Question

A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$ and another plate $Y$ of radius $4R$ is made from an iron late of thickness $\frac{t}{4}$ . The ratio between moments of inertia $\frac{I_x}{I_x}$ is

• A. 1
• B. 16
• C. 32
• D. 64

Answer 1

The correct option is D 64

$\begin{array}{c}discx:M=\pi R^{2}t\sigma \\ I_x=\frac{\left(\pi R^{2}t\sigma \right)}{2}=\frac{M{R}^2}{2}\\ disy=M=\pi {\left(4r\right)}^2.\frac{t}{4}\sigma \\ =4M\\ T_y=\frac{4M{\left(4R\right)}^2}{2}\\ =64\left(\frac{4R^2}{2}\right)=64J\\ =\frac{I_y}{i_x}=64\end{array}$