Question

A ring of mass $0.250\text{kg}$ and radius $200\text{cm}$ and another ring of mass $0.500\text{kg}$ and radius $400\text{cm}$ have the same center. Find the moment of inertia of the system of two rings about the axis passing through their centers and perpendicular to their plane.

• A. $0.07{\text{kg-m}}^2$
• B. $0.08{\text{kg-m}}^2$
• C. $0.09{\text{kg-m}}^2$
• D. $0.06{\text{kg-m}}^2$

Answer 1

The correct option is C $0.09{\text{kg-m}}^2$

Given radius of inner ring $r_1=20$$\text{cm}$
and mass of inner ring $m_1=0.250$ $\text{kg}$
Radius of outer ring $r_2=40\text{cm}$
and mass of outer ring, $m_2=0.500$ $\text{kg}$
Moment of inertia of inner ring $I_1=m_1{r}_1^2$
$I_1=0.250\times (0.20{)}^2$
$I_1=0.01{\text{kg-m}}^2$
Moment of inertia of outer ring $I_2=m_2{r}_2^2$
$I_2=0.500\times (0.40{)}^2$
$I_2=0.08{\text{kg-m}}^2$
Total moment of inertia of system of rings about axis $\text{OO}$',
$I=I_1+I_2$
$I=0.01+0.08$
$I=0.09{\text{kg-m}}^2$