A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f₁V (f₁ < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f₂V. Then :
- (a)f₂ = f₁
- (b)f₂ = (1 − a/g) f₁
- (c)f₂ > f₁
- (d)f₂ = (a/g) f₁
Correct — A, f₂ = f₁. A floating body sinks until the weight of the water it pushes aside equals its own weight. On Earth this balance is ρ_water × (f₁V) × g = ρ_sphere × V × g, so the submerged fraction is f₁ = ρ_sphere / ρ_water — it depends only on the ratio of densities. On the spaceship the acceleration a plays the role of gravity, and it multiplies both the weight and the buoyant force equally: ρ_water × (f₂V) × a = ρ_sphere × V × a. The a cancels, leaving f₂ = ρ_sphere / ρ_water = f₁. Changing the strength of the effective gravity does not change how much of a floating body is submerged.
- (b)f₂ = (1 − a/g) f₁ — This wrongly assumes the submerged fraction scales with the acceleration. Both the weight and the buoyant force scale with the same a, so it cancels and the fraction is unchanged.
- (c)f₂ > f₁ — A weaker effective gravity does not push the body deeper. Because buoyancy and weight fall in the same proportion, the equilibrium depth — and the submerged fraction — stays exactly the same.
- (d)f₂ = (a/g) f₁ — Again this ties the submerged fraction to the acceleration. The fraction depends only on the density ratio ρ_sphere / ρ_water, which is the same on Earth and on the ship, so f₂ = f₁.
For a floating body, the submerged fraction equals the ratio of the body's density to the fluid's density (Archimedes' principle). This ratio contains no g: the acceleration due to gravity multiplies both the body's weight and the buoyant force, so it cancels out of the floating condition. Replacing gravity with any other effective acceleration leaves the submerged fraction unchanged.
The tempting answers all make the fraction depend on the acceleration a. The clean way to see the trap is to write the floating balance with a in place of g on both sides — it cancels immediately. Whether the effective gravity is Earth's g or a spaceship's a, a cork floats with the same portion above water.
- A body floats when the weight of the fluid it displaces equals its own weight.
- Submerged fraction = ρ_body / ρ_fluid — independent of the value of gravity.
- In the accelerating ship, the acceleration a acts as the effective gravity and cancels from both sides.
- Hence f₂ = f₁; the fraction submerged is the same on Earth and on the ship.
- Assuming the submerged fraction changes when gravity is weaker or stronger.
- Forgetting that both weight and buoyancy scale with the same acceleration and cancel.
A floating body is moved to a different gravity (Moon, lift, or accelerating spaceship) and you are asked how the submerged fraction changes — recognise that it depends only on the density ratio, so it does not change.
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
Same buoyancy principle — a body floats or sinks by comparing its density with the fluid's. Iron (specific gravity ≈ 7.8) floats on denser mercury (≈ 13.6) but sinks in water (1), exactly the density-ratio logic that fixes the submerged fraction here.
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
Answer(b) 2 only
States Archimedes' principle directly — the buoyant force equals the weight of displaced fluid, the balance that sets the submerged fraction in this question.
- practice — not a real PYQ
A block floats with 60% of its volume submerged in water on Earth. Taken to the Moon (where gravity is about g/6), the fraction of its volume submerged in water becomes about:
- (a)10%
- (b)60%
- (c)100%
- (d)36%
Answer(b) 60% — the submerged fraction depends only on the density ratio, not on the strength of gravity.
- practice — not a real PYQ
A solid body floats in water only when its density is:
- (a)greater than water's
- (b)equal to water's
- (c)less than water's
- (d)zero
Answer(c) less than water's — a body floats only if it is less dense than the fluid, so it can displace enough fluid to balance its weight.