Exams › JEE Main › Physics
A capillary tube of radius r = 0.2 mm is dipped vertically into a liquid of density rho = 1 g/cc. A small piston (x) inserted into the capillary maintains a constant air pressure P1 = 2*10⁴ dynes/cm² on the hemispherical meniscus. The ambient pressure is P0 = 10⁵ dynes/cm² and the surface tension of the liquid is T = 72 dynes/cm. Ignoring the weight of the curved part of the liquid, find the rise (or fall) h of the liquid column in cm.
- h = 4.6 cm (liquid is depressed below the outside level)
- h = 4.6 cm (liquid rises above the outside level)
- h = 2.3 cm (liquid rises)
- h = 8.2 cm (liquid depressed)
Correct answer: h = 4.6 cm (liquid is depressed below the outside level)
Solution
The piston applies P1 above the meniscus. The pressure jump across the meniscus is 2T/r. Setting up the hydrostatic balance between the pressure inside the tube at the level of the outside free surface and the ambient pressure P0 gives the column height h. Since P1 + 2T/r exceeds P0, the liquid inside is pushed down (depressed).
Related JEE Main Physics questions
- A body is in motion inside a liquid, and the viscous resistive force on it is directly proportional to its speed. What are the dimensions of the proportionality constant?
- A capillary tube has its inner surface lined with wax and is then placed in water. Relative to a clean, unwaxed capillary, how do the contact angle (θ) and the height (h) to which water rises change?
- A charged, isolated spherical soap bubble of radius r has internal pressure equal to atmospheric pressure. If the charge on the bubble is given by Xπ√(2Tε), what is the value of X?
- Two capillary tubes, one of length L and radius R and the other of length 2L and radius 2R, are joined one after the other in series. If the flow rate through a single capillary is X = πPR⁴ / 8ηL, then the combined flow rate through the series arrangement is:
- A liquid will fail to wet the surface of a solid when the angle of contact is
- A gold sphere of a given size falls through a viscous liquid and attains a terminal speed of 0.2 m/s. If the gold has density 19.5 kg/m³ and the liquid has density 1.5 kg/m³, what terminal speed will a silver sphere of the same size have in the same liquid, given that silver has density 10.5 kg/m³?
⚔️ Practice JEE Main Physics free + battle 1v1 →