Question

The wheel of a motorcycle 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

The radius of wheel of a motorcycle = 35 cm = 0.35 m.
So, the distance covered by this wheel in 1 revolution will be equal to perimeter of wheel i.e. $2\mathrm{\pi }r=2\times \frac{22}{7}\times 0.35=2.2\mathrm{m}.$
Since speed is given to be $66\mathrm{km}/\mathrm{hr}=66\times \frac{1000\mathrm{m}}{60\min }=1100\mathrm{m}/\min .$
As we know $\mathrm{speed}=\frac{\mathrm{distance}}{\mathrm{time}}$
$$\begin{gathered} \Rightarrow 1100=\frac{\mathrm{number}\mathrm{of}\mathrm{revolutions}\times \mathrm{perimeter}\mathrm{of}\mathrm{wheel}}{\mathrm{time}} \\ \Rightarrow 1100=\frac{\mathrm{number}\mathrm{of}\mathrm{revolutions}\times 2.2}{1} \\ \Rightarrow \mathrm{number}\mathrm{of}\mathrm{revolutions}=\frac{1100}{2.2}=500\mathrm{revolutions}. \end{gathered}$$