Question

A solid sphere (radius \(R\)) recast into disc. MOI about edge remains same. Find disc radius.

• A. \(\frac{2R}{\sqrt{15}}\)
• B. \(R\sqrt{\frac{2}{15}}\)
• C. \(\frac{4R}{\sqrt{15}}\)
• D. \(\frac{R}{4}\)

Hint:

Edge MOI = CM MOI + \(MR^2\).

Answer 1

The Correct Option is A

Understanding the 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
\[ \frac{2}{5}MR^2 = \frac{3}{2}Mr^2 \] \[ r^2 = \frac{4}{15}R^2 \Rightarrow r = \frac{2R}{\sqrt{15}} \] Final Answer: \[ \frac{2R}{\sqrt{15}} \]