Exams › JEE Advanced › Physics
A cube of ice floats partly in water and partly in a liquid X. Given that the specific gravity of liquid X is 0.4 and the specific gravity of ice is 0.9, find the ratio of the volume of ice submerged in water to the volume of ice submerged in liquid X.
- 1:1
- 2:1
- 1:2
- 9:4
Correct answer: 1:2
Solution
Equilibrium: rho_w * V_w + rhoₓ * Vₓ = rho_ice * (V_w + Vₓ). With rho_w = 1, rhoₓ = 0.4, rho_ice = 0.9: V_w + 0.4*Vₓ = 0.9*V_w + 0.9*Vₓ. Rearranging: V_w - 0.9*V_w = 0.9*Vₓ - 0.4*Vₓ => 0.1*V_w = 0.5*Vₓ => V_w/Vₓ = 0.5/0.1 = 5/1. Wait — that gives 5:1, not 1:2. Let me redo: V_w + 0.4Vₓ = 0.9(V_w + Vₓ) = 0.9V_w + 0.9Vₓ. So V_w - 0.9V_w = 0.9Vₓ - 0.4Vₓ => 0.1V_w = 0.5Vₓ => V_w = 5Vₓ => V_w:Vₓ = 5:1. But this is not among the options! Check: ice density 0.9, water density 1, liquid density 0.4. Buoyancy = weight: 1*V_w + 0.4*Vₓ = 0.9*(V_w+Vₓ). V_w + 0.4Vₓ = 0.9V_w + 0.9Vₓ. 0.1V_w = 0.5Vₓ. V_w:Vₓ = 5:1. None of the given options (1:1, 2:1, 1:2, 9:4) match. The question may have swapped water and liquid X, or the ice density differs. If we swap: rho_ice = 0.9, rho_water (liquid X at bottom) = 0.4, rhoₓ (liquid on top) = 1 — that does not physically make sense. The problem is likely defective or has a typo in densities. Given available options and the closest algebraic scenario, marking defective.
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 →