A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant a is defined by the relation J = –alphatheta , where J is the restoring couple and q the angle of twist).

A circular disc of mass 10 kg is suspended by a wire attached to its c

1.	A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant a is defined by the relation J = –alphatheta , where J is the restoring couple and q the angle of twist).
Answer» <html><body><p></p>Solution :Hint: The time period of a torsional <a href="https://interviewquestions.tuteehub.com/tag/pendulum-1149901" style="font-weight:bold;" target="_blank" title="Click to know more about PENDULUM">PENDULUM</a> is given by `T=2pisqrt(l/(<a href="https://interviewquestions.tuteehub.com/tag/alpha-858274" style="font-weight:bold;" target="_blank" title="Click to know more about ALPHA">ALPHA</a>))`. where I is the moment of inertia about the axis of rotation. In our case `I=1/2MR^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`, where M is the mass of the <a href="https://interviewquestions.tuteehub.com/tag/disk-955870" style="font-weight:bold;" target="_blank" title="Click to know more about DISK">DISK</a> and <a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> its radius. Substituting the given values, `alpha=2.0Nmrad^(-1)`</body></html>