A large, uniform, solid sphere $($mass $=102$ kg $)$ with a radius of $20\mathrm{.}0$ cm is suspended by a vertical wire. In order to rotate the sphere about the wire by an angle of $0\mathrm{.}85$ radians and hold it in that orientation, a torque of $0\mathrm{.}17$ Nm is needed. What is the period of oscillation of the rotating system once the sphere is released?

$T=$

s

Hint: The sphere and wire form a torsional pendulum. 'Torsion' refers to the twisting of the wire. The angular frequency of a torsional pendulum depends on its torsional spring constant $($the ratio of torque divided by angle, $)$ and the rotational inertia: $=\sqrt[\phantom{2}]{\frac{}{\text{I}}}$ From the angular frequency, the period can be calculated.