A straight thin uniform rod of length 4L and mass 4M is bent into a square. Its M.I about one side is

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$\frac{5}{3} {ML}^{2}$

$\frac{7}{6} {ML}^{2}$

$\frac{{ML}^{2}}{3}$

$\frac{{ML}^{2}}{48}$

answer is A.

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Detailed Solution

Each side is $\frac{4 L}{4} = L$ in length,

and each side has a mass of $\frac{4 M}{4} = M$ .

The MI of the side that faces the axis is $M L^{2}$ .

MI of the side parallel to the axis is 0

MI of the two sides near the axis is $2 \times \frac{M L^{2}}{3} = \frac{2 M L^{2}}{3}$

Thus the total of the system is $M L^{2} + \frac{2 M L^{2}}{3} = \frac{5 M L^{2}}{3}$

Hence the correct answer is $\frac{5 M L^{2}}{3} .$

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