Question

The wheel of a motor cycle is of radius $35\text{cm}$ . How many revolutions per minute must the wheel make so as to keep a speed of $66\text{km/h}$

Answer 1

Step 1: Find the distance covered by the wheel in one revolution

Radius of the wheel $=35\text{cm}$

Speed of wheel $=66\text{km/h}$

We know that

$1$ revolution of the wheel $=$Circumference of the wheel $=\text{2πr}$

$=2\times \frac{22}{7}\times 35=220\text{cm}$

Step 2: Convert the speed of wheel in $\text{cm/min}$

Speed of the wheel

$$\begin{gathered} =66\text{km/hr} \\ \text{=}\frac{66\times 1000\times 100}{60}\text{cm/min} \\ \text{=110000 cm/min} \end{gathered}$$

Step 3: Find the number of revolution in $1$ min

Number of revolutions in $1$ min $=\frac{\text{Speed of the wheel}}{\text{Distance covered in 1 revolution}}$

$$\begin{gathered} =\frac{110000}{220} \\ =500 \end{gathered}$$

Hence required number of revolutions are $500$