MHT CET · Physics · Mechanical Properties of Fluids
In capillary tube having area of cross-section ' \(A\) ', water rises to a height ' \(h\) '. If cross sectional area is reduced to \(\frac{A}{9}\), the rise of water in the capillary tube is
- A h
- B 4 h
- C 3 h
- D 2h
Answer & Solution
Correct Answer
(C) 3 h
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & h=\frac{2 T \cos \theta}{r \rho g} \\ & \Rightarrow h \propto \frac{1}{r} \\ & \text { And } A=\pi r^2 \Rightarrow r \propto \sqrt{A} \\ & \Rightarrow h \propto \frac{1}{\sqrt{A}} \\ & \text { Now, } \frac{h_2}{h_1}=\sqrt{\frac{A_1}{A_2}} \\ & \Rightarrow \frac{h_2}{h}=\sqrt{\frac{A}{A / 9}}=3 \\ & \Rightarrow h_2=3 h\end{aligned}\)
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