Question

M.O.I. of a ring of radius $R$ and mass $M$ about a line passing throught its center and perpendicular to its plane is $I$. Find out the M.O.I $\left(I_t\right)$ about an axis which is a tangent and also perpendicular to the plane of circle as shown in figure.

• A. $I+M{R}^2$
• B. $I-M{R}^2$
• C. $I-MR$
• D. $I+MR$

Answer 1

The correct option is A $I+M{R}^2$

Given M.O.I. about center, $I_z=I_{com}=I$
Radius of circle $=R$

As we know from parallel axis theorem
$I_t=I_{com}+M{d}^2$
Where $d$ perpendicular/shortest
distance between axis $I_{com}$ and $I_t$.
$\therefore I_t=I+M{R}^2$