Question

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s. It is then turned off and coasts to a stop in an additional 40 s. The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?
a.2
b.-0.5
c.0.5
d.-2

Answer 1

Answer:

option D

Explanation:

given,

angular speed of the fan = 120 rev/min

time = 20 sec

After 40 s fan comes to rest

ration angular acceleration of the first 20 s to last 40 s.

angular acceleration for first 20 s

$\alpha_1= \dfrac{\Delta \omega}{t}$

$\alpha_1= \dfrac{120}{20}$

$\alpha_1=6 rev/s^2$

for last 40 s

$\alpha_2= \dfrac{\Delta \omega}{t}$

$\alpha_2= \dfrac{0-120}{40}$

$\alpha_2= -3 rev/s^2$

now, ratio

$\dfrac{\alpha_1}{\alpha_2}=\dfrac{6}{-3}$

$\dfrac{\alpha_1}{\alpha_2}=-2$

hence, the correct answer is option D