=I_3$ ( Using perpendicular axis theorem)

By symmetry MOI

About $1$ and $2$ Axis are same i.e.

$I_1=I_2$

$\therefore 2I_1=I_3=M{R}^2 \left(\because I_{com}=M{R}^2\right)$

$I_1=\frac{M{R}^2}{2}\Rightarrow C\to IV$

Similarly in disc

$2I_1=\frac{M{R}^2}{2}\left\{\because I_{\mathrm{com}}=\frac{M{R}^2}{2}\right\}$

$I_1=\frac{M{R}^2}{4}\Rightarrow D\to III$