MHT CET · Physics · Mechanical Properties of Fluids
Three liquids have same surface tension and densities \(\varrho_{1}, Q_{2}\), and \(\varrho_{3}\left(\varrho_{1}>\varrho_{2}>\varrho_{3}\right)\).
In three identical capillaries, rise of liquid is same. The corresponding angles of contact \(\theta_{1}, \theta_{2}\) and \(\theta_{3}\) are related as
- A \(\theta_{1}>\theta_{2}>\theta_{3}\)
- B \(\theta_{1} < \theta_{2}>\theta_{3}\)
- C \(\theta_{1}>\theta_{2} < \theta_{3}\)
- D \(\theta_{1} < \theta_{2} < \theta_{3}\)
Answer & Solution
Correct Answer
(D) \(\theta_{1} < \theta_{2} < \theta_{3}\)
Step-by-step Solution
Detailed explanation
Rise of a liquid in a capillary tube is given by,
\(\mathrm{h}=\frac{2 \mathrm{T} \cos \theta}{\mathrm{r} \rho \mathrm{g}}\)
or \(\cos \theta=h r \rho g / 2 T\)
where \(\theta=\) angle of contact,
\(\mathrm{r}=\) radius of capillary tube
\(\mathrm{T}=\) surface tension
\(\rho=\) density of liquid
now given that \(h\), \(T\) and \(r\) are constants for all three liquids,
and \(\rho_{1}>\rho_{2}>\rho_{3}\),
therefore \(\cos \theta_{1}>\cos \theta_{2}>\cos \theta_{3}\)
or \(\theta_{1} < \theta_{2} < \theta_{3}\)
now as the liquid is rising in all three capillaries therefore angles of contact will be acute,
\(0 \leq \theta_{1} < \theta_{2} < \theta_{3} < \frac{\pi}{2}\)
\(\mathrm{h}=\frac{2 \mathrm{T} \cos \theta}{\mathrm{r} \rho \mathrm{g}}\)
or \(\cos \theta=h r \rho g / 2 T\)
where \(\theta=\) angle of contact,
\(\mathrm{r}=\) radius of capillary tube
\(\mathrm{T}=\) surface tension
\(\rho=\) density of liquid
now given that \(h\), \(T\) and \(r\) are constants for all three liquids,
and \(\rho_{1}>\rho_{2}>\rho_{3}\),
therefore \(\cos \theta_{1}>\cos \theta_{2}>\cos \theta_{3}\)
or \(\theta_{1} < \theta_{2} < \theta_{3}\)
now as the liquid is rising in all three capillaries therefore angles of contact will be acute,
\(0 \leq \theta_{1} < \theta_{2} < \theta_{3} < \frac{\pi}{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A particle performing SHM has time period \(\frac{2 \pi}{\sqrt{3}}\) and path length \(4 \mathrm{~cm}\). The displacement from mean position at which acceleration is equal to velocity isMHT CET 2009 Hard
- Two identical current carrying coils with same centre are placed with their planes perpendicular to each other. If current \(I=\sqrt{2} \mathrm{~A}\) and radius of the coil is \(\mathrm{R}=1 \mathrm{~m}\), then magnetic field at centre is equal to ( \(\mu_0=\) permeability of free space)MHT CET 2024 Medium
- A pipe open at both ends of length \(1.5 \mathrm{~m}\) is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency \(330 \mathrm{~Hz}\). If speed of sound in air is \(330 \mathrm{~m} / \mathrm{s}\) then the length of the pipe immersed in water is (Neglect end correction)MHT CET 2021 Easy
- A coil is wound on a core of rectangular cross-section. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the self-inductance increases by a factorMHT CET 2025 Medium
- A string of mass \(0.1 \mathrm{kgm}^{-1}\) has length 0.9 m . It is fixed at both ends and stretched such that it has a tension of 40 N . The string vibrates in three segments with amplitude 0.3 cm . The amplitude (maximum) of the particle velocity is (in m/s)MHT CET 2025 Medium
- P and Q are two non-zero vectors inclined to each other at an angle ‘p’ and ‘q’ are unit vectors along P and Q respectively. The component of Q in the direction of Q will beMHT CET 2019 Medium
More PYQs from MHT CET
- Which of the following alkenes is most easily formed by dehydrohalogenation of alkyl halides?MHT CET 2025 Medium
- Which of the following is a character of catalyst?MHT CET 2020 Medium
- Which of the following is used as an antiseptic in soap?MHT CET 2020 Easy
- A clock pendulum having coefficient of linear expansion, has a period of at If the clock is used in a climate where the temperature is how much time does the clock lose in each oscillation?MHT CET 2019 Easy
- What is the total volume occupied by atoms in bcc unit cell?MHT CET 2022 Easy
- Which of the following alkenes, on oxidation by \(\mathrm{KMnO}_4\) in dil. \(\mathrm{H}_2 \mathrm{SO}_4\) forms adipic acid?MHT CET 2025 Medium