A uniform disc having mass m and radius r is suspended by a wire attached to its centre. If the time period of torsional oscillations is T , determine the torsional constant of the wire.

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Quantrex Academy · Accepted Answer

Correct answer: A. (2 π^2 m r^2)/(T^2)

The time period of torsional oscillations is given by:

T = 2 \pi \sqrt{\dfrac{I}{C}}

where

I is the moment of inertia of the disc and

C

is the torsional constant of the wire.<br><br>The moment of inertia of a uniform disc about an axis passing through its centre and perpendicular to its plane is:<br><br>

I = \dfrac{m r^2}{2}

<br><br>Substituting the value of

I

in the expression for

T

:<br><br>

T = 2 \pi \sqrt{\dfrac{m r^2}{2 C}}

<br><br>Squaring both sides:<br><br>

T^2 = 4 \pi^2

\left(

\dfrac{m r^2}{2 C} \right)

T^2 =

\dfrac{2 \pi^2 m r^2}{C}

Rearranging for

C

:

C =

\dfrac{2 \pi^2 m r^2}{T^2}

A uniform disc having mass m and radius r is suspended by a wire...

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