NDA (II) 2022 General Ability Test · Question 134 of 150

Correct — A, the packet will float in both water and liquid B. Work out the packet's own density first. One litre is 1000 cm³ and the mass is 800 g, so the density is 800 ÷ 1000 = 0.8 g per cm³. An object floats when its average density is less than that of the liquid. Here 0.8 is less than water's 1.0 and less than liquid B's 1.5, so the packet floats in both. In water it settles with 80 per cent of its volume submerged, and in the denser liquid B it rides higher still, with about 53 per cent submerged.

• (b)The packet will sink in both water and liquid B. — Sinking in both would require the packet to be denser than 1.5 g per cm³, that is a mass above 1500 g for a one-litre volume. Its mass is only 800 g, so it is lighter than either liquid.
• (c)The packet will sink in water but will float in liquid B. — This would need the packet's density to fall between 1.0 and 1.5. At 0.8 it is below both, so it cannot sink in water. This option is chosen when 800 g is read as heavy without dividing by the volume.
• (d)The packet will float in water and sink in liquid B. — The order is impossible. Liquid B is denser than water, so anything that floats in water must float even more easily in B; a body can sink in the lighter liquid and float in the heavier one, never the other way round.

A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces, which is Archimedes' principle. Comparing that upthrust with the body's weight reduces to a single comparison of densities. If the body's average density is less than the fluid's it floats, partly submerged; if the two are equal it stays in neutral equilibrium wherever it is placed; if the body is denser it sinks. For a floating body the fraction of its volume that is submerged equals the ratio of its density to the fluid's density.

The only real work in this item is the unit conversion, since the mass is given in grams and the volume in litres while the liquid densities are in grams per cubic centimetre. Once you write 1 litre as 1000 cm³ the packet's density is 0.8 g per cm³ and everything follows. Option (d) can be rejected on logic alone without any arithmetic, because a denser liquid always provides more upthrust, so no object can float in water and then sink in a liquid denser than water. This is also the physics behind an iron ball that sinks in water but floats on mercury, and behind the higher buoyancy swimmers feel in salt water.

• 1 litre equals 1000 cm³, so a mass of 800 g in 1 litre gives a density of 0.8 g per cm³.
• A body floats when its average density is less than the density of the liquid, and sinks when it is greater.
• The submerged fraction of a floating body equals the ratio of its density to the liquid's density — 0.8 in water and about 0.53 in liquid B.
• Archimedes' principle states that the upthrust equals the weight of the fluid displaced.

• Comparing the mass of the packet with the density of the liquid without dividing by the volume.
• Forgetting that 1 litre is 1000 cm³, not 100 or 10.
• Accepting an option in which a body floats in the lighter liquid and sinks in the heavier one, which cannot happen.

As a numerical like this, as a which-metal-floats item, or as an assertion-and-reason pair about a body floating on mercury but sinking in water.

• practice — not a real PYQ

  A block of density 0.6 g cm⁻³ floats in water. The fraction of its volume that remains submerged is

  • (a)0.4
  • (b)0.6
  • (c)1.0
  • (d)1.67

  Answer(b) 0.6 — the submerged fraction equals the ratio of the body's density to the liquid's density.

• practice — not a real PYQ

  An object of mass 500 g and volume 250 cm³ is placed in water. It will

  • (a)float with half its volume submerged
  • (b)float fully submerged
  • (c)sink
  • (d)remain suspended at mid-depth

  Answer(c) sink — its density is 500 ÷ 250 = 2 g cm⁻³, twice that of water.