Question

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

Answer 1

Answer: 280 revolutions

Given data is stated from the figure, as the total revolution before coming to rest will be given from the area of the graph. The information in the figure is that the at 8 sec, the revolution per min be 600 which further reduces and come to rest by 24 sec. therefore the  graph can be divided into a trapezium by the 8 sec and a right angled triangle by 8 to 24 sec. calculate the area and we will get our answers.

Area of trapezium $=\frac { 1 }{ 2 } \times \quad sum\quad of\quad parallel\quad sides\quad \times \quad height$

$=\frac { 1 }{ 2 } \times 2400+600\times \frac { 8 }{ 60 }$ = ( the time being converted into minutes)

$\Rightarrow$ Area of trapezium = 200 revolutions

And the Area of right angled triangle $=\frac { 1 }{ 2 } \times base\times height$

$=\frac { 1 }{ 2 } \times 600\times \frac { 16 }{ 60 }$

= 80 revolutions.

Therefore the total revolution before rest is 200 + 80 = 280 revolutions