A fly wheel rotates about an axis. Due to friction at the axis, it experiences an angular retardation proportional to its angular velocity. If its angular velocity falls to one fourth while it makes n rotations, how many roations will it make before coming to rest ?

Options

A. n
B. `(n)/(2)`
C. `(n)/(3)`
D. `(n)/(4)`

Answer

C

Explanation

`alpha = - k omega`
`(d omega)/(dt) = - k (d theta)/(dt)`
`underset(omega_(0))overset(omega_(0)/(4))int domega = - k underset(0)overset(n)int d theta`
`(3)/(4) omega_(0) = kn`
`underset(omega_(0))overset(0)int d omega = - k underset(0)overset(n)int d theta`
`omega_(0) = k n'`
`rArr n' = (omega_(0))/(k) = (4n)/(3)`
`Deltan = (4n)/(3) - n = (n)/(3)`