Question

If $l _{ xy }$ is the moment of inertia of a ring about a tangent in the plane of the ring and $I_{x^{\prime} y^{\prime}}$ is the moment of inertia of a ring about a tangent perpendicular to the plane of the ring then

• A. $I_{x y}=I_{x^{\prime} y}$
• B. $I_{x y}=\frac{1}{2} I_{x^{\prime} y}$
• C. $I_{x^{\prime} y^{\prime}}=\frac{3}{4} I_{x y}$
• D. $I_{x y}=\frac{3}{4} I_{x^{\prime} y}$

Answer 1

Answer: (D)

$I_{x y}$, moment of inertia of a ring about its tangent in the plane of ring $I_{x^{\prime} y}=\frac{3}{2} MR ^2$
Moment of inertia about a tangent perpendicular to the plane of ring $I_{x y}=2 MR ^2$
$\therefore I_{x y}=\frac{3}{4}\left(2 M^2\right)=\frac{3}{2} M R^2 \text { or } I_{x y}=\frac{3}{4} I_{x^1 y} 1$