Question

A solid sphere of mass M and radius R having a moment of inertia I about its diameter is recast into a solid disc fo radius r and thickness t. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains I. Then R and r are related as

• A. $r=\sqrt{\frac{2}{15}}R$
• B. $r=\sqrt{\frac{2}{15}}R$
• C. $r=\frac{2}{15}R$
• D. $r=\frac{2}{\sqrt{15}}R$

Answer 1

The correct option is B $r=\sqrt{\frac{2}{15}}R$

$I_{AB}=\frac{2}{5}M{R}^2=I$ (given) (i)
$I_{A^{\prime }{B}^{\prime }}=I_{Y{Y}^{\prime }}+M{r}^2=I\frac{1}{2}M{r}^2+M{r}^2$
$=\frac{3}{2}M{r}^2=1$ (given) (ii)
From Eqs. (i) and (ii), $\frac{2}{5}M{R}^2=\frac{3}{2}M{r}^2\Rightarrow r=\frac{2}{\sqrt{15}}R$