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A uniform disc of radius 5.0 cm and mass...

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.

Text Solution

Verified by Experts

The situation is shown in figure . The moment of inertia of the about the wire is
`l = mr^((2)/(2)) = ((0.200 kg) (5.0 xx 10^(-2) m)^(2))/(2)`
`= 2.5 xx 10^(-4) kg-m^(2)`
The time period is given by
`T = 2 pi sqrt((l)/(k)) or k = sqrt((4 pi^(2) l)/(T^(2))`
`= (4 pi^(2) (2.5 xx 10^(-4) lg-m^(2)))/((0.20s)^(2) = 0.25 kg-m^(2)//s^(2)`
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