Question

The moment of inertia of a thin circular disc about an axis passing through its center and perpendicular to its plane is $1$. Then, the moment of inertia of the disc about an axis parallel to its diameter and touching the edge of the rim is

• A. $I$
• B. $2 \,I$
• C. $\frac{3}{2}\, I$
• D. $\frac{5}{2}\, I$

Answer 1

Answer: (D)

$\frac{5}{2}\, I$

Answer 2

Moment of inertia of a circular disc about an axis passing through center of gravity and perpendicular to its plane
$I=\frac{1}{2} M R^{2} ...(i)$
From E (i) $M R^{2}=2 I$
Then, moment of inertia of disc about tangent in a plane
$=\frac{5}{4} M R^{2}$
$=\frac{5}{4}(2 I)$
$=\frac{5}{2} I$