A `25kg` uniform solid with a `20cm` radius respectively by a verticle wire such then the point suspended is velocity about the center of the sphere torque of `0.10`rad and then montain the sphere then at angle of `1.0` rod minimum the statement if sphere is then roleased its period of the oscillation will be

Options

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

Answer

D

Explanation

`tau = -k theta`
`0.1 = - k (1. 0)`, where k is torsional constant of the wire
`k = (1)/(10) T = 2 pi sqrt((1)/(k)) = 2pi sqrt(((2)/(5) xx 25xx (2)^(2))/(1 //10))`
`= 2pi sqrt(10 xx 2 xx 2 xx 10) = 4 pi` second