The moment of inertia I of a particle with mass m located at a distance r from the axis of rotation is:
[tex]I=mr^2[/tex]
If a system is formed by many particles, the total moment of inertia of the system with respect to a given axis is:
[tex]I_T=\Sigma I_i=\sum_{i\mathop{=}1}^nm_ir_i^2[/tex]
The distance from a point (x,y) and the y-axis is simply the x-coordinate.
Then, the total moment of inertia of the described system is:
[tex]\begin{gathered} I_T=m_1r_1^2+m_2r_2^2+m_3r_3^2 \\ \\ =m_1x_1^2+m_2x_2^2+m_3x_3^2 \\ \\ =\left(8.3kg\right)\left(-3m\right)^2+\left(3.5kg\right)\left(-2m\right)^2+\left(7.7kg\right)\left(5m\right)^2 \\ \\ =74.7kg\cdot m^2+14.0kg\cdot m^2+192.5kg\cdot m^2 \\ \\ =281.2kg\cdot m^2 \end{gathered}[/tex]
Therefore, the correct choice is option D) 281.2 kg*m^2.
