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
Correct — B, 2 and 3. The word doing all the work is AVERAGE. A nail is solid iron through and through, so its average density is iron's density, about 7.8 g per cubic centimetre against water's 1.0 — statement 2 holds, and the nail sinks. A ship is a hollow steel shell enclosing a very large volume of air, so its average density is its total mass divided by its total volume including that air, and that figure comes out below 1.0 — statement 3 holds, and the ship floats. Same metal, different average density, opposite outcomes.
- (a)1 and 2 — Statement 2 is fine, but statement 1 says the ship's average density is GREATER than water's. If that were true the ship would sink, which contradicts the premise of the question.
- (c)2 and 4 — Statement 4 makes the ship's average density exactly equal to water's. That is the condition for neutral buoyancy — the body would hang fully submerged at whatever depth you left it, like a submarine at trim, not ride with its hull above the waterline.
- (d)1 and 4 — This pairs two statements that cannot both be true — the ship's density cannot be simultaneously greater than and equal to water's — and it also leaves out the nail, which is half of what the question asks about.
A body immersed in a fluid is pushed up by a buoyant force equal to the weight of the fluid it displaces, which is Archimedes' principle. Whether it floats therefore depends on a comparison of densities, not on what it is made of. If the body's average density is less than the fluid's, it rises until only part of it is submerged and settles there; if greater, it sinks; if exactly equal, it stays put wherever it is placed. For a floating body the submerged fraction equals the ratio of the two densities, which is why a loaded ship rides lower than an empty one.
Every wrong option here comes from ignoring the word 'average'. Read the ship as 'iron, therefore dense' and you pick a statement that makes it sink. The correct picture is that a ship's volume is mostly enclosed air, so the mass is spread over a far larger volume than the steel alone occupies. This is also why the same steel plate that floats as a hull sinks the instant it is crushed into a ball — nothing about the metal changed, only the volume it encloses. Statement 4 is worth dwelling on because equality of density is a real physical state, just not the state of a floating ship.
- Iron has a density of about 7.8 g per cubic centimetre against water's 1.0, so solid iron sinks.
- A ship's average density counts the enclosed air, so it comes out below the density of water.
- Archimedes' principle — the buoyant force equals the weight of fluid displaced.
- Average density equal to the fluid's means neutral buoyancy: the body stays fully submerged at any depth.
Floating is decided by average density, which is total mass divided by total volume including any enclosed air.
- Reading 'iron' and concluding the ship must be denser than water, without applying the word average.
- Treating equal density as the condition for floating on the surface; it is the condition for staying fully submerged.
- Thinking the buoyant force depends on the depth of the body rather than on the volume it displaces.
Asked as a statement-and-code set like this, or as a numerical item giving a body's mass and volume and asking whether it floats in a named liquid.
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 instead of a ship — a cloud stays up because the density of the droplet-and-air mass is below that of the surrounding air. Density, not weight, decides flotation in every medium.
The volume of a sealed packet is 1 litre and its mass is 800 g. The packet is first put inside water with density 1 g cm⁻³ and then in another liquid B with density 1.5 g cm⁻³. Then which one of the following statements holds true?
- (a) The packet will float in both water and liquid B.
- (b) The packet will sink in both water and liquid B.
- (c) The packet will sink in water but will float in liquid B.
- (d) The packet will float in water and sink in liquid B.
Answer(a) The packet will float in both water and liquid B.
The numerical version of this card, one year earlier: 800 g in 1 litre gives an average density of 0.8, below both liquids, so it floats in both. Same rule, arithmetic instead of words.
All objects experience a buoyancy when they are immersed in a fluid. Buoyancy is
- (a) a downward force
- (b) a downward pressure
- (c) an upward force
- (d) an upward pressure
Answer(c) an upward force
The definition underneath both items. Note the deliberate force-versus-pressure split in the options — buoyancy is a force, and that distinction is itself a repeat NDA test.
- practice — not a real PYQ
A solid block floats in water with three-quarters of its volume submerged. The density of the block is
- (a)0.25 g per cubic centimetre
- (b)0.75 g per cubic centimetre
- (c)1.0 g per cubic centimetre
- (d)1.33 g per cubic centimetre
Answer(b) 0.75 g per cubic centimetre — for a floating body the submerged fraction equals the ratio of the body's density to the fluid's.
- practice — not a real PYQ
A steel sheet is first shaped into an open bowl and then crushed into a solid ball. Placed in water, the bowl floats and the ball sinks because
- (a)the density of steel changes when it is crushed
- (b)the mass of the sheet increases when it is crushed
- (c)crushing reduces the volume enclosed, raising the average density above that of water
- (d)the buoyant force acts only on curved surfaces
Answer(c) crushing reduces the volume enclosed, raising the average density above that of water — the steel itself is unchanged.