Question

The two spheres, one of which is hollow and other solid, have identical masses and moment of inertia about their respective diameters. The ratio of their radii is given by

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

Answer 1

Answer: (C)

$\sqrt{3}:\sqrt{5}$

Given:-

Both spheres are identical in mass and moment of inertia.

$i.e$ $m_{hollow}=m_{solid}$ and $I_{hollow}=I_{solid}$

$I_{hollow}=\frac{2m_{\left(hollow\right)}{r}_{\left(hollow\right)}^2}{3}$

$I_{solid}=\frac{2m_{\left(solid\right)}{r}_{\left(solid\right)}^2}{5}$

$\frac{r_{\left(hollow\right)}}{r_{\left(solid\right)}}=\sqrt{\frac{3}{5}}$