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Q.

A thin rod of mass 6m and length 6L is bent into regular hexagon. The M.I of the hexagon about a normal axis to its plane and through centre of system is

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a

{mL}^{2}

b

3 {mL}^{2}

c

5 {mL}^{2}

d

11 {mL}^{2}

answer is C.

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Detailed Solution

Question Image

$x^{2} = l^{2} - \frac{l^{2}}{4} = \frac{3 l^{2}}{4}$

$x = \frac{\sqrt{3}}{2} l$

$I_{1} = \frac{m l^{2}}{12} + m {(\frac{\sqrt{3} l}{2})}^{2}$

$= \frac{m l^{2}}{12} + \frac{3 m l^{2}}{4} = \frac{5 m l^{2}}{12}$

$for 6 rods = \frac{5 m l^{2}}{6} \times 6 = 5 m l^{2}$

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