Three identical uniform rods each of length 1 m and mass 2 kg are arranged to form an equilateral triangle. What is the moment of inertia of the system ….

Q: Three identical uniform rods each of length 1 m and mass 2 kg are arranged to form an equilateral triangle. What is the moment of inertia of the system about an axis passing through one Conner and perpendicular to the plane of the triangle ?

(a) 4 kg m2

(b) 3 kg m2

(c) 2 kg m2

(d) 3/2 kg m2

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Ans: (b)
Sol: Let ABC is an equilateral triangle and Axis passing through vertex A .

Moment of Inertia of the system I = IAB + IAC + IBC

$\displaystyle I = \frac{ml^2}{3} + \frac{ml^2}{3} + [ \frac{ml^2}{12} + m (\frac{\sqrt{3}l}{2})^2] $

$\displaystyle I = 2\frac{ml^2}{3} + \frac{10 ml^2}{12} $

$\displaystyle I = \frac{18 ml^2}{12} $

$\displaystyle I = \frac{3 ml^2}{2} $

$\displaystyle I = \frac{3}{2}\times 2 \times 1^2 $

I = 3 kg-m2