The wheel of a motor cycle is of radius 21 cm. How many revolutions per minute must the wheel make so as to keep a speed of 77km/hr.
Please answer the question using same radius and speed as above only.

Dear Student,

Please find below the solution to the asked query:

Given : Speed of motor cycle  77 km / hr.

We know 1 km  =  100000 cm  , So

Speed of motor cycle  =  7700000 cm  / hr 

Motor cycle cover total distance in 1 hr ( 60 minutes ) =  7700000 cm                                (  We know 1 hr  = 60 minutes )

Then ,

Motor cycle cover total distance in 1 minute  =  $\frac{7700000}{60} = \frac{385000}{3}$ cm

The wheel of a motor cycle is of radius 21 cm.

So,

Total distance cover by motor cycle in one revolution =  Circumference of wheel ( Circle )

Let , Total number of revolution by wheel in a minute  =  x  , So

$$\begin{gathered} x \left( 2 \mathrm{\pi } \mathrm{r} \right) = \frac{385000}{3} \\ \Rightarrow x \left( 2 \times \frac{22}{7} \times 21 \right) = \frac{385000}{3} \\ \Rightarrow x \left( 2 \times 22 \times 3 \right) = \frac{385000}{3} \\ \Rightarrow 132 x= \frac{385000}{3} \\ \Rightarrow x= \frac{385000}{132 \times 3} \\ \Rightarrow x= \frac{8750}{9} \\ \Rightarrow x= 972.222 \approx \mathbf{972} \end{gathered}$$
Therefore,

Total number of revolution by wheel in a minute  = 972                                            ( Ans )


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