Diameters of the front and rear wheels of a tractor are 80 cm and 2 m, respectively. How many revolutions will the rear wheel make in the distance in which the front wheel makes 1400 revolutions?
560 revolutions
Step 1: Convert all measurements into the same unit (SI unit: metre).
Diameter of front wheel = 80 cm = \(80 \div 100 = 0.8\,\text{m}\).
Diameter of rear wheel = 2 m (already in metres).
Step 2: Find the circumference of each wheel.
The circumference of a wheel is given by the formula: \(C = \pi \times d\).
Front wheel circumference = \(\pi \times 0.8 = 0.8\pi\,\text{m}\).
Rear wheel circumference = \(\pi \times 2 = 2\pi\,\text{m}\).
Step 3: Find the total distance travelled by the front wheel in 1400 revolutions.
Total distance = Number of revolutions \(\times\) circumference.
\(= 1400 \times 0.8\pi = 1120\pi\,\text{m}\).
Step 4: Find how many revolutions the rear wheel makes to cover the same distance.
Revolutions = \(\dfrac{\text{Total distance}}{\text{Circumference of rear wheel}}\).
\(= \dfrac{1120\pi}{2\pi} = 560\).
Final Answer: The rear wheel makes 560 revolutions.