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JEE Advanced 2006
Exam
JEE Advanced
Year
2006
Subject
Physics
Chapter
Rotational Motion

JEE Advanced 2006 · Physics · Rotational Motion

A solid sphere of radius R has moment of inertia J about its...

 A solid sphere of radius \text{ A solid sphere of radius }R  has moment of inertia \text{ has moment of inertia }J  about its qeometrical axis. If it is \text{ about its qeometrical axis. If it is }melted into a disc of radius rr and thickness tt. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to II, then the value of rr is equal to A solid sphere of radius R has moment of inertia J about its qeometrical axis. If it is melted into a disc of radius r

Options

  1. A215R\frac{2}{\sqrt{15}} R
  2. B25R\frac{2}{\sqrt{5}} R
  3. C315R\frac{3}{\sqrt{15}} R
  4. D315R\frac{\sqrt{3}}{\sqrt{15}} R

Correct answer

A. 215R\frac{2}{\sqrt{15}} R

Step-by-step solution

23MR2=12Mr2+Mr2\frac{2}{3} M R^2=\frac{1}{2} M r^2+M r^2 or 23MR2=32Mr2⇒r=215R\frac{2}{3} M R^2=\frac{3}{2} M r^2 \Rightarrow r=\frac{2}{\sqrt{15}} R
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