MHT CET · Physics · Mechanical Properties of Fluids
Water rises in a capillary tube of radius ' \(r\) ' up to height ' \(h\) '. The mass of water in capillary is ' \(m\) '. The mass of water that will rise in capillary of radius \(\mathrm{r} / 3\) will be
- A m
- B \(\frac{\mathrm{m}}{3}\)
- C \(\frac{m}{6}\)
- D \(\frac{\mathrm{m}}{9}\)
Answer & Solution
Correct Answer
(B) \(\frac{\mathrm{m}}{3}\)
Step-by-step Solution
Detailed explanation
Rise of water in capillary tube is given by
\(\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\mathrm{rgg}}\)
For water, \(\cos \theta=1\)
Also, the radius of capillary tube becomes (r/3).\(
\therefore \quad \mathrm{h}^{\prime}=\frac{3 \cdot 2 \mathrm{~T}}{\mathrm{r} \rho \mathrm{~g}} \Rightarrow \mathrm{~h}^{\prime}=3 \mathrm{~h}\)
Now, \(m=\pi r^2 \mathrm{~h} \times \rho\)
\(\therefore \quad \mathrm{m}^{\prime}=\pi(\mathrm{r} / 3)^2(3 \mathrm{~h}) \times \rho=\frac{\pi \mathrm{r}^2 \mathrm{~h} \rho}{3}=\frac{\mathrm{m}}{3}\)
\(\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\mathrm{rgg}}\)
For water, \(\cos \theta=1\)
Also, the radius of capillary tube becomes (r/3).\(
\therefore \quad \mathrm{h}^{\prime}=\frac{3 \cdot 2 \mathrm{~T}}{\mathrm{r} \rho \mathrm{~g}} \Rightarrow \mathrm{~h}^{\prime}=3 \mathrm{~h}\)
Now, \(m=\pi r^2 \mathrm{~h} \times \rho\)
\(\therefore \quad \mathrm{m}^{\prime}=\pi(\mathrm{r} / 3)^2(3 \mathrm{~h}) \times \rho=\frac{\pi \mathrm{r}^2 \mathrm{~h} \rho}{3}=\frac{\mathrm{m}}{3}\)
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
- Heat energy is incident on the surface at the rate of \(1000 \mathrm{~J} / \mathrm{min}\). If coefficient of absorption is 0.8 and coefficient of reflection is 0.1 then heat energy transmitted by the surface in 5 minutes isMHT CET 2023 Hard
- The point charges \(+\mathrm{q},-\mathrm{q},-\mathrm{q},+\mathrm{q},+\mathrm{Q}\) and -q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of hexagon ' \(O\) ' due to the five charges at \(A, B, C, D\) and \(F\) is twice the electric field at centre ' \(O\) ' due to charge \(+Q\) at \(E\) alone. The value of Q is
MHT CET 2025 Medium - An iron rod is placed parallel to magnetic field of intensity . The magnetic flux through the rod is and its cross-sectional area is . The magnetic permeability of the rod in isMHT CET 2016 Medium
- The \(p-V\) diagram of a system undergoing thermodynamic changes is as shown in the figure. The work done by the system in going from \(A \rightarrow B \rightarrow C\) is \(30 \mathrm{~J}\). If \(68 \mathrm{~J}\) of heat is given to the system, then the change in the internal energy of the system between \(\mathrm{A}\) and \(\mathrm{C}\) is
MHT CET 2022 Easy - Three samples \(\mathrm{X}, \mathrm{Y}\), and Z of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X, adiabatic for Y and isobaric for Z. If the final pressures are equal for the three samples, the ratio of the initial pressures is \((r=3 / 2)\)MHT CET 2025 Hard
- From a disc of mass ' \(M\) ' and radius ' \(R\) ', a circular hole of diameter ' \(R\) ' is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about perpendicular axis passing through the centre isMHT CET 2023 Medium
More PYQs from MHT CET
- The statement pattern \([(p \rightarrow q) \wedge \sim q] \rightarrow r\) is a tautology when \(r\) is equivalent toMHT CET 2025 Medium
- Identify the products of following reaction?
\(\text { Formaldehyde }+ \text { Benzaldehyde } \xrightarrow[\text { ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {i) conc. } \mathrm{NaOH}} \text { Products }\)MHT CET 2025 Medium - Water rises up to height ' \(X\) ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' \(d\) ' in a mine, the water level rises up to height ' \(Y\) '. If ' \(R\) ' is
the radius of earth then the ratio \(\frac{Y}{X}\) isMHT CET 2024 Medium - In which of the following plants male flower floats on the surface of water?MHT CET 2021 Hard
- A particle having a charge \(100 \mathrm{e}\) is revolving in a circular path of radius \(0.8 \mathrm{~m}\) with 1.r.p.s The magnetic field produced at the center of the circle in SI unit is ( \(\mu_0\) permeability of vacuum, \(\left.\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right)\)MHT CET 2021 Hard
- The current drawn from the battery in the given network is (Internal resistance of the battery is negligible)
MHT CET 2024 Easy