When a celling fan is switched off, its angular velocity falls to half while it makes `36` rotations. How many more rotations will it make before coming to rest ?

Options

A. 18
B. 12
C. 36
D. 48

Answer

B

Explanation

By using equation `omega^(2)=omega_(0)^(2)-2alphatheta`
`((omega_0)/(2))^2=omega_0^2-2alpha(2pin)impliesalpha=(3)/(4)(omega_0^2)/(4pixx36)`,`(n=36)`
Now let fan completes total `n^(`)` revolution from the starting to come to come to rest
`0=omega_0^2-2alpha(2pin^(`))impliesn^(`)=(omega_0^2)/(4alphapi)`
Substituting the value of `alpha` equation (i)
`n^(`)=(omega_0^2)/(4pi)(4xx4pixx36)/(3omega_0^2)=48` revolutions
Number of rotation `=48-36=12`