Question

A solid sphere and a hollow sphere of the same mass have the same moments of inertia about their respective diameters, the ratio of their radii is

• A. $(5{)}^{1/2}:(3{)}^{1/2}$
• B. $(3{)}^{1/2}:(5{)}^{1/2}$
• C. $3:2$
• D. $2:3$

Answer 1

The correct option is A $(5{)}^{1/2}:(3{)}^{1/2}$

$\begin{array}{c}\text{M.I of Solid sphere}{I}_1=\frac{2}{5}m{v}_1^2\\ \text{MI of hollow sphere}{I}_2=\frac{2}{3}m{v}_2^2\\ \begin{array}{cc}\frac{2}{5}m{r}_1^2& =\frac{2}{3}m{v}_2^2\\ \Rightarrow & \frac{r_1}{r_2}=\frac{(5{)}^{1/2}}{(3{)}^{1/2}}\end{array}\\ \text{Hence option}A\text{is correct}\end{array}$