Mechanical properties of fluids practice · Mixed difficulty

Option C (3 cm) is correct because it is calculated by comparing the capillary rise equations for the two liquids, considering the differences in surface tension, angle of contact, and density.

Option B (Statement I is true, Statement II is true; Statement II is not the correct explanation for Statement I) is correct. Concrete ships were indeed built, and they were filled with air to reduce their average density, but the air filling is not the primary reason why any object floats (density is).

Both statements are true. A sudden fall in pressure indicates a storm due to rising air and condensation, and air always flows from areas of high pressure to areas of low pressure.

Option B (Conservation of energy) is correct. Bernoulli's equation is a direct application of the principle of conservation of energy to fluid flow.

Option C ($2.32 \times 10^6 {~N}$) is correct because it is the force calculated from the pressure difference at the given depth and the area of the window.

Option A is correct because both the assertion and reason are true, and the reason correctly explains why raindrops reach a terminal velocity.

Option C is correct. Liquids that rise in a capillary tube have an acute angle of contact.

Option B is correct because the density is calculated using the fraction of the log submerged in water and the density of water.

Option C (decreases) is correct because the surface tension of most liquids decreases as temperature increases due to increased molecular kinetic energy.

Option C (A is true but R is false) is correct because kerosene oil spreading on water is due to lower surface tension, not just the existence of surface tension.

Option D ($10m{s^{ - 1}}$) is correct because it is calculated using Bernoulli's equation, relating pressure difference to fluid velocity.

Option D ($R/10$) is correct because the volume of the big drop equals the sum of the volumes of the 1000 small droplets.

Option C ($0.2 {~m}$) is correct because the velocity head is calculated using the formula $v^2 / (2g)$, where v is the velocity and g is the acceleration due to gravity.

Option C (500 Pa) is correct because it is calculated using Bernoulli's equation, considering the change in velocity due to the change in cross-sectional area.

Option A (becomes zero) is correct because at the boiling point, the intermolecular forces weaken significantly, reducing surface tension to zero.

Option A is correct because it calculates the viscous force using Stokes' Law, given the terminal velocity and radius of the raindrop.

Option C (zero) is correct because in free fall, the effective weight of both the liquid and the body becomes zero, resulting in no buoyant force.

Option D (${75^ \circ }C$) is correct because the surface tension of water decreases as temperature increases.

Option A is correct. At the critical temperature, the surface tension of a liquid becomes zero as the distinction between liquid and gas phases disappears.

Option D (8 km) is correct because the depth is calculated using the compressibility of water and the change in density due to pressure.

Option D ($128 \sqrt{\frac{2h}{g}}$) is correct because it is derived from Torricelli's law and integrating the flow rate over the changing height.

Option B is correct because the height the ball jumps out of the water depends on the ratio of the densities of water and the ball, and the initial depth.

Option C ($5 \times 10^4 {~N}$) is correct because the buoyant force is equal to the weight of the fluid displaced by the object, which is the product of the fluid's density, the object's volume, and the acceleration due to gravity.

Option C (increase in all directions) is correct because pressure applied to an enclosed fluid is transmitted equally in all directions, according to Pascal's Law.

The force exerted on the bottom of the bottle is 300 N. This is calculated using Pascal's principle, which states that pressure is transmitted equally throughout a fluid.

Option A (the weight of aluminium is half the weight of steel) is correct because equal apparent weights in water imply equal buoyant forces, which depend on volume. Since aluminum is less dense, it must have a larger volume and therefore a smaller density times twice the volume of steel to have the same weight.

Option C (Where speed is more) is correct because according to Bernoulli's principle, pressure is lower where fluid speed is higher.

Option B is correct. Surface tension decreases with increasing temperature, so the capillary rise is higher in cold water.

Option A is correct. In an artificial satellite, the effective gravitational acceleration is zero, leading to the liquid rising to the full length of the capillary tube because the weight component that opposes the capillary rise is absent.

Option C is correct because the water will rise to the top of the capillary tube and stay there without overflowing. The radius of curvature adjusts to maintain the equilibrium height.