# One centipoise is equal to\begin{align} & A)1kg-{{m}^{-1}}{{s}^{-1}} \\ & B)1000kg-{{m}^{-1}}{{s}^{-1}} \\ & C)0.1kg-{{m}^{-1}}{{s}^{-1}} \\ & D)0.001kg-{{m}^{-1}}{{s}^{-1}} \\ \end{align}

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Hint: Poise, is the unit of viscosity of a fluid. Students must know what is 1 poise equal to in terms of MKS unit system. Students must also know how to convert poise to centipoise, using mathematical expressions.

Formula used:
\begin{align} & 1poise=1kg-{{m}^{-1}}{{s}^{-1}} \\ & 1centipoise={{10}^{-2}}poise \\ \end{align}

Students must be familiar that viscosity appears in the following formula for a liquid,
$F=\eta A\dfrac{u}{y}$…(1), where F is the frictional force fluid, A is the area, u is the velocity of topmost layers of fluid, y is the distance between the topmost and the lowermost layers (which has zero velocity) and finally, $\eta$is the coefficient of viscosity.
Rearranging equation (1), we get.
$\eta =\dfrac{F}{A}\dfrac{y}{u}$, now putting unit of force as $kg-m{{s}^{-2}}$, distance as m, velocity as $m{{s}^{-1}}$and area as ${{m}^{2}}$, we get the unit of coefficient of viscosity i.e. 1 poise.
\begin{align} & \Rightarrow 1poise=\dfrac{kg-m{{s}^{-2}}}{{{m}^{2}}}\times \dfrac{m}{m{{s}^{-1}}} \\ & \Rightarrow 1poise=kg-{{m}^{-1}}{{s}^{-1}} \\ \end{align}
Now, we know that one centipoise is equal to ${{10}^{-2}}$poise.
\begin{align} & \Rightarrow 1centipoise={{10}^{-2}}poise \\ & \Rightarrow 1centipoise={{10}^{-2}}kg-{{m}^{-1}}{{s}^{-1}} \\ & \Rightarrow 1centipoise=0.001kg-{{m}^{-1}}{{s}^{-1}} \\ \end{align}

So, the correct answer is “Option D”.

$\tau =\eta \dfrac{\partial u}{\partial y}$, where, $\tau$is the pressure and $\dfrac{\partial u}{\partial y}$ is the shear velocity.