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When a celling fan is switched off, its ...

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

A

`24`

B

`36`

C

`18`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
D
Here `theta = 36 xx 2pi, omega = (omega_(0))/(2)`
As `omega^(2) = omega_(0)^(2) = 2 alpha theta`,
`((omega_(0))/(2))^(2) - omega_(0)^(2) = 2 alpha (36 xx 2pi)`
`- (3omega_(0)^(2))/(4) = 144pi alpha or alpha = - (omega_(0)^(2))/(192 pi)`
Again. form `2 alpha theta = omega^(2) - omega_(0)^(2)`,
As finally fan will stop, So `omega = 0`
and `omega_(0)//2 =` Initialy angular velocity
`2 (-(omega_(0)^(2))/(192pi)theta) = 0 - ((omega_(0)^(2))/(2)), theta = 24 pi`
Let no. be rotations be `n`
`:. 24 pi = 2pi n or n = 12`
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