A sphere is hung with a wire, `45^(@)` rotation of th esphere about the wiere generates a restoring torque of 6.0Nm. If the moment of inertia of the sphere is `0.080kgm^(2)`, deduce the frequency of angular oscillations.

Explanation

Here, `theta=45^(@),=(pi)/(4)rad, tau=6.0Nm, `
`I=0.080kgm^(2)`
Restoring torque per unit angular diplacement
`C=(tau)/(theta)=(6.0)/(pi//4)=(6xx4)/(22//7)=7.636Nm rad^(-1)`
Frequency, `v=(1)/(2pi)sqrt ((C)/(I))=(7)/(2xx22)sqrt((7.636)/(0.080))`
`=1.55Hz`