Question

Two discs of mass $2\text{kg}$ and $3\text{kg}$ of radius $1\text{m}$ and $2\text{m}$ respectively placed together are rotated about an axis through their common centre as shown in figure. Find the net moment of inertia of the system about given axis.

• A. $6{\text{kg-m}}^2$
• B. $5{\text{kg-m}}^2$
• C. $1{\text{kg-m}}^2$
• D. $7{\text{kg-m}}^2$

Answer 1

The correct option is D $7{\text{kg-m}}^2$

Given:
Mass of disc 1, $m_1=2\text{kg}$ having radius $r_1=1\text{m}$
Mass of disc 2, $m_2=3\text{kg}$ having radius $r_2=2\text{m}$.
Moment of inertia of disc of mass $2\text{kg}$ $I_1=\frac{m_1{r}_1^2}{2}$
$=\frac{2\times 1^2}{2}=1{\text{kg-m}}^2$

Moment of inertia of disc of mass $3\text{kg}$,
$I_2=\frac{m_2{r}_2^2}{2}$
$=\frac{3\times 2^2}{2}=6{\text{kg-m}}^2$

Net moment of inertia of both discs about given axis
$I_{net}=I_1+I_2=(1+6){\text{kg-m}}^2$
$=7{\text{kg-m}}^2$