A ceiling fan is rotating about its own axis with uniform angular velocity `omega`. The electric current is switched off then due to constant opposing torque is its angular velocity is reduced to `(2 omega)/3` as it completes `30` rotations. The number of rotations further it makes before coming to rest is

Options

A. `18`
B. `12`
C. `9`
D. `24`

Answer

D

Explanation

`alpha` is constant
`theta=(omega_(1)^(2)-omega_(2)^(2))/(2alpha)` and `(theta_(1))/(theta_(2))=(omega^(2)-(2omega//3)^(2))/((2omega//3)^(2)-0)`