A pulley of a radius of 0.9 m is used to lift the bucket from the well. If it took 3.6 rotations for the pulley to take water out of the well, how deep is the water in the well?


Given:

Radius of the pulley = r = 0.9 m
Numbers of rotation = n = 3.6


To Find :

Depth of the water = h = S =?


Solution:


When the pulley performs one complete rotation, the angle 𝜽 = 2𝛑 radians and the length of the arc traveled is 

S = r𝜽 

by putting values

S = 0.9 m ｘ 2𝛑 

S = 5.6 m

5.6 m is the length of the arc of the pulley traveled in one rotation. so by the unitary method

1 rotation of the pulley = 5.6 m 

3.6 rotation of the pulley = 3.6 ｘ 5.6 m 

3.6 rotation of the pulley = 20.16 m = 20 m
 
As in the 3.6 rotation of the pulley, the water bucket is taken out of the well which is equal to the length of the arc of 20 m. So, the depth of the water in the well is 20 m.



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