MHT CET · Physics · Mechanical Properties of Fluids
The angle of contact between glass and water is \(0^{\circ}\) and water rises in a glass capillary upto 6 cm (Surface tension of water is T). Another liquid of surface tension ' \(2 \mathrm{~T}^{\prime}\), angle of contact \(60^{\circ}\) and relative density 2 will rise in the same capillary up to \(\left(\cos 0^{\circ}=1, \cos 60^{\circ}=0.5\right)\)
- A 1.5 cm
- B 2 cm
- C 3 cm
- D 4.0 cm
Answer & Solution
Correct Answer
(C) 3 cm
Step-by-step Solution
Detailed explanation
\(\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{r \rho g}\)
For water:
\(\begin{array}{r}
6=\frac{2 T \cos (0)}{r \times 1 \times g} \\
\therefore \quad r=\frac{2 T}{6 g}=\frac{T}{3 g}
\end{array}\)
For other liquid:
\(h=\frac{4 \mathrm{~T} \cos 60}{\mathrm{r} \times 2 \times \mathrm{g}}=\frac{4 \mathrm{~T} \times 0.5}{\frac{\mathrm{~T}}{3 \mathrm{~g}} \times 2 \times \mathrm{g}}=3 \mathrm{~cm}\)
For water:
\(\begin{array}{r}
6=\frac{2 T \cos (0)}{r \times 1 \times g} \\
\therefore \quad r=\frac{2 T}{6 g}=\frac{T}{3 g}
\end{array}\)
For other liquid:
\(h=\frac{4 \mathrm{~T} \cos 60}{\mathrm{r} \times 2 \times \mathrm{g}}=\frac{4 \mathrm{~T} \times 0.5}{\frac{\mathrm{~T}}{3 \mathrm{~g}} \times 2 \times \mathrm{g}}=3 \mathrm{~cm}\)
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