Question

A circular disc $X$ of radius $R$ is made from an iron pole of thickness $t$, and another disc Y of radius $4R$ is made from an iron plate of thickness $\frac {t}{4}$. then the relation between the moment of inertia $I_X$ and $I_Y$ is

• A. $I_y=32I_x$
• B. $I_y=16I_x$
• C. $I_y=32\,I_x$
• D. $I_y=64\,I_x$

Answer 1

Answer: (D)

If t is the thickness and R is the radius of the disc, then mass $= πR^2tρ$
$ρ =$ density of the material of the disc.
Moment of inertia of disc X,
$I_{x}=\frac{1}{2}\pi R^{4}t\rho\,...\left(i\right)$
Moment of inertia of disc Y,
$I_{y}=32\,\pi R^{4}t\rho\,...\left(ii\right)$
From equation $\left(i\right)$ and $\left(ii\right)$
$I_{y}=64\,I_{x}$