Answer
64.8k+ views
Hint:We have the values of all required quantities in the question. We would calculate the area of the square plate at first as the dimension of one of the sides is given.
Using that value of area, and the formula for viscous force we can obtain the required value of distance between the plates.
Complete step-by-step answer:
As per the question, the following values of given to us:
Side of the plate \[ = 0.1m = a\]
Velocity of the plate \[ = dv = 0.1m{s^{ - 1}}\]
Viscous force \[ = F = 0.002N\]
Coefficient of viscosity \[ = 0.001poise\]
From here, we can calculate the area of the plate is \[ = {a^2} = (0.1 \times 0.1){m^2}\]
Thus, area \[ = 0.01{m^2}\]
Coefficient of Viscosity \[ = \eta = 0.001poise\]
But, we need to take the value in decaPoise, therefore we divide it by \[10\]
Therefore, \[\eta = \dfrac{{0.001}}{{10}}decapoise = 0.0001decapoise\]
We have the velocity of the plate given,
Now, using the expression for viscous force, we get:
\[F = \eta A\dfrac{{dv}}{{dx}}\]
Where:
\[F = \] Viscous force
\[\eta = \] Coefficient of viscosity
\[A = \] Area of the plate
\[dv = \] Velocity with which the plate moves
\[dx = \] Distance between the plates.
For the above expression, we need to find the value of \[dx\].
Putting the values, in the expression we get:
\[0.002 = \dfrac{{0.0001 \times 0.01 \times 0.1}}{{dx}}\]
Rearranging the equation we get:
\[dx = \dfrac{{0.0001 \times 0.01 \times 0.1}}{{0.002}}\]
Thus, we obtain:
\[dx = 0.00005m\]
This is the required solution.
Note:The unit poise is in the MKS unit, therefore, we need to convert it to deca poise, and otherwise we may get erroneous results. Viscosity is defined as a resistance experienced by a fluid while it flows. This is a property of the fluid. Viscous force is defined as the force between a body and the fluid, while it flows.
Using that value of area, and the formula for viscous force we can obtain the required value of distance between the plates.
Complete step-by-step answer:
As per the question, the following values of given to us:
Side of the plate \[ = 0.1m = a\]
Velocity of the plate \[ = dv = 0.1m{s^{ - 1}}\]
Viscous force \[ = F = 0.002N\]
Coefficient of viscosity \[ = 0.001poise\]
From here, we can calculate the area of the plate is \[ = {a^2} = (0.1 \times 0.1){m^2}\]
Thus, area \[ = 0.01{m^2}\]
Coefficient of Viscosity \[ = \eta = 0.001poise\]
But, we need to take the value in decaPoise, therefore we divide it by \[10\]
Therefore, \[\eta = \dfrac{{0.001}}{{10}}decapoise = 0.0001decapoise\]
We have the velocity of the plate given,
Now, using the expression for viscous force, we get:
\[F = \eta A\dfrac{{dv}}{{dx}}\]
Where:
\[F = \] Viscous force
\[\eta = \] Coefficient of viscosity
\[A = \] Area of the plate
\[dv = \] Velocity with which the plate moves
\[dx = \] Distance between the plates.
For the above expression, we need to find the value of \[dx\].
Putting the values, in the expression we get:
\[0.002 = \dfrac{{0.0001 \times 0.01 \times 0.1}}{{dx}}\]
Rearranging the equation we get:
\[dx = \dfrac{{0.0001 \times 0.01 \times 0.1}}{{0.002}}\]
Thus, we obtain:
\[dx = 0.00005m\]
This is the required solution.
Note:The unit poise is in the MKS unit, therefore, we need to convert it to deca poise, and otherwise we may get erroneous results. Viscosity is defined as a resistance experienced by a fluid while it flows. This is a property of the fluid. Viscous force is defined as the force between a body and the fluid, while it flows.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)