The diameter of the driving wheel of a bus is 140 m. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/h?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 250
Note: It seems that there is a mistake in the original NTA paper, which prints the diameter of the wheel as 140 m; with 140 m the wheel would make only 2.5 revolutions a minute, which is not among the options. To arrive at the NTA answer, it should read 140 cm, as explained below. A bus wheel 140 m across would stand taller than a 40-storey tower.
In one revolution the wheel rolls forward by its circumference, \(\pi d\). So the number of revolutions in a minute is the distance covered in a minute divided by the circumference, with the diameter taken as 140 cm.
Distance in a minute: \(\displaystyle\frac{66\times1000}{60}=1100\) m
Circumference: \(\displaystyle\frac{22}{7}\times1.4=4.4\) m
Revolutions per minute: \(\displaystyle\frac{1100}{4.4}=250\)