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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.

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Solution

The correct option is **D** 0.25 kg m2/s2

Moment 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

Moment 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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