Q25 / 160 · WBJEE 2015 · Chemistry
The units of surface tension and viscosity of liquids respectively are
- A$\mathrm{kg} \mathrm{m}^{-1} \mathrm{s}^{-1}, Nm^{-1}$
- Correct answerB$\mathrm{kg} \mathrm{s}^{-2}, \mathrm{kg} \mathrm{m}^{-1} \mathrm{s}^{-1}$
- C$\mathrm{Nm}^{-1}, \mathrm{kg} \mathrm{m}^{-1} \mathrm{s}^{-2}$
- D$\mathrm{kg} \mathrm{s}^{-1}, \mathrm{kg} \mathrm{m}^{-2} \mathrm{s}^{-1}$
Solution
From the formula, Surface tension, $(\gamma)$
$$
=\frac{\Delta W}{\Delta A}=\frac{\mathrm{J}}{\mathrm{m}^{2}}=\frac{\mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-2}}{\mathrm{m}^{2}}=\mathrm{kg} \mathrm{s}^{-2}
$$
Form the formula, $F=\eta \cdot A \cdot \frac{d V}{d x}$ or, $\eta$ (coefficient of viscosity)
$$
=\frac{F}{A \cdot \frac{d V}{d x}}=\frac{\mathrm{N}}{\mathrm{m}^{2} \cdot \frac{\mathrm{ms}^{-1}}{\mathrm{m}}}=\mathrm{Nm}^{-2} \cdot \mathrm{s}
$$
or $\mathrm{kg} \mathrm{ms}^{-2} \cdot \mathrm{m}^{-2} \cdot \mathrm{s}=\mathrm{kg} \mathrm{m}^{-1} \mathrm{s}^{-1}$
Hence, the correct answer is option: 'B'.