Physics - Rotation Question with Solution | TestHub

The moment of inertia of a uniform solid sphere about its diameter is given by the formula $I=\frac{2}{5}M{R}^2$. For the first sphere, with mass $M$ and radius $R$, its moment of inertia is $I_1=\frac{2}{5}M{R}^2$. For the second sphere, with mass $M$ and radius $2R$, its moment of inertia is $I_2=\frac{2}{5}M(2R{)}^2=\frac{2}{5}M(4R^2)=\frac{8}{5}M{R}^2$. The ratio $I_1/I_2$ is $\frac{I_1}{I_2}=\frac{\frac{2}{5}M{R}^2}{\frac{8}{5}M{R}^2}=\frac{2}{8}=\frac{1}{4}$. Oh wait, I made a mistake in calculation. Let me recheck. $I_2=(2/5)M(2R{)}^2=(2/5)M(4R^2)=(8/5)M{R}^2$. So $I_1/I_2=(2/5)M{R}^2/((8/5)M{R}^2)=2/8=1/4$. The options are 1:2, 1:4, 1:8, 1:16. My option A is 1:2, B is 1:4. So B is correct. Let me re-read the question and options. The ratio $I_1/I_2=\frac{\frac{2}{5}M{R}^2}{\frac{2}{5}M(2R{)}^2}=\frac{R^2}{(2R{)}^2}=\frac{R^2}{4R^2}=\frac{1}{4}$. So the ratio is $1:4$. Option B is correct.