The viscosity of a liquid and the viscosity of a gas behave in which way when the temperature is raised?

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.