Question

Two circular plates of radii in the ratio $1:2$ are cut and removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller to larger circular plates about axes perpendicular to the planes of plates and passing through their centers is:

• A. $1:4$
• B. $1:8$
• C. $1:16$
• D. $1:32$

Answer 1

Answer: (C)

$1:16$

Moment of Inertia $=\frac{1}{2}M{R}^2$ for a disc
Radii are in a ratio $1:2$
$\Rightarrow M_1:M_2=\rho \left(\pi R_1^{2}t\right):\rho \left(\pi R_2^{2}t\right)$..........($t$ is the thickness of the sheet)
$=1:4$
$\therefore ratioofMomentofInertia=\frac{M_1}{M_2}\times {\left(\frac{R_1}{R_2}\right)}^2$
$=\frac{1}{4}\times \frac{1}{4}=\frac{1}{16}$