Mechanical properties of fluids practice · Mixed difficulty

Option B ($3.3 \times {10^{ - 2}}$) is correct because it is the surface tension calculated from the work done and the change in area of the soap film.

Option B (falls) is correct. The water level falls because the stone displaces its weight in water when embedded in ice, but only its volume when submerged after the ice melts. Since stone's density is greater than water, its volume is less than the volume of water of equal weight.

Option D (0.085416667) is correct because the height is inversely proportional to the radius of the tube.

Option D (Both (1) and (2)) is correct because in the absence of gravity, there is no weight and hence no upward thrust.

Option B is correct. Both the assertion and the reason are true, but the reason does not fully explain why the liquid neither rises nor falls. The angle of contact determines the shape of the meniscus, which affects the pressure difference and thus the rise or fall.

Option D (32p) is correct because the momentum depends on the mass and terminal velocity, both of which are affected by the radius.

Option D is correct. Surface tension minimizes the surface area, leading to a spherical shape.

Option C (remain unchanged) is correct because the barometric height depends on atmospheric pressure, which is independent of the local value of g.

Option C ($\frac{{18.03}}{{19.83}}$) is correct because the specific gravity is calculated by dividing the weight of the wax in air by the loss of weight of the wax in water.

Option A is correct because when a drop of water is broken into smaller drops, the total surface area increases, leading to an increase in surface energy.

Option D (0.4) is correct because velocity is calculated by dividing the flow rate by the cross-sectional area, with proper unit conversions.

Option C (${R_e} = \frac{{\rho vd}}{\eta }$) is correct because it represents the standard formula for Reynolds number, relating density, velocity, diameter, and viscosity.

Option B (40 m/s) is correct because the velocity of efflux is calculated using the formula v = sqrt(2gh), where h is the height of the water column.

Option B (Liquid of high viscosity and low density flowing through a pipe of small radius) is correct because these conditions favor laminar flow, which is more streamlined.

Option B ($8 \pi R^2 T$) is correct because the work done is the difference in surface energy between the 27 small drops and the original large drop.

Option C (the same in all the vessels) is correct because the force exerted by a liquid on the base of a vessel depends only on the height of the liquid column and the area of the base, and since the masses are equal and the vessels are identical, the height will adjust such that the force is the same.

Option C ($\frac{{{A_2}}}{{{A_1}}}$) is correct because the equation of continuity states that $A_1v_1 = A_2v_2$, therefore the ratio of velocities is inversely proportional to the ratio of areas.

Option A (Increases) is correct because the sugar solution is denser than ice, and the melted ice adds water to the solution, increasing the liquid level.

Option A is correct because both the Assertion and Reason are true, and the Reason correctly explains why it's difficult for a man to walk on sand while a camel can walk easily.

Option B ($4\pi {R^2}T$) is correct because the change in surface energy is the surface tension multiplied by the change in surface area, and the total surface area increases when the drop splits.

Option C (A is true but R is false) is correct because a larger bubble has lower excess pressure and expands at the expense of the smaller one, but the excess pressure is inversely proportional to the radius, not directly proportional.

Option D is correct because the height of liquid rise in a capillary tube is inversely proportional to the radius of the tube.

Option B (Lighter) is correct because when the parrot flies, it no longer exerts its weight on the cage floor, effectively reducing the weight felt by the boy.

Option C (${F_c} < {F_A}$) is correct because a concave meniscus indicates that the adhesive forces between the liquid and the tube are stronger than the cohesive forces within the liquid.

Option C is correct. The formula for capillary rise is $h=\frac{{2 S \cos \theta}}{{r \rho g}}$.

Option D ($1: 27$) is correct because excess pressure is inversely proportional to the radius, and volume is proportional to the cube of the radius.

Option D (equal in all the vessels) is correct because the force on the base depends only on the weight of the liquid, which is the same for all vessels since they have equal mass.

Option D is correct. Both the assertion and the reason are false statements regarding capillary action and liquid behavior in tubes.

Option A is correct because the height of water raised in a capillary tube is inversely proportional to the radius of the tube, as described by the Jurin's law.

Option C (If assertion is true but reason is false) is correct because a solid sphere under high pressure compresses uniformly, but its geometrical shape does not change.