Question

two steel balls of 2mm and 1mm acquire the same terminal velocity in two liquids X and y of same density . what is the ratio of the coefficient of viscosity of X and y​

Answer 1

The ratio of the coefficient of viscosity of X and y is 4.

Given:

Two steel balls of 2mm and 1mm acquire the same terminal velocity in two liquids X and y of the same density.

To Find:

The ratio of the coefficient of viscosity of X and y.

Solution:

To find the ratio of the coefficient of viscosity of X and y we will follow the following steps:

As we know,

When an object is dipped in a liquid or fluid then it experiences some forces and the net effect of the forces gives the object some velocity that velocity is known as terminal velocity. It happens because of the viscosity of the fluid.

The downward force of gravity is equal to the sum of buoyancy and force due to viscosity.

Hence,

Terminal velocity =

$v \: = 2 {r}^{2} \frac{(d - d0)g}{9n}$

Coefficient of viscosity:

$n \: = 2 {r}^{2} \frac{(d - d0)g}{9v}$

Here,

v is terminal velocity and r is the radius of the object, n is the coefficient of viscosity and d is the density of the object and d0 is the density of the medium.

So,

The coefficient of viscosity is directly proportional to the square of the radius because other factors are constant as given in the question:

So,

The ratio of the coefficient of viscosity of the two objects will be:

$\frac{n1}{n2} = \frac{ {r1}^{2} }{ {r2}^{2} }$

According to the question:

r1 = 2mm

r2 = 1mm

Now,

Putting values we get,

$\frac{n1}{n2} = \frac{ {r1}^{2} }{ {r2}^{2} } = \frac{ {2}^{2} }{ {1}^{2} } = 4$

Henceforth, the ratio of the coefficient of viscosity of X and y is 4.

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