Question

A table fan rotating at a speed of $2400rpm$ is switched off and the resulting variation of the rpm with time is shown in the figure. The total number of revolutions of the fan it comes to rest is :

• A. $420rev$
• B. $280rev$
• C. $190rev$
• D. $16800rev$

Answer 1

The correct option is B $280rev$

Total revolution before stopping$=$area of $OABC+$area of $△BCD$

So, Area of trapezium$=\frac{1}{2}\times$(Sum of parallel sides)$\times$ height

$=\frac{1}{2}(2400+600)\times \frac{8}{60}$ on converting from secs into minutes.

$=\frac{1}{2}\times 3000\times \frac{8}{60}$

$=200$revolutions.

Area of triangle$=\frac{1}{2}\times$b$\times$h

$=\frac{1}{2}\times 600\times \frac{16}{80}=80$ revolutions.

So total revolution$=200+80=280$revolutions.