Question

Starting from rest, a fan take five seconds to attain the maximum speed of 400 rpm. Assume constant acceleration, find the time taken by the fan attaining half the maximum speed.

• A. 11 s
• B. 2.0 s
• C. 5.0 s
• D. 2.5 s

Answer 1

The correct option is D 2.5 s

The maximum angular velocity is given, $w_m=400rpm=400\times \frac{2\pi }{60}=\frac{40\pi }{3}rad/sec$

Initial angular velocity is $w_m=0$

So the angular acceleration, $\alpha =\frac{w_m-w-0}{t}=\frac{40\pi /3-0}{5}=\frac{8\pi }{3}rad/se{c}^2$

Let the time $t_{1/2}$ taken by the fan attaining half the maximum speed.

Now using, $w=w_0+\alpha t$ we get $w_m/2=0+\alpha t_{1/2}$

or $t_{1/2}=\frac{w_m}{2\alpha }=\frac{\left(40\pi /3\right)}{2\left(8\pi /3\right)}=2.5s$