List of top Physics Questions on mechanical properties of fluid asked in JEE Advanced

An incompressible liquid is filled in a container. There is air above the liquid and a massless movable piston with a hole is also placed on the air. A thin capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the hole on the piston as shown in the figure. The air in the container is isothermally compressed from the original volume V₀ to $\frac{100}{101}$V₀ with the movable piston. Considering air as an ideal gas, the height (h) of the liquid column in the capillary above the liquid level in cm is:

(given T_water=0.075N/m, P₀=10⁵N/m², g=10m/sec², $\rho l$=10³kg/m³, $\theta=0$)

An incompressible liquid is filled in a container. There is air above the liquid and a massless movable piston with a hole is also placed on the air. A thin capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the hole on the piston as shown in the figure. The air in the container is isothermally compressed from the original volume V₀ to $\frac{100}{101}$V₀ with the movable piston. Considering air as an ideal gas, the height (h) of the liquid column in the capillary above the liquid level in cm is:

(given T_water=0.075N/m, P₀=10⁵N/m², g=10m/sec², $\rho l$=10³kg/m³, $\theta=0$)

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma=\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a 1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{a 2}$, the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$, respectively.Which of the following statement(s) is(are) correct?

A cylindrical tube, with its base as shown in the figure, is filled with water It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ} P_{1}$ and $P_{2}$ are pressures at points $1$ and $2$, respectively located at the base of the tube Let $\beta=\left(P_{1}-P_{2}\right) /(\rho g d)$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity Which of the following statement(s) is(are) correct?

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$, at a height $L$ above the hinge at point $O$ a block of weight $\alpha W$ is attached at the point $P$ of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(2 \sqrt{2})$ W. Which of the following statement(s) is(are) correct?

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test tube with some air (ideal gas) trapped as shown in the figure. The test tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially, the bottle is sealed at atmospheric pressure p₀ = 10⁵Pa so that the volume of the trapped air is V₀ = 3.3 cc. When the bottle is squeezed from outside at a constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p₀ + Δp without changing its orientation. At this pressure, the volume of the trapped air is V₀ – ΔV.
Let ΔV = X cc and Δp = Y × 10³ Pa.