Question

The wheel of a motor cycle is of radius 35 cm . How many revolutions per minute must the wheel make so as to keep a speed of 66 km / hr ?

Answer 1

Radius of the wheel, r = 35 cm
circumference = $2\mathrm{\pi r}=2\mathrm{\pi }\times 35=220\mathrm{cm}$
Distance covered by the wheel in one revolution = 220 cm
Let the number of revolutions required be x.
So, distance covered by the wheel in x revolutions = 220x
Distance covered by the wheel in one minute = 220x
The wheel covers $\frac{66\times 1000\times 100}{60}=110000\mathrm{cm}$ in one minute
$$\begin{gathered} So,220x=110000 \\ \Rightarrow x=\frac{110000}{220}=500 \end{gathered}$$
Hence, 500 revolutions per min are needed.