Question

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

Answer 1

Answer:

Let the number of revolutions be n

Diameter of wheel=77cm=77×10^(-2)m

Radius of wheel(r)=77/2cm=77/2×10^(-2)m

Speed=v m/s

Distance covered in 1 revolution=2πr

Distance covered in n revolutions=n×2πr

Total time taken(T)=1minute 28 seconds=60+22 seconds=88s

According to question,

T=n×2πr/v

88=[n×2×(22/7)×(77/2)×10^(-2)]/v =(n×22×11×10^(-2))/v

n=(88×v)/(22×11×10^(-2))

=(4×v×10^2)/11

n=400v/11

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Answer 2

Given :

Diameter = 77 cm

Radius = 77/2 = 38.5 cm

Convert it into m = 38.5/100 = 0.385 m

Speed = 1.1 m/s

Time = 1 min 28 Sec = 60 + 28 = 88 sec

Find :

The number of complete revolution.

Solution :

Distance = Speed × Time

➡ 1.1 × 88

➡ 96.8 m

Number of revolution = distance / circumference

$= > \frac{96.8 \times 7 }{2 \times 22 \times 0.385}$

$= > \frac{968 \times7 \times 100}{2 \times 22 \times 0385 \times 10}$

$= > 8 \times 5$

$= > 40.$

Hence :

The number of complete revolution is 40.