Question 570: Centre of Mass and Rotational Motion

Question

A square lamina of side '$$b$$' has same mass as a disc of radius '$$R$$' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $$\frac{b}{R}$$ is

Accepted Answer

$$\begin{aligned}
& \mathrm{I}_{	ext {lamina }}=\frac{\mathrm{Mb}^2}{6} \
& \mathrm{I}_{	ext {disc }}=\frac{\mathrm{MR}^2}{2} \
& 	ext { Given } \frac{\mathrm{Mb}^2}{6}=\frac{\mathrm{MR}^2}{2} \
& \frac{\mathrm{b}^2}{\mathrm{R}^2}=3 \
& 	herefore \quad \frac{\mathrm{b}}{\mathrm{R}}=\frac{\sqrt{3}}{1}
\end{aligned}$$

Answer

$$1: 1$$

Answer

$$\sqrt{3}: 1$$

Answer

$$\sqrt{6}: 1$$

Answer

$$1: \sqrt{3}$$

Centre of Mass and Rotational Motion

A square lamina of side '$b' has same mass as a disc of radius 'R' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio \frac{b}{R}$ is

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