Question

A circular disc $X$ of radius $R$ is made from an iron plate 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. $I_Y=8I_x$
• B. $I_Y=16I_x$
• C. $I_Y=32I_x$
• D. $I_Y=64I_x$

Answer 1

Answer: (D)

$I_Y=64I_x$

Mass of disc = $\pi r^{2}t\rho$

now $I_x=\frac{\pi R^{4}t\rho }{2}$

now $I_Y=\frac{\pi (4R{)}^{4}t/4\rho }{2}$

from above 2 equations $I_Y=64I_x$