Fluids: Buoyancy, Viscosity and Surface Tension Notes

The correct answer is D. By Archimedes' principle the upthrust on a body equals the weight of the fluid it displaces, and that weight is the volume of the body actually immersed multiplied by the density of the fluid and by the acceleration due to gravity. Only those two properties of the situation enter the expression. Option A is wrong because the weight of the body decides whether it floats or sinks but not the size of the upthrust; a kilogram of lead and a kilogram of cork displace very different volumes. Option B is wrong because shape matters only in so far as it changes the volume immersed; a lump and a sheet of the same metal fully submerged receive the same upthrust. Option C is wrong because it replaces volume with mass, and two bodies of equal mass but different density displace different volumes of fluid.

The correct answer is B, 8 per cent. A floating body displaces its own weight of fluid, so the fraction of its volume that lies below the surface equals the ratio of its density to the density of the fluid, here 920 divided by 1000, which is 0.92. That means 92 per cent of the iceberg is submerged and the remaining 8 per cent stands above the water. Option A, 6 per cent, is wrong because it would require an ice density of 940 kilograms per cubic metre. Option C, 92 per cent, is wrong because that is the submerged fraction, and it is the commonest error in this question, since the candidate stops one step too early. Option D, 20 per cent, is wrong by a wide margin and would need a density ratio of 0.8. The same calculation explains why only the tip of an iceberg is seen at sea.

The correct answer is B, the centre of mass of the displaced fluid. The upthrust on a body is the resultant of the pressure forces of the fluid around it, and that resultant acts through the centre of gravity of the fluid the body has pushed aside, which is why the point is called the centre of buoyancy. Option A is wrong because the centre of gravity of the body depends on how the body's own mass is distributed, and the two points coincide only when the body is of uniform density and fully submerged. Option C is wrong because the metacentre is a separate point, defined where the line of the upthrust cuts the centre line of a slightly tilted body, and it lies above the centre of gravity in stable flotation. Option D describes the metacentre rather than the centre of buoyancy.

The correct answer is D, a Newtonian fluid. In such a fluid the shearing stress is directly proportional to the rate of shear, so the coefficient of viscosity, which measures the resistance to deformation, keeps the same value whatever the stress applied; water, air, petrol and thin oils behave in this way. Option A, a Bingham plastic, is wrong because it will not flow at all until a yield stress is exceeded, toothpaste being the familiar example. Option B, a pseudoplastic fluid, is wrong because its apparent viscosity falls as the shear rate rises, which is how paint spreads when it is brushed. Option C, a dilatant fluid, is wrong because its apparent viscosity rises with the shear rate, as in a thick paste of cornflour and water that hardens when struck. The last three are grouped together as non-Newtonian fluids.

The correct answer is C. In a capillary tube the height of rise is directly proportional to the surface tension of the liquid and inversely proportional to its density and the radius of the tube. If a liquid climbs higher than water in the same tube, the most natural explanation is that its surface tension is greater than that of water, which is the same as saying that the surface tension of water is less than that of the liquid. Option D states the relation the wrong way round and would make the liquid rise less than water. Option A is wrong because viscosity decides how fast the liquid rises, not how far; the final height is a matter of equilibrium. Option B is wrong because raising the temperature lowers surface tension, which would reduce the rise rather than increase it.

The correct answer is A, hydraulic brakes. Pascal's law says that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of the vessel, so a modest push on the brake pedal creates a pressure in the brake fluid that is passed to the wider pistons at every wheel, where it becomes a large force. The hydraulic lift and the hydraulic press work the same way. Option B is wrong because a barometer measures atmospheric pressure by balancing it against a column of mercury. Option C is wrong because a hydrometer floats in a liquid and measures relative density, which rests on the law of flotation. Option D is wrong because a siphon works on the difference in pressure caused by the difference in the height of the two liquid levels.

The correct answer is B, pascal second, equal to a newton second per square metre, which follows from Newton's law of viscosity, where the shearing stress in pascals is divided by the velocity gradient in reciprocal seconds. Option A, the poise, is wrong because it is the CGS unit of the same quantity, and one pascal second equals ten poise. Option C, stokes, is wrong because it is the CGS unit of kinematic viscosity, which is the coefficient of viscosity divided by the density and is measured in square metres per second in SI units. Option D, newton per metre, is wrong because it is the unit of surface tension, a force per unit length, and the pairing of surface tension with viscosity is a favourite way of setting a trap in this chapter.

The correct answer is B, surface tension. Cohesive forces pull the molecules at the surface of a liquid inward, so the surface behaves like a stretched membrane and takes the smallest area that can enclose the given volume; for a fixed volume the shape of least surface area is a sphere, which is why a free drop and a soap bubble are both round. Option A, viscosity, is wrong because it governs resistance to flow and so decides the speed of falling, not the shape. Option C, capillarity, is wrong because it is a consequence of surface tension together with adhesion, and describes the rise or fall of a liquid in a narrow tube rather than the shape of a drop. Option D, buoyancy, is wrong because it is the upthrust of a surrounding fluid and explains floating, not shape; large falling drops are in fact flattened by air resistance.

The correct answer is C. In a liquid, viscosity comes chiefly from cohesion between molecules; heating weakens that cohesion, so the layers slide past one another more easily and the viscosity falls, which is why engine oil becomes thinner as the engine warms and why honey flows freely when it is warmed. In a gas, viscosity comes from the transfer of momentum by molecules moving between layers; heating makes those molecules move faster, so more momentum is carried across and the viscosity rises. Option A and option B are wrong because they treat the two states alike. Option D is wrong because it reverses both results. This contrast is one of the most frequently asked single facts from the chapter and is worth memorising as a pair.

The correct answer is C, it remains unchanged. While the ice floats it displaces a volume of water whose weight equals the weight of the ice, by the law of flotation. When the ice melts it becomes water of exactly that weight, and water of that weight occupies exactly the volume the floating ice was displacing, so the level neither rises nor falls. Option A is wrong because the melted water fills the space the submerged part of the ice occupied and adds nothing further. Option B is wrong because no water leaves the glass. Option D is wrong because the balance holds throughout the melting, so there is no intermediate change. If the ice contained a stone or a cork the answer would differ, and that is the version examiners use to catch candidates who have learnt the result without the reasoning.