Question

Two spherical balls $A$ and $B$ are connected by the massless rod. The masses of ball $A$ and $B$ are $2\text{kg}$ and $5\text{kg}$. Find the moment of inertia of the system about the axis passing perpendicular to the length of rod as shown in figure bellow.

• A. $10{\text{kg-m}}^2$
• B. $18{\text{kg-m}}^2$
• C. $23{\text{kg-m}}^2$
• D. $20{\text{kg-m}}^2$

Answer 1

The correct option is C $23{\text{kg-m}}^2$

Given:
mass of ball $A;m_A=2\text{kg}$
Distance of ball $A$ from axis of rotation $r_A=3\text{m}$
Mass of ball $B,m_B=5\text{kg}$
Distance of ball $B$ from axis of rotation $r_B=1\text{m}$

Let $I_A=$ moment of inertia of ball $A$
$I_B=$ moment of inertia of ball $B$
So, total moment of inertia of the system $I=I_A+I_B$

$I=m_A{r}_A^2+m_B{r}_B^2$

$=2\times 3^2+5\times 1^2$
$=23{\text{kg-m}}^2$

So, moment of inertia of system is $23{\text{kg-m}}^2$