An electric fan is rotating at a speed of 600 rev/minute. When the power supply is stopped, it stops after 60 revolutions. The time taken to stop is

Correct Option: The correct answer is 12 s.

To find the time taken for the electric fan to come to a stop, we can use the equations of uniformly retarded rotational motion.

Step 1: Convert the initial rotational speed into revolutions per second (rev/s)
The fan's initial speed is given as:
$n_0=600rev/min$
Since 1 minute = 60 seconds, we convert this to seconds:
$n_0=\frac{600}{60}=10rev/s$

Step 2: Identify the final rotational speed
Since the fan comes to a complete stop, its final speed is:
$n=0rev/s$

Step 3: Calculate the average rotational speed
Under constant angular deceleration, the average speed is the arithmetic mean of the initial and final speeds:
$n_{\text{avg}}=\frac{n_0+n}{2}$
Substituting the values:
$n_{\text{avg}}=\frac{10+0}{2}=5rev/s$

Step 4: Solve for the time taken to stop
The total number of revolutions ($N$) is related to the average speed and time ($t$) by the formula:
$N=n_{\text{avg}}\times t$
Rearranging the equation to solve for $t$:
$t=\frac{N}{n_{\text{avg}}}$
Given that $N=60$ revolutions, we substitute the values:
$t=\frac{60}{5}=12s$

Thus, the time taken for the fan to stop is 12 s.