A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket.

Time in which bucket ascends = 1 minute 28 seconds = 60 + 28 = 88 seconds.

Speed of bucket = 1.1 m/sec

Distance covered by bucket while ascending = Speed × Time = 1.1 × 88 = 96.8 m.

Radius of wheel = $\dfrac{\text{Diameter}}{2} = \dfrac{77}{2}$ = 38.5 cm.

Circumference of circle = 2πr = $2 \times \dfrac{22}{7} \times 38.5$ = 242 cm = 2.42 m.

Let n be the no. of revolutions of wheel.

Distance covered by bucket = Distance covered by wheel

⇒ 96.8 = 2.42 × n

⇒ n = $\dfrac{96.8}{2.42}$ = 40.

Hence, wheel makes 40 revolutions in raising the bucket.