The diameter of a cycle wheel is 126 cm. A cyclist takes 16\(\frac{1}{2}\) minutes to reach the destination at a speed of 90 km/h. How many revolutions will the wheel make during the journey? (take \(\pi \) = \(\frac{22}{7}\))
Answer & explanation
Correct answer: option 2
Diameter = 126 cm
Radius = \(\frac{126}{2}\) = 63 cm = \(\frac{63}{100}\) mtr
Time = 16 \(\frac{1}{2}\) = \(\frac{33}{2}\) min = \(\frac{33}{2}\) × 60 sec. =33 × 30 sec
Speed = 90 km/hr = 90 × \(\frac{5}{18}\) m/sec = 25 m/sec
Total distance traveled = speed × time = 25 × 33 × 30 mtr
Total no. of Revolution = \(\frac{Total\;distance}{2\pi\ r}\)
= \(\frac{25\;×\;33\;×\;30}{2\;×\;\frac{22}{7}\;×\;\frac{63}{100}}\)
= \(\frac{25\;×\;33\;×\;30\;×\;7\;×\;100}{2\;×\;22\;× 63}\)
= 6250