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

Options

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

Answer

C

Explanation

`theta_(3)= 2pi xx 10= 20pi` rad
`theta= omega_(0)t+ (1)/(2) alpha t^(2) rArr 20pi = 0 + (1)/(2) alpha (3)^(2)`
`rArr alpha= (40pi)/(9) "rad"//s^(2)`
`theta` in t= 6s
`theta= omega_(0)t + (1)/(2) alpha t^(2)`
`rArr theta_(6)= 0 + (1)/(2) xx (40pi)/(9)xx (6)^(2)= 80pi` rad
Angle turned in next 3 sec
`theta= theta_(6)- theta_(3)= 60pi` rad
Number of revolution `= (60pi)/(2pi)= 30` rev