MHT CET · Physics · 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 \(\frac{\mathrm{b}}{\mathrm{R}}\) is
- A \(1:1\)
- B \(\sqrt{3}:1\)
- C \(\sqrt{6}:1\)
- D \(1:\sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{3}:1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{I}_{\text {lamina }}=\frac{\mathrm{Mb}^2}{6} \\ & \mathrm{I}_{\text {disc }}=\frac{\mathrm{MR}^2}{2} \\ & \text { Given } \frac{\mathrm{Mb}^2}{6}=\frac{\mathrm{MR}^2}{2} \\ & \quad \frac{\mathrm{b}^2}{\mathrm{R}^2}=3 \\ & \therefore \quad \frac{\mathrm{b}}{\mathrm{R}}=\frac{\sqrt{3}}{1}\end{aligned}\)
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