A wire frame in the shape of an equilateral triangle is hinged at one vertex and can swing freely in a vertical plane. The side is 1/√3 m. The time period of small oscillations is:
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Question

A wire frame in the shape of an equilateral triangle is hinged at one vertex and can swing freely in a vertical plane. The side is 1/√3 m. The time period of small oscillations is:

G1 Physics · Accepted Answer

For the equilateral wire frame pivoted at a vertex, calculate I about the hinge and the centre-of-mass distance h. The frame gives I=M a²/2 and h=a/√3. Hence T=2π√[I/(Mgh)]=2π√(a√3/2g). With a=1/√3 m and g≈10 m s⁻², this reduces to π/√5 s. Correct option: 4.