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  • Three identical rods , each of length l are joined to from a rigid equilateral triangle . Its radius of gyration about an axis passing through a corner and perpendicular to the plane of triangle is

Three identical rods , each of length l are joined to from a rigid equilateral triangle . Its radius of gyration about an axis passing through a corner and perpendicular to the plane of triangle is 

Option: 1

l


Option: 2

l / \sqrt 2


Option: 3

l/2


Option: 4

l/3


Answers (1)

best_answer

 

 

Radius of gyration (K) -

Radius of Gyration of a body about an axis is the effective distance from the axis where the whole mass can be assumed to be concentrated so that moment of inertia remains the same.

- wherein

I= MK^{2}

K= \sqrt{\frac{I}{M}}

 

 

MI of system w.r.t  an axis perpendicular to plane and passing through  one centre 

= \frac{ml^2}{3}+ \frac{ml^2}{3} + \left [ \frac{ml^2}{12}+m\left [ \frac{\sqrt3l}{2} \right ] ^2 \right ] \\\\ = \frac{2ml^2}{3}+\frac{10ml^2}{12} = \frac{18}{12}ml^2

NOW \\\\ 3mk^2 = \frac{3}{2}ml^2\\\\k=l/\sqrt2

 

 

 

 

Posted by

Anam Khan

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