Question

Point masses of $1,2,3$ and $4\text{kg}$ are lying at the points $(0,0,0),(2,0,0),(0,3,0)\text{and}(-2,-2,0)$ respectively. What will be the moment of inertia of the system about $x$ - axis?

• A. $51{\text{kg m}}^2$
• B. $43{\text{kg m}}^2$
• C. $67{\text{kg m}}^2$
• D. $40{\text{kg m}}^2$

Answer 1

The correct option is B $43{\text{kg m}}^2$


Moment of inertia about $x$ - axis
$I=I_A+I_B+I_C+I_D$

Here, $A$ and $B$ masses are lying on the axis, hence $MOI$ for $A$ and $B$ is zero.

$C$ is at a perpendicular distance of $3\text{units}$ from $x$ - axis and $D$ is at $2\text{units}$ from $x$ - axis.

Hence, $I=\Sigma m{r}^2$
$I=0+0+3\times (3{)}^2+4(2{)}^2$
$I=43\text{kg}{\text{m}}^2$