Three identical rods, each of length L, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the triangle is $\frac{L}{\sqrt{n}}$ . The value of n is

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Detailed Solution

Let mass of each rod = M

Then, $M o I$ of the system about an axis passing through the corner and perpendicular to the triangle is

$\begin{array}{l} = \frac{M x^{2}}{3} + \frac{M x^{2}}{3} + \frac{M x^{2}}{12} + M {[\frac{\sqrt{3}}{2} x]}^{2} \\ = \frac{3}{2} M x^{2} \end{array}$

Let radius of gyration =K

Then,

$\begin{array}{l} 3 M \times k^{2} = \frac{3}{2} M x^{2} \\ \Rightarrow k = \frac{x}{\sqrt{2}} \end{array}$

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