﻿ 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.      : Kaysons Education

# 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

### 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.

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