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 r/4. Then the relation between Ac moments of inertia $I_x$ and $I_{\gamma }$ is

• A. $I_{\gamma }=32I_x$
• B. $I_{\gamma }=16I_x$
• C. $I_{\gamma }=I_x$
• D. $I_{\gamma }=64I_x$

Answer 1

Answer: (D)

Mass of disc $(X),m_x=\pi R^{2}t\rho$ where, $\rho =$ density of material of disc $\therefore$ $I_x=\frac{1}{2}{m}_x{R}^2=\frac{1}{2}\pi R^{2}t\rho R^2$ $I_x=\frac{1}{2}\pi \rho t{R}^2$ ...(i) Mass of disc (Y) $m_Y=\pi {(4R)}^2\frac{t}{4}\rho =4\pi R^{2}t\rho$ and $I_Y=\frac{1}{2}{m}_y{(4R)}^2=\frac{1}{2}4\pi R^{2}t\rho .16R^2$ $\Rightarrow$ $I_Y=32\pi t\rho R^2$ ...(ii) $\therefore$ $\frac{I_Y}{I_X}=\frac{32\pi t\rho R^2}{\frac{1}{2}\pi \rho t{R}^4}=64$ $\therefore$ $I_Y=64I_X$