Question 444: Centre of Mass and Rotational Motion

Question

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the plane of the square, is ______________ kg m
2
.

Accepted Answer

$I=\left(m_{A}+m_{B}+m_{C}+m_{D}ight) r^{2}$
$$
\begin{aligned}
&\mathrm{I}_{	ext {net }}=(1+2+3+4) \cdot\left(\frac{a}{\sqrt{2}}ight)^{2} 	ext {, where a = side of square } \\
&=10 	imes \frac{1^{2}}{2}=5 \mathrm{~kg} \mathrm{~m}^{2}
\end{aligned}
$$

Centre of Mass and Rotational Motion

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the plane of the square, is ______________ kg m 2 .

Integer / Numeric Answer Type