The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?

Given:

Speed of the bus = 66 km/hr

Converting the speed into cm/min

Since, 1 km = 1000 m, 1 m = 100 cm, and 1 hour = 60 minutes

So, speed of the bus = $\frac{66\times 1000\times 100}{60}$ cm/min

= 1,10,000 cm/min

Now, diameter D of the wheel = 140 cm

We know that $\mathbf{D}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{2}\mathbf{\times }\mathbf{r}$

So, radius $\mathbf{r}\mathbf{=}\frac{\mathbf{D}}{\mathbf{2}}$

$=\frac{140}{2}= 70 \mathrm{cm}$

And, the circumference of a circle is given by $\mathbf{2}\mathbf{\pi r}$,

So, the wheel's circumference = $2\times \frac{22}{7}\times 70$

= 440 cm

Thus, the distance covered by the wheel at each rotation = 440 cm

And revolutions per minute (RPM)

= $\frac{\mathbf{Required}\mathbf{ }\mathbf{speed}}{\mathbf{Distance}\mathbf{ }\mathbf{covered}\mathbf{ }\mathbf{in}\mathbf{ }\mathbf{one}\mathbf{ }\mathbf{rotation}}$

= $\frac{1,10,000}{440}$

= 250

Hence, the required number of revolutions is 250 per minute.