When a ceiling fan is switched off, its angular velocity reduces to 50% while it makes 36 rotations. How many more rotations will it make before coming to rest?(Assume uniform angular retardation)

Options

A. 18
B. 16
C. 12
D. 10

Answer

C

Explanation

In 36 rotations, it will describe an angle `36xx2pi=72pi`
We use `omega^(2)=omega_(0)^(2)+2alpha theta`, in this case, for the first part
`omega=(omega^(2))/(2) and theta=72pi`
`therefore" "(omega_(0)^(2))/(4)=omega_(0)^(2)+2alpha(72pi)`
`therefore" "(-3omega_(0)^(2))/(4)=144 pi " "therefore" "alpha " "=(-3omega_(0)^(2))/(4xx144)`
`alpha` is `-ve`, because it is a retarded motion.
In the second half , `omega=0`
`therefore 0=(omega_(0)^(2))/(4)-2xx(3omega_(0)^(2))/(4xx144pi)xxtheta`
`therefore" "theta'=(omega_(0)^(2)xx4xx144pi)/(2xx4xx3omega_(0)^(2))=24pi`
`therefore" No. of rotations N"=(24pi)/(2pi)=12`