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

Explanation

The situation is shown in ure. The moment of inertia of the disc about the wire is
`I=(mr^2)/2=((0.20kg)(5.0xx10^-2m)^2)/2`
`=2.5xx106-4kg-m^2` The time period is given by
`T=2pisqrt(l/k)`
or `k=(4pi^2I)/T^2`
`=(4pi^2(2.5xx10^-4kg-m^2))/((0.20s)^2)`
`=0.25(kg-m^2)/s^2`
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