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. 24
B. 36
C. 18
D. 12

Answer

D

Explanation

From third equation of angular motion , `omega^2=omega_0^2-2alphatheta`
`[Here, omega=(omega_0)/(2),theta=36xx2pi]`
`therefore" "(omega_0/(2))^2=omega_0^2-2alphaxx36xx2pi`
`or" "4xx36pialpha=(3omega_0^2)/(4)`
`or" "alpha=(omega_0^2)/(16xx12pi)" "....(i)`
According to the question again applying the third equation of angular motion
`omega^2=omega_0^2-2alphatheta" "[Here,omega=0]`
`therefore" "0=((omega0)/(2))^2-2xx(omega_0^2theta)/(16xx12pi)`
`or " "theta=24pi`
`or" "theta=12xx2pi`
`but" "2pi=1cycle `
`so," " theta=12cycle`