Question

A system consists of two identical spheres each of mass $1.5\text{kg}$ and radius $50\text{cm}$ at the ends of a light rod. The distance between the centres of the two spheres is $5\text{m}$. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint ?

• A. $18.75{\text{kgm}}^2$
• B. $19.05{\text{kgm}}^2$
• C. $18.75{\text{kgm}}^2$
• D. $1.905{\text{kgm}}^2$

Answer 1

The correct option is B $19.05{\text{kgm}}^2$



Moment of inertia of the sphere about its diametral axis is $\frac{2}{5}m{r}^2$

Using parallel axis theorem,
Moment of inertia of the sphere about COM of the system is $\frac{2}{5}m{r}^2+m{(\frac{l}{2}+r)}^2$

Due to symmetry,
Moment of inertia of the system about center of rod is $\frac{4}{5}m{r}^2+2m{(\frac{l}{2}+r)}^2$

Here
$m=1.5\text{kg}$
$r=0.5\text{m}$
$\frac{l}{2}+r=2.5\text{m}$
On substitution
$I_{com}=\frac{4}{5}\left(1.5\right)(0.5{)}^2+2(1.5\left)\right(2.5{)}^2=0.3+3\left(6.25\right)=19.05{\text{kg.m}}^2$