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

Options

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

Answer

D

Explanation

`omega^(2) = omega_(0)^(2) + 2 alpha theta` as after 36 rotations `omega = omega_(0)//2`
`(omega_(0)^(2))/(4) = omega_(0)^(2) + 2 alpha theta :. Omega_(0)^(2) = -(8 alpha theta)/(3)` Now, `omega = 0` (after it comes to rest)
`:. -omega_(0)^(2) = 2 alpha theta_(1) or (8 alpha theta)/(3) = 2 alpha theta_(1)`
`:. theta = theta_(1) xx (6)/(8)`
`:.` No. of rotations `= (8)/(6) xx 36 = 48`
No. of rotations more `=48-36=12`