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_(1)^(2))/(2theta) and (theta_(1))/(theta_(2)) = (omega^(2)-(2omega//3)^(2))/((2omega//3)^(2)-0)`