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 disc of radius $2 R$ about its diameter
$I _{ d }=\frac{1}{4} M _{ d }(2 R )^{2}$
Given, $I_{ s }=I_{d}$
$\frac{2}{5} M _{ s } R ^{2}=\frac{1}{4} M _{ d }(2 R )^{2}$
$\frac{ M _{ s }}{ M _{ d }}=\frac{5}{2}$