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Question

A wire frame in the shape of an equilateral triangle is hinged at one vertex so that it can swing freely in a vertical plane, with the plane of the triangle always remaining vertical. The side of the frame is 13m. The time period in seconds of small oscillations of the frame will be :

A
π2
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B
π2
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C
π6
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D
π5
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Solution

The correct option is D π5
G = C.M of system
Time period T=2πImgd
ICM moment of inertial of the shape about C.M.
=116ml2 ( Here l= length of side d = distance of C.M. from point of contact)
=23l2l24=23×32l=l3
I = moment of oscillation about point of contact O
=16ml2+md2=16ml2+ml23=12ml2 (by applying parallel axis theorem)
So,T=2π     12ml2mg.l3=2π3l2g
Now l=13mT=2π12g=π5
I have taken g = 10 m/s2

934939_119427_ans_2d2b3bfbb1634fceacab7b9dd9aa09a7.JPG

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