Question

A uniform disc 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 ceiling. The hanging disc is rotated about the wire through an angle and is released. If the disc makes torsional oscillations with time period 0.20 s. The torsional constant of the wire is :

• A. $0.25kg{m}^2/s^2$
• B. $0.5kg{m}^2/s^2$
• C. $25kg{m}^2/s^2$
• D. $2.5kg{m}^2/s^2$

Answer 1

The correct option is A $0.25kg{m}^2/s^2$

The situation is shown in figure The moment of inertia of the disc about the wire is
$I=\frac{m{r}^2}{2}=\frac{\left(0.200kg\right)(5.0\times {10}^{-2}m{)}^2}{2}=2.5\times {10}^{-4}kg-m^2$
The time period is given by
$T=2\pi \sqrt{\frac{I}{C}}orC$

$=\frac{4{\pi }^{2}I}{T^2}=\frac{4{\pi }^2(2.5\times {10}^{-4}kg-m^2)}{(0.20s{)}^2}$

$=0.25kg{m}^2/s^2$