Home
Class 11
PHYSICS
A sphere is hung with a wire 30^(@) rota...

A sphere is hung with a wire `30^(@)` rotation of the sphere about the wire generates a restoring torque of 4.6 Nm. If the moment of inertia of the sphere is 0.082 kg `m^2`, deduce the frequency of angular oscillations.

Text Solution

Verified by Experts

The correct Answer is:
`1.65`
Here `theta = 30^(@) = (pi)/(6) "rad", tau = 4.6 Nm `
`I = 0.082 kg m^(2)`
Restoring torque per unit angular displacement
`C = (tau)/(theta) = ( 4.6)/(pi//6)`
`= (4 . 6 xx 6 xx 7)/(22) = 8.78 Nm rad^(-1)`
`:.` Frequency ` v = (1)/(2pi) sqrt((C)/(I))`
`= (7)/( 2 xx 22) sqrt((8.78)/(0.082)) = 1.65 Hz`
Promotional Banner

Similar Questions

Explore conceptually related problems

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.

A sphere hung with a wire 60^(@) rotation of the sphere about the wire produces a restoring torqueof 4.1Nm. If the moment of inertis of the sphere is 0.082 kg m^(2) . Find the frequencyof angular oscillations.

A sphere is hanged with a wire. A restoring torque of 5 Nm is produced when 30^(@) rotation of the sphere is allowed to take place. What will be the frequency of angular oscillations if the moment of inertia of the sphere is 0.092 kg m ?

The moment of inertia of a sphere is 20" kg-m"^(2) about the diameter. The moment of inertia about any tangent is

Find the moment of inertia of solid sphere of mass M about a diameter as shown in Fig.

A sphere of mass 10 kg and radius 0.5 m rotates about a tangent. The moment of inertia of the solid sphere about tangent is

Find the moment of inertia of a sphere about a tangent to the sphere, while the mass of the sphere is M and the radius of the sphere is R.

The moment of inertia of a sphere is 40 kg- m^2 about its diametric axis. Determine the moment of inertia about any tangent.