JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) is
- A \(\sqrt{2}\)
- B \(2\)
- C \(4\)
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(I_{1}=\frac{M R^{2}}{2}=\frac{\rho\left(\pi R^{2}\right) t \cdot R^{2}}{2}\) \(I \propto R^{4}\) \(\frac{I_{1}}{I_{2}}=\frac{R_{1}^{4}}{R_{2}^{4}}=\frac{1}{16}\) \(\therefore \frac{R_{1}}{R_{2}}=\frac{1}{2}\)
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