Question

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

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

Answer 1

Answer: (D)

coefficient of viscosity

Answer 2

Pascal is unit of pressure. Pascal is unit of pressure, hence its dimensional formula is $\left[ ML ^{-1} T ^{-2}\right.$ ] $\therefore$ Dimensional formula of Pascal-second is $\left[ ML ^{-1} T ^{-1}\right]$ 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 $\eta =\frac{\left[ MLT ^{-2}\right]}{\left[ L ^{2}\right]\left[ LT ^{-1} / L \right]}$ $=\left[ ML ^{-1} T ^{-1}\right]$ Hence, Pascal-second has dimensions of coefficient of viscosity.