A `25kg` uniform solid sphere with a `20cm` radius is suspended by a vertical wire such that the point of suspension is vertically above the center 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 sphere is then released, its time period of the oscillation will be

Options

A. `pi "second"`
B. `sqrt(2)pi "second"`
C. `2pi "second"`
D. `4pi "second"`

Answer

D

Explanation

`tau = - k theta `
`0.1 = - k(1.0) `where `k` is torsional constant of the wire
`k = (1)/(10)`
`T = 2pi (sqrt(1))/(k)`
`= 2pi sqrt((2)/(5) xx 25 xx(2)^(2))/(1//10)`
`= 2 pi sqrt(10 xx 2xx 2xx 10) = 4 pi sec`