The diameter of wheel is 0.70 m. Find the distance covered by it in 500 revolutions.

If the wheel takes 5 minutes to make 500 revolutions; find its speed in :

(i) m/s

(ii) km/hr

(i)Given:

Diameter of wheel = 0.70 m

Radius = $\dfrac{\text{Diameter}}{2}$

= $\dfrac{0.70}{2}$ m

= 0.35 m

As we know, the circumference of the circle = 2πr

$2 \times \dfrac{22}{7} \times 0.35\\[1em] = \dfrac{44}{7} \times 0.35\\[1em] = \dfrac{15.40}{7}\\[1em] = 2.2 \text{ m}$

Distance traveled by wheel in 500 revolutions = Circumference of the wheel x 500

= 2.2 x 500 m

= 1100 m

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Time taken by wheel = 5 min = 5 x 60 sec = 300 sec.

$\text{Speed} = \dfrac{1100}{300}\\[1em] = 3\dfrac{2}{3} \text{ m}/\text{s}$

Hence, the speed = $3\dfrac{2}{3}$ m/s.

(ii) Speed = $3\dfrac{2}{3}$ m/s

$= 3\dfrac{2}{3} \times \dfrac{3600}{1000} \text{ km}/\text{hr}\\[1em] = \dfrac{11}{3} \times \dfrac{3600}{1000} \text{ km}/\text{hr}\\[1em] = \dfrac{39600}{3000} \text{ km}/\text{hr}\\[1em] = 13.2 \text{ km}/\text{hr}$

Hence, the speed = 13.2 km/hr.