JEE MAIN - Physics (2022 - 30th June Morning Shift - No. 20)
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 m2.
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Answer
5
Explanation
$I=\left(m_{A}+m_{B}+m_{C}+m_{D}\right) r^{2}$
$$ \begin{aligned} &\mathrm{I}_{\text {net }}=(1+2+3+4) \cdot\left(\frac{a}{\sqrt{2}}\right)^{2} \text {, where a = side of square } \\\\ &=10 \times \frac{1^{2}}{2}=5 \mathrm{~kg} \mathrm{~m}^{2} \end{aligned} $$
$$ \begin{aligned} &\mathrm{I}_{\text {net }}=(1+2+3+4) \cdot\left(\frac{a}{\sqrt{2}}\right)^{2} \text {, where a = side of square } \\\\ &=10 \times \frac{1^{2}}{2}=5 \mathrm{~kg} \mathrm{~m}^{2} \end{aligned} $$
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