Question

What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)

Answer 1

mass of the sphere m_s

mass of the rod m_r

radius of the sphere R

length of the rod L.

Moment of inertia of the sphere about the center of mass of the system (by parallel axis theorem)

$I_s=\frac{2}{5}m_s R^2+m_s L^2$

$I_s=\frac{2}{5}m_s R^2+m_s \left (\frac{R}{2} \right ) ^2$

$I_s=\frac{13}{20}m_s.R^2$

Moment of inertia of rod about the center of mass of the system (by parallel axis theorem)

$I_r=\frac{1}{12}m_r L^2+m_r*\left ( \frac{L}{2}+\frac{R}{2} \right )^2$

$I=I_r+I_s=\frac{13}{20}m_s.R^2+\frac{1}{12}m_r L^2+m_r*\left ( \frac{L}{2}+\frac{R}{2} \right )^2$

just substituing values to find the solutution.