MHT CET · Physics · Current Electricity
Water rises to a height of \(20 \mathrm{~mm}\) in a capillary tube of cross-sectional area \(A\). If the area of cross-section of the tube is made \(\left(\frac{A}{4}\right)\), then water will rise to a height of
- A 2 cm
- B 6 cm
- C 4 cm
- D 3 cm
Answer & Solution
Correct Answer
(C) 4 cm
Step-by-step Solution
Detailed explanation
Capillary rise is given by,
\(\begin{aligned}
& h=\frac{2 T \cos \theta}{r \rho g} \\
& \Rightarrow h \propto \frac{1}{r} \propto \frac{1}{\sqrt{A}}
\end{aligned}\)
If \(A\) become one-fourth, \(h\) becomes twice.
\(h^{\prime}=40 \mathrm{~mm}=4 \mathrm{~cm}\)
\(\begin{aligned}
& h=\frac{2 T \cos \theta}{r \rho g} \\
& \Rightarrow h \propto \frac{1}{r} \propto \frac{1}{\sqrt{A}}
\end{aligned}\)
If \(A\) become one-fourth, \(h\) becomes twice.
\(h^{\prime}=40 \mathrm{~mm}=4 \mathrm{~cm}\)
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