MCQ
$Pascal-Second$ has dimension of
- AForce
- BEnergy
- CPressure
- ✓Coefficient of viscosity
✓
Answer
Correct option: D.
Coefficient of viscosity
d
Pascal is unit of pressure, hence its dimensional formula is
Pascal is unit of pressure, hence its dimensional formula is
$\left[M L^{-1} T^{-2}\right]$
$\therefore$ Dimensional formula of Pascal-second is $\left[M L^{-1} T^{-1}\right]$
By 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 $\eta=\frac{\left[M L T^{-2}\right]}{\left[L^{2}\right]\left[L T^{-1} / L\right]}$
$=\left[M L^{-1} T^{-1}\right]$
Hence, Pascal-second has dimensions of coefficient of viscosity.
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