A Metal Sphere Of Diameter  enters Water After Falling A Distance h freely In The Gravitational Field Of The Earth. After Entrance In Water, Its Velocity Remains Unchanged. Calculate The Value Of h. The Coefficient Of Viscosity Of Water , Density Of Water  and Acceleration Due To Gravity = 10 N/kg.     

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Question

A metal sphere of diameter  enters water after falling a distance h freely in the gravitational field of the earth. After entrance in water, its velocity remains unchanged. Calculate the value of h. The coefficient of viscosity of water , density of water  and acceleration due to gravity = 10 N/kg.     

Solution

Correct option is

80 m

The velocity attained by the sphere in falling freely from a height h is 

            

This is the terminal velocity of the sphere in water. Hence by Stokes’ law, we have  

            

where r is the radius of the sphere,  is the density of the material of the sphere,  is the density of water and  is coefficient of viscosity of water. Putting the given values

   

From eq. (i), we have  

      

         

          = 80 m.   

SIMILAR QUESTIONS

Q1

The relative velocity between two layers of water is 8.0 cm/s. If the perpendicular distance between the layers is 0.1 cm, find the velocity gradient.

Q2

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Q3

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Q4

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Q5

An air bubble of radius 1.0 mm rises with uniform velocity through a viscous liquid of density 1625 kg/m3. Calculate the velocity of the bubble if the coefficient of viscosity of the liquid is 10 poise and the density of air is negligible. (g = 10 m/s2). 

Q6

An air bubble of radius 0.1 mm is moving upwards in water with a velocity of 0.35 cm/s. If the density of water is  and gravitational acceleration is 9.8 m/s2 and the density of the air is negligible, then find out the coefficient of viscosity of water.     

Q7

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Q8

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Q9

Water is flowing through two horizontal pipes of different diameters which are connected together. In the first pipe the speed of water is 4.0 m/s and the pressure is . Calculate the speed and pressure of water in the second pipe. The diameters of the pipes are 3.0 cm and 6.0 cm respectively.

Q10

A liquid is kept in a cylindrical vessel which is being rotated about its axis. The liquid rises at the sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev/s, find the difference in the heights of liquid at the centre of the vessel and at its sides.