Question

We have two spheres, one of which is hollow and other is solid. They have identical mass and moment of inertia about its tangent. The ratio of their radii is given by

• A. $\frac{\sqrt{3}}{\sqrt{5}}$
• B. $\frac{\sqrt{5}}{\sqrt{7}}$
• C. $\frac{\sqrt{21}}{5}$
• D. $\frac{\sqrt{7}}{5}$

Answer 1

Answer: (C)

$I_{1}=\frac{2}{3} m R_{1}^{2}+m R_{1}^{2}$
$I_{1}=\frac{5}{3} m R_{1}^{2}$
$I_{2}=\frac{2}{5} m R_{2}^{2}+m R_{2}^{2}$
$I_{2}=\frac{7}{5} m R_{2}^{2}$
$I_{1}=I_{2}$
$\frac{5}{3} m R_{1}^{2}=\frac{7}{5} m R_{2}^{2}$
$\left(\frac{R_{1}}{R_{2}}\right)^{2}=\frac{21}{25}$
$\frac{R_{1}}{R_{2}}=\frac{\sqrt{21}}{5}$