When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotations it will make in the next 3 seconds?

Options

A. 10
B. 20
C. 30
D. 40

Answer

C

Explanation

In first three seconds , angle rotated `theta = 2pi //V = 2pi xx 10 `
Using , `theta = omega_(0) t + (1)/(2) alpha t^(2)`
`therefore 2 pi xx 10 = 0 + (1)/(2) alpha xx 3^(2) = (9)/(2) alpha " " …. (i)`
For the rotation of fan in next three seconds , the total time of rotation = 3 + 3 = 6 s
Let total number of rotation = N
Then angle of rotation , `theta = 2 pi N`
`therefore 2 pi N = 0 + (1)/(2) alpha xx 6^(2) = 18 alpha " " .... (ii)`
Dividing (ii) by (i) , we get N = 40
No. of rotations in last three seconds = 40 - 10 = 30 rotations