Whether an object will float or sink in a liquid, depends on
- (a)mass of the object only
- (b)mass of the object and density of liquid only
- (c)difference in the densities of the object and liquid
- (d)mass and shape of the object only
Correct — C, difference in the densities of the object and liquid. Two forces decide the outcome — the weight of the object pulling down, and the upthrust of the liquid pushing up. By Archimedes' principle the upthrust equals the weight of the liquid displaced. Put an object of volume V wholly under the surface and the weight pulling down is the object's density times V times g, while the upthrust pushing up is the liquid's density times V times g. The volume and g are common to both, so the comparison reduces to the two densities alone. If the object is less dense than the liquid it rises and floats; if it is denser it sinks; if the densities are equal it hangs in the liquid wherever it is placed.
- (a)mass of the object only — Mass by itself decides nothing. A ten-tonne steel ship floats and a ten-gram steel nut sinks in the same water. What matters is mass compared with the volume it occupies, which is density.
- (b)mass of the object and density of liquid only — This gets the liquid right but stops halfway on the object. Without the object's volume you cannot turn its mass into a density, and it is the density that has to be compared.
- (d)mass and shape of the object only — Shape matters, but only because of the volume it encloses — hammering a steel sheet into a hollow bowl lowers its average density without altering its mass. And the option leaves out the liquid altogether, so it cannot answer a question about floating in a liquid at all.
Archimedes' principle states that a body immersed wholly or partly in a fluid experiences an upthrust equal to the weight of the fluid it displaces. Comparing that upthrust with the body's weight gives the law of flotation — a body floats when its average density is less than that of the fluid, and when it floats it sinks far enough for the weight of fluid displaced to equal its own weight. Density is mass per unit volume, and the density of pure water is 1000 kilograms per cubic metre, or one gram per cubic centimetre.
The words 'average density' carry all the weight here, and they are what makes the iron-ship puzzle dissolve. Iron is about eight times as dense as water, so a solid lump of it sinks. A ship built of the same iron is mostly hollow, and the air enclosed in the hull is counted in the ship's volume, so the ship taken as a whole is less dense than water and floats. The same logic explains why a person floats more easily in the Dead Sea — there the liquid's density has been raised by dissolved salts rather than the body's lowered. Watch out for the option that names only one of the two densities; the phrase 'difference in the densities' in the key is the giveaway that both bodies in the comparison must appear.
- Archimedes' principle — the upthrust on an immersed body equals the weight of the fluid displaced.
- A body floats if its average density is less than that of the liquid, and sinks if it is greater.
- A floating body displaces its own weight of liquid; a fully immersed body displaces its own volume.
- The density of pure water is 1000 kg per cubic metre, and ice at about 917 is why ice floats on water.
- Sea water is denser than fresh water, so a ship floats slightly higher in the sea than in a river.
- Reasoning from mass or weight alone instead of density.
- Forgetting that the air enclosed inside a hollow body counts towards its volume.
- Naming only one of the two densities when the comparison needs both.
NDA asks it conceptually, as here, or through the iron nail and the iron ship, or numerically with a body of given mass and volume placed in a liquid of stated density.
The clouds float in the atmosphere because of their low
- (a) temperature
- (b) velocity
- (c) pressure
- (d) density
Answer(d) density
The same rule applied to a fluid rather than a liquid — clouds stay up for exactly the reason a cork stays up in water, because the floating body is less dense than what surrounds it.
An iron nail sinks in water whereas an iron ship floats. Which of the following statements is correct in this regard ? 1. Average density of ship is greater than that of the water 2. Average density of iron nail is greater than that of the water 3. Average density of the ship is less than that of the water 4. Average density of the ship is equal to that of the water Select the correct answer using the code given below :
- (a) 1 and 2
- (b) 2 and 3
- (c) 2 and 4
- (d) 1 and 4
Answer(b) 2 and 3
The same principle set as the classic iron-nail-and-iron-ship puzzle, and the clearest demonstration that it is average density, not the material or the mass, that decides.
Which one of the following metals floats in cold water?
- (a) Magnesium
- (b) Calcium
- (c) Potassium
- (d) Copper
Answer(c) Potassium
The same density test applied to metals, and a reminder that being a metal says nothing about whether a substance floats.
- practice — not a real PYQ
A block of relative density 0·8 is placed in water. It will
- (a)sink to the bottom
- (b)float with part of it above the surface
- (c)remain suspended in the middle
- (d)dissolve
Answer(b) float with part of it above the surface — being less dense than water it floats, and it settles until it displaces its own weight of water.
- practice — not a real PYQ
A ship moving from a river into the sea will
- (a)rise slightly in the water
- (b)sink slightly deeper
- (c)float at exactly the same level
- (d)capsize
Answer(a) rise slightly in the water — sea water is denser, so a smaller volume of it has to be displaced to support the same weight.