1. Tardigrade
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  3. Physics
  4. A 25 kg uniform solid sphere with a 20 cm radius is suspended by a vertical wire such that the point of suspension is vertically above the centre of the sphere. A torque of 0.10 N - m is required to rotate the sphere through an angle of 1.0 rad and then maintain the orientation. If the sphere is then released, its time period of the oscillation will be:

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Q. A $25\, kg$ uniform solid sphere with a $20\, cm$ radius is suspended by a vertical wire such that the point of suspension is vertically above the centre of the sphere. $A$ torque of $0.10\, N - m$ is required to rotate the sphere through an angle of $1.0$ rad and then maintain the orientation. If the sphere is then released, its time period of the oscillation will be:

Oscillations

Solution:

$\tau=-k \theta$
$0.1=-k(1.0)$, where $k$ is torsional constant of the wire.
$k =\frac{1}{10} $
$T =2 \pi \sqrt{\frac{I}{k}} $
$=2 \pi \sqrt{\frac{\frac{2}{5} \times 25 \times(.2)^{2}}{1 / 10}} $
$=2 \pi \sqrt{10 \times .2 \times .2 \times 10}=4 \pi \,sec$