Question

''Pascal-second'' has the dimensions of:

• A. force
• B. energy
• C. pressure
• D. coefficient of viscosity

Answer 1

Answer: (D)

Pascal is unit of pressure.
Pascal is unit of pressure, hence its dimensional formula is $[M{L}^{-1}{T}^{-2}$ ]
$\therefore$ Dimensional formula of Pascal-second is $\left[M{L}^{-1}{T}^{-1}\right]$
From the formula of coefficient of viscosity, we have
$\eta =\frac{F}{A(\Delta v/\Delta z)}$
where $F$ is force, $A$ is area and $\frac{\Delta v}{\Delta z}$ is velocity gradient.
$\therefore$ Dimensions of $\eta =\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]\left[L{T}^{-1}/L\right]}$
$=\left[M{L}^{-1}{T}^{-1}\right]$
Hence, Pascal-second has dimensions of coefficient of viscosity.