Question:
A solid sphere (radius \(R\)) recast into disc. MOI about edge remains same. Find disc radius.
A solid sphere (radius \(R\)) recast into disc. MOI about edge remains same. Find disc radius.
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Edge MOI = CM MOI + \(MR^2\).
Updated On: Apr 23, 2026
- \(\frac{2R}{\sqrt{15}}\)
- \(R\sqrt{\frac{2}{15}}\)
- \(\frac{4R}{\sqrt{15}}\)
- \(\frac{R}{4}\)
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The Correct Option is A
Solution and Explanation
Concept:
Use parallel axis theorem.
Step 1: Sphere MOI
\[ I = \frac{2}{5}MR^2 \]
Step 2: Disc MOI about edge
\[ I = I_{cm} + MR^2 = \frac{1}{2}Mr^2 + Mr^2 = \frac{3}{2}Mr^2 \]
Step 3: Equate
\[ \frac{2}{5}MR^2 = \frac{3}{2}Mr^2 \] \[ r^2 = \frac{4}{15}R^2 \Rightarrow r = \frac{2R}{\sqrt{15}} \] Conclusion: \[ \frac{2R}{\sqrt{15}} \]
Step 1: Sphere MOI
\[ I = \frac{2}{5}MR^2 \]
Step 2: Disc MOI about edge
\[ I = I_{cm} + MR^2 = \frac{1}{2}Mr^2 + Mr^2 = \frac{3}{2}Mr^2 \]
Step 3: Equate
\[ \frac{2}{5}MR^2 = \frac{3}{2}Mr^2 \] \[ r^2 = \frac{4}{15}R^2 \Rightarrow r = \frac{2R}{\sqrt{15}} \] Conclusion: \[ \frac{2R}{\sqrt{15}} \]
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