Question

Three particles of masses $2\text{kg},3\text{kg}$ and $5\text{kg}$ are situated at the vertices of a right angled triangle $\Delta ABC$ as shown in figure. Find the moment of inertia of the system about line $PQ$ perpendicular to the $BC$ and in the plane of $\Delta ABC$.

• A. $40{\text{kg-m}}^2$
• B. $80{\text{kg-m}}^2$
• C. $32{\text{kg-m}}^2$
• D. $48{\text{kg-m}}^2$

Answer 1

The correct option is B $80{\text{kg-m}}^2$

Given:
$m_1=2\text{kg}$ ; $m_2=3\text{kg}$ ; $m_3=5\text{kg}$
$r_1=4\text{m}$ ; $r_2=4\text{m}$ ; $r_3=0\text{m}$

Total moment of inertia of system $I=I_1+I_2+I_3$
$=m_1{r}_1^2+m_2{r}_2^2+m_3{r}_3^2$
$=2\times 4^2+3\times 4^2+5\times 0^2$
$=80{\text{kg-m}}^2$