Question

Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere'smoment of inertia to that of the smaller sphere isSelect one:O a. 2O b. 4O C. 1/2O d. 8/5O e.' 4/5

Answer 1

For the smaller sphere with mass M and radius, R the moment of inertia is

$I_{\text{small}}=\frac{2MR^2}{5}$

For the larger sphere with mass M and radius 2R the moment of Intertia is

$I_{\text{larger}}=\frac{2M(2R)^2}{5}$

The ratio between the larger and the small spheres can be calculated as

$\frac{I_{\text{larger}}}{I_{s\text{mall}}}=\frac{\frac{2M(2R)^2}{5}}{\frac{2M(R)^2}{5}}$

we simplify

$\frac{I_{\text{larger}}}{I_{s\text{mall}}}=\frac{\frac{2M(4)(R)^2}{5}}{\frac{2M(R)^2}{5}}$$\frac{I_{\text{larger}}}{I_{s\text{mall}}}=\frac{4}{1}=4$

ANSWER

The ratio is 4

b. 4