A bucket is raised from a well by means of a rope which is wound around 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.

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answer is B.

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Detailed Solution

Given:
Diameter of wheel (d) = 77 cm
Time of bucket ascends in (t) = 1 minute 28 seconds
Speed of bucket ascending = Distance = m/s
Now,
Radius = Half the diameter.

⇒ r = d 2 ⇒ r = 772 c m A s d = 77 c m

In meters it can be written as:

⇒ r = 772 c m ⇒ r = 77 2 × 100 m (∵ 100 c m = 1 m, 772 c m = 1100 × 772)

Circumference of a circle is given as

2 π r

, substituting the values, we get

⇒ 2 π r = 2 × 227 × 77 2 × 100 m ⇒ 2 π r = 22 × 11 100 m

Let number of revolutions taken be x, then the distance covered by the bucket is

2 π r × x

, substituting the values:

⇒ 2 π r × x = 22 × 11 100 × x m → (1)

The total distance actually covered is given by,

s p e e d = d i s t a n c e t i m e

⇒Distance(d) = speed X time
Speed = 1.1 m/s (given)
Time (t) = 1 minute 28 seconds
t = (60 + 28) seconds as 1 min=60 seconds
t = 88 seconds
d = (1.1 X 88) m
d=