Question

Find the M.O.I $\left(I\right)$ of a uniform solid sphere of radius $R$ and mass $M$ about its tangent

• A. $\frac{2}{3}M{R}^2$
• B. $\frac{2}{5}M{R}^2$
• C. $\frac{5}{3}M{R}^2$
• D. $\frac{7}{5}M{R}^2$

Answer 1

The correct option is D $\frac{7}{5}M{R}^2$


As we know,
M.O.I of sphere about its center
$I_{com}=\frac{2}{5}M{R}^2$

From parallel axis theorem,
$I=I_{com}+M{d}^2$
Here $\left(d\right)$ is perpendicular/shortest
distance between axis $I_{com}$ and $I$

$\Rightarrow I=\frac{2}{5}M{R}^2+M{R}^2$
$=\frac{7}{5}M{R}^2$