question_answer

A uniform disc. of radius 5cm and mass 200 g 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, then what will be. the torsional constant of the wire (in \[kg\text{-}{{m}^{2}}\text{/}{{s}^{2}}\]).

A)  0.15                      

B)  0.17   

C)  0.20                      

D)  0.23

E)  0.25

Correct Answer: E

Solution :

                The situation is shown below The moment of inertia of disc about the wire is \[I=\frac{m{{v}^{2}}}{2}=\frac{0.2\times 5\times {{10}^{-2}}}{2}\]                    \[=2.5\times {{10}^{-4}}kg\text{-}{{m}^{2}}\] The time period, \[T=2\pi \sqrt{\frac{I}{K}}\] \[\Rightarrow \]               \[K=\frac{4{{\pi }^{2}}I}{{{T}^{2}}}\]                      \[=\frac{4{{\pi }^{2}}(2.5\times {{10}^{-4}})}{0.2}\]                      \[=0.25\,kg\text{-}{{m}^{2}}\text{/}{{s}^{2}}\]