Question

Two discs are rotating about the same axis passing through their centres and perpendicular to both discs' planes. If disc $1$ has mass $5\text{kg}$ and $30\text{cm}$ radius and disc $2$ has mass $7\text{kg}$ and $60\text{cm}$ radius, then find the moment of intertia about an axis $\text{OO'}$.

• A. $1.26{\text{kg-m}}^2$
• B. $1.96{\text{kg-m}}^2$
• C. $1.48{\text{kg-m}}^2$
• D. $1.16{\text{kg-m}}^2$

Answer 1

The correct option is C $1.48{\text{kg-m}}^2$

Given, mass of disc $1$, $m_1$= $5\text{kg}$
& radius of disc 1, $r_1$= $30\text{cm}$
Mass of disc 2, $m_1$= $7\text{kg}$
& radius of disc 2, $r_2$ = $60\text{cm}$

MOI of disc 1 about an axis $\text{OO'}$ ,
$I_1=\frac{m_1{r}_1^2}{2}=\frac{5\times (0.30{)}^2}{2}=0.225{\text{kg-m}}^2$
MOI of disc 2 about an axis $\text{OO'}$' ,
$I_2=\frac{m_2{r}_2^2}{2}=\frac{7\times (0.60{)}^2}{2}=1.26{\text{kg-m}}^2$

$\therefore I=I_1+I_2=0.225+1.26=1.48{\text{kg -m}}^2$
$I=1.48{\text{kg-m}}^2$