Exams › JEE Advanced › 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 Advanced Physics questions
- A capillary tube with a square-shaped internal cross-section, each side of length 'a', is inserted vertically into a liquid of density ρ and surface tension σ. If the liquid adheres to the tube walls with a contact angle θ, approximately how high will the liquid rise inside the tube? (Ignore the surface tension effects at the corners of the tube.)
- A hot air balloon with a total mass of 480 kg, including passengers and 1 kg sandbags, is floating steadily at a height of 100 m. The balloon's buoyancy is determined by its fixed volume, V. If N sandbags are removed, the balloon ascends to a stable height of approximately 150 m. The air density changes with altitude according to ρ(h) = ρ₀e⁻ʰ/ʰ₀, where ρ₀ = 1.25 kg/m³ and h₀ = 6000 m. What is the value of N?
- A container accelerates horizontally to the left with acceleration g/2. A uniform rod of length L is partially submerged vertically in a liquid contained in the accelerating container. The density of the liquid is rho and the density of the rod is rho/2. If the length of the rod submerged in the liquid is sqrt(a/b)*L, where a and b are the least positive integers (in lowest terms), find (a + b).
- A vertical U-tube (communicating tube) contains a liquid of density rho and surface tension T. The tube has inner radius r. When the entire system accelerates horizontally with acceleration a, the pressure at point A (at the liquid surface in the left arm, taking the meniscus correction into account) is given by which of the following expressions? (Take atmospheric pressure as P0, and assume the contact angle is 0 deg.)
- A space 2.5 cm wide between two large parallel plane surfaces is filled with oil. The force required to drag a very thin plate of area 0.5 m² at a speed of 0.5 m/s, placed exactly midway between the two surfaces, is 1 N. Find the coefficient of viscosity of the oil.
- A ball of mass 10 kg and density 1 g/cm³ is attached to the base of a container by a spring (spring constant k = 200 N/m). The container is filled with a liquid of density 1.1 g/cm³. The entire system accelerates upward at 2 m/s². Find the elongation (extension) of the spring. (Take g = 10 m/s²)
⚔️ Practice JEE Advanced Physics free + battle 1v1 →