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Question

# A uniform disc of radius 5.0 cm and mass 200 g is fixed at its centre to a metal rod, the other end of which is fixed to a celling. The hanging disc is rotated about the rod through an angle and is released. If the disc makes torsional oscillations with time period 0.20 s, find the torsional constant of the rod.

A
0.50 kg m2/s2
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B
0.75 kg m2/s2
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C
0.125 kg m2/s2
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D
0.25 kg m2/s2
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Solution

## The correct option is D 0.25 kg m2/s2Moment of inertia of the disc about an axis passing through the rod is I=mr22=(0.200 kg)(5.0×10−2m2)22 I=2.5×10−4kg - m2 The time period is given by T=2π√Ik k=4π2IT2 k=4π2(2.5×10−4 kg-m2)(0.20s)2=0.25 kg-m2/s2

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