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A uniform of radius 5.0 cm and mass 200 ...

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