The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L(R<L) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :
Held on 23 Jan 2026 · Verified 6 Jul 2026.
43MR2+127ML2
83MR2+61ML2
43MR2+61ML2
83MR2+127ML2
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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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