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# A square plate $0.1m$ side moves parallel to a second plate with a velocity of $0.1m{s^{ - 1}}$. Both plates are immersed in water. If the viscous force is $0.002N$ and the coefficient of viscosity $0.001poise$, distance between the plates is:(A) $0.1m$(B) $0.05m$(C ) $0.005m$(D) $0.0005m$

Last updated date: 30th May 2024
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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.

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.