Four particles, each of mass 1kg are placed at four corners of a square of side 2m. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______\mathrm{kg}{m}^{2}.
Held on 27 Jan 2024 · Verified 6 Jul 2026.
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Net gravitational force at the center of a square is found to be $F_{1}$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio $\frac{F_{1}}{F_{2}}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is $\_\_\_\_$. 
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