When a solid body is partially or completely immersed in a fluid, the fluid exerts an upward force on the body. The magnitude of the force is equal to 1. the mass of the body 2. the weight of the displaced fluid by the body Which of the above is/are correct?
- (a)1 only
- (b)2 only
- (c)Both 1 and 2
- (d)Neither 1 nor 2
Correct — B, 2 only. By Archimedes' principle the upward (buoyant) force on a body immersed in a fluid equals the weight of the fluid displaced by the body — so statement 2 is correct. Statement 1 (the force equals the mass of the body) is wrong: the buoyant force equals a weight (of displaced fluid), not the body's mass, and it does not depend on the body's own mass.
- (a)1 only — Statement 1 is false — the buoyant force is not equal to the mass of the body.
- (c)Both 1 and 2 — Statement 1 is incorrect, so both statements cannot be right.
- (d)Neither 1 nor 2 — Statement 2 is the correct statement of Archimedes' principle, so 'neither' is wrong.
Archimedes' principle states that when a body is partly or fully immersed in a fluid, it experiences an upward buoyant force (upthrust) equal to the weight of the fluid it displaces. This force explains flotation: a body floats when the weight of displaced fluid equals its own weight. The key phrase is 'weight of the displaced fluid', not 'mass of the body'.
Statement 1 confuses 'mass of the body' with the correct 'weight of displaced fluid'. Only statement 2 matches Archimedes' principle, so the answer is '2 only'. Note that the buoyant force is a weight (measured in newtons), not a mass.
- Archimedes' principle: buoyant force = weight of the fluid displaced.
- The upthrust acts vertically upward through the centre of buoyancy.
- A body floats when the weight of displaced fluid equals its own weight.
- The buoyant force depends on the fluid's density and the volume displaced, not on the body's mass.
- The buoyant force equals the WEIGHT of the displaced fluid, not the mass of the body.
- It is a force (in newtons); do not equate it with a mass (in kilograms).
Tests Archimedes' principle — that the upthrust equals the weight of displaced fluid — through statements or flotation problems.
Assertion (A): An iron ball floats on mercury but gets immersed in water. Reason (R): The specific gravity of iron is more than that of mercury.
- (a) Both A and R are individually true and R is the correct explanation of A
- (b) Both A and R are individually true but R is not a correct explanation of A
- (c) A is true but R is false
- (d) A is false but R is true
Answer(c) A is true but R is false — iron floats on mercury (specific gravity about 13.6) but sinks in water; iron's specific gravity is less than mercury's, so R is false.
UPSC prelims tested buoyancy and flotation through relative density (iron on mercury versus in water) — the same Archimedes/buoyancy principle.
A pumpkin weighs 7.5 N. On submerging it completely in water, ¾ L of water gets displaced. The acceleration due to gravity at the place where the pumpkin was weighed is 10 m/s². Which one of the following is the correct value of the density of the pumpkin?
- (a) 10 kg/m³
- (b) 100 kg/m³
- (c) 1000 kg/m³
- (d) 10000 kg/m³
Answer(c) 1000 kg/m³
A previous NDA GAT item computing the buoyant force on a pumpkin from the water it displaces — a direct application of Archimedes' principle.
- practice — not a real PYQ
A body floats in a liquid when the weight of the liquid it displaces is
- (a)less than its weight
- (b)equal to its weight
- (c)greater than its weight
- (d)zero
Answer(b) equal to its weight — this is the law of flotation.
- practice — not a real PYQ
The buoyant force on a submerged body depends on
- (a)the mass of the body
- (b)the volume of fluid displaced and the fluid's density
- (c)the colour of the body
- (d)the depth alone
Answer(b) the volume of fluid displaced and the density of the fluid.