Mechanical properties of fluids practice · Mixed difficulty

Option A (is less than atmospheric pressure) is correct because for an angle of contact less than 90 degrees, the pressure inside the meniscus is less than atmospheric pressure.

Option C (Infinity) is correct because when two soap bubbles of equal radii coalesce, the interface between them becomes flat, resulting in an infinite radius of curvature.

Option D (Zero) is correct because the buoyant force acting on the bag filled with water equals the weight of the water, resulting in zero net weight.

Option D (Statement I is false; Statement II is true) is correct because a ship's floating depends on buoyant force due to water displacement, independent of atmospheric pressure, while the statement about buoyant force is correct.

Option B ($90^{\circ}$) is correct because if the liquid levels inside and outside the tube are the same, the angle of contact is 90 degrees.

Option C (Constant, non-viscous, incompressible, temperature-independent flow) is correct because Bernoulli's equation is derived under these assumptions.

Option A ($\frac{{R}}{10}$) is correct because the radius of the small drop is calculated by equating the volume of the big drop to the total volume of the small droplets.

Option D (Barometer) is correct because a barometer measures atmospheric pressure and does not rely on Bernoulli's principle, unlike the other options.

Option A ($1.013 \times 10^5 \mathrm{~Nm}^{-2}$) is correct because standard atmospheric pressure is defined as 101325 Pascals, which is equivalent to $1.013 \times 10^5 \mathrm{~Nm}^{-2}$.

Option D (Pascal's law) is correct because hydraulic lifts and hydraulic brakes operate based on Pascal's principle, which states that pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and the walls of the container.

Option A (Both A and R are true and R is the correct explanation of A) is correct because the larger area of a camel's feet reduces the pressure on the sand, making it easier to walk.

Option D (If Assertion is false but the Reason is true) is correct because pressure is a scalar quantity, not a vector, but the formula P=F/A correctly uses force as a vector.

Option B ($1.47 \times {10^3}N$) is correct because it is calculated using Pascal's law for pressure transmission in fluids.

Option A ($\frac{4 \mathrm{S}}{\mathrm{R}}$) is correct because the pressure inside a soap bubble exceeds the outside pressure by $\frac{4S}{R}$ due to the two air-liquid interfaces.

Option B is correct because the surface tension of a liquid generally decreases as the temperature increases due to increased molecular kinetic energy.

Option C (0.0009 m) is correct because it is calculated by using the formula for viscous force, $F = \eta A \frac{dv}{dx}$, and solving for the distance $dx$.

Option A ($\frac{2 S \cos \theta}{\rho r g}$) is correct because it is the standard formula for capillary rise, relating surface tension, contact angle, density, radius, and gravity.

Option B (force of surface tension predominates the force of gravity) is correct because surface tension effects are more significant for smaller volumes due to the surface area to volume ratio.

Option B ($\frac{{1}}{{8}}$) is correct because Poiseuille's equation for the rate of flow of liquid through a tube is $V = \frac{{\pi p r^4}}{{8 \eta l}}$, so N = 1/8.

Option B (Angle of contact may be $90^{\circ}$) is correct because if the angle of contact is 90 degrees, the liquid neither rises nor falls in the capillary tube.

Option A is correct because surface tension and force gradient both have the same units (N/m), and surface tension is indeed the force gradient along the surface of a liquid.

Option C (Area of the bottom surface) is correct because the pressure at a depth in a liquid depends on the depth, density, and gravity, but not the area of the bottom.

Option C ($\frac{V}{4}$) is correct because according to the equation of continuity, when the radius doubles, the area quadruples, and the velocity must decrease by a factor of 4 to maintain constant flow rate.

Option D ($64 \mathrm{~m} / \mathrm{s}$) is correct because it is calculated using the principle of continuity (A1v1 = A2v2).

Option B ($750\mathrm{ }/kg\mathrm{ }{m^3}\;\;$) is correct because the density of the wood is calculated by considering the fraction of the log submerged in water and using the principle of buoyancy.

The correct answer is None of these because the area A required to support the man is 2 m², which is not among the given options.

Option D ($4^{1 / 3} {~W}$) is correct because the work done is proportional to the surface area, and the radius is proportional to the cube root of the volume, so $W' = (4)^{1/3}W$.

Option D (Zero) is correct because in gravity-free space, there is no weight or buoyant force, so the terminal velocity is zero.

Option C (81.9 kN) is correct because it is the gross lift calculated using Bernoulli's principle and the given air speeds, density, and wing dimensions.

Option B (surface tension) is correct because surface tension causes the water film between the hairs to contract, pulling the hairs together.