Question

Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected with a massless rod of length $2R$. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is:

• A. $M{R}^2/10$
• B. $41M{R}^2/10$
• C. $21M{R}^2/2$
• D. $5M{R}^1/2$

Answer 1

The correct option is A $M{R}^2/10$

By parallel axis theorem, the moment of inertia of a solid sphere about any parallel axis is

$I^{\prime }=I+m{x}^2$

$\Rightarrow I^{\prime }=\frac{2}{5}M{\left(\frac{R}{2}\right)}^2+M(2R{)}^2$

because the moment of inertia of solid sphere is $\frac{2}{5}M{R}^2$

$\therefore$ Total moment of inertia is

$2\left(\frac{2}{5}M{\left(\frac{R}{2}\right)}^2\right)+M(2R{)}^2$

$=\frac{M{R}^2}{5}+4M{R}^2=\frac{21}{5}M{R}^2$