Question

Pascal second has the dimension of:
A. Force
B. Coefficient of viscosity
C. Pressure
D. Energy

Answer 1

For solving this question, we need to know the units of all the quantities given as the options. Therefore, first we will find the units and then compare them with the given one to get the correct answer.

Formulas used:
$\eta = \dfrac{{Fr}}{{Av}}$ ,
where, $\eta$ is coefficient of viscosity, $F$ is the tangential force, $r$is the distance between the layers, $A$ is area and $v$ is velocity
$P = \dfrac{F}{A}$,
where, $P$ is the pressure, $F$ is the force and $A$ is area
$E = Fd$, where, $E$ is the energy, $F$ is the force and $d$ is the distance

Complete step by step answer:
First , we will find the unit of the term given in the question which is Pascal second. We know that Pascal is the unit of pressure and pressure $P = \dfrac{F}{A}$.
Therefore we can say that Pascal second is similar to unit $\dfrac{{Ns}}{{{m^2}}}$

Now, we have to find which of the given options has the same unit.Let us first consider option A which is force. We know that the unit of force is newton N. Our second option B is coefficient of viscosity which is given by $\eta = \dfrac{{Fr}}{{Av}}$

Unit of Coefficient of viscosity
\dfrac{{N \times m}}{{{m^2} \times \left( {\dfrac{m}{s}} \right)}} \\\ \therefore\dfrac{{Ns}}{{{m^2}}} \\\
Here, we can see that the unit of Coefficient of viscosity is the same as Pascal second.Hence, option B is the correct answer.

Note: Let us consider other two options and find their units, too.
Option C is given as pressure which is defined as force per unit area.
$P = \dfrac{F}{A}$
The unit of pressure $= \dfrac{N}{{{m^2}}} \ne \dfrac{{Ns}}{{{m^2}}}$
The last option is energy which is given as $E = Fd$
The unit of energy $= Nm \ne \dfrac{{Ns}}{{{m^2}}}$