Question

The moment of inertia of a solid sphere of radius $R$ about its diameter is same as that of a disc of radius $2R$ about its diameter. The ratio of their masses is

• A. $5:2$
• B. $5:8$
• C. $4:1$
• D. $2:1$

Answer 1

Answer: (A)

The moment of inertia of a solid sphere of radius $R$ about its diameter
$I_{s}=\frac{2}{5}M_{s}R^{2}$
The moment of inertia of a disc of radius $2R$ about its diameter
$I_{d}=\frac{1}{4}M_{d}\left(\right.2R \left(\left.\right)^{2}$
Given, $I_{s}=I_{d}$
$\frac{2}{5}M_{s}R^{2}=\frac{1}{4}M_{d}\left(\right.2R \left(\left.\right)^{2}$
$\frac{M_{s}}{M_{d}}=\frac{5}{2}$