NDA (II) 2017 General Ability Test · Question 109 of 150

Correct — B, Decrease. Any body immersed in a fluid feels an upward force called buoyancy or upthrust, and by Archimedes' principle that force equals the weight of the fluid the body displaces. The spring balance does not read the true weight; it reads the difference between the downward pull of gravity and the upward push of the water. Since the upthrust is always upward and never zero for a submerged body, the reading is always smaller than the weight in air. The loss in weight is exactly the weight of water displaced, which is what lets the same experiment measure density.

• (a)Increase — Nothing in water pushes a submerged body downward more than gravity already does. Water pressure acts on every face, but it is greater on the lower face than the upper one, so the net effect is upward.
• (c)Remain exactly the same — The true weight of the body is unchanged, but the question asks what the weighing gives, and the balance now records an apparent weight reduced by the upthrust. Only in a vacuum would the two coincide.
• (d)Increase or decrease cannot be predicted — It is entirely predictable. The upthrust is upward for every fluid and every submerged body, so the apparent weight always falls; only the size of the fall depends on the volume displaced.

Pressure in a fluid grows with depth, so the water pushing up on the bottom face of a submerged body is stronger than the water pushing down on its top face. The unbalanced part of those forces is the upthrust. Archimedes' principle puts a number on it: the upthrust equals the weight of the fluid displaced, which for a fully submerged body is the density of the fluid multiplied by the volume of the body and by the acceleration due to gravity. Apparent weight is therefore the real weight minus that quantity.

Notice what the size of the loss depends on. It is set by the volume of the body and the density of the liquid, not by what the body is made of. Immerse the same object in a denser liquid and it loses more weight; that is why an iron ball sinks in water but floats on mercury. If the upthrust happens to equal the weight, the body floats with part of it above the surface, and a floating body displaces exactly its own weight of fluid. This is the physics behind a ship, a submarine's ballast tanks, a hydrometer and the ancient crown problem.

• Upthrust equals the weight of the fluid displaced — Archimedes' principle.
• Apparent weight in a fluid equals true weight minus upthrust, so a submerged body always weighs less on the balance.
• The upthrust on a fully submerged body depends on its volume and on the density of the fluid, not on the material of the body.
• A floating body displaces a weight of fluid equal to its own weight, and the submerged fraction equals the ratio of the two densities.
• Iron, of density about 7.8 grams per cubic centimetre, sinks in water but floats on mercury, whose density is about 13.6.

• Believing the body's real weight has changed; only the balance reading changes.
• Thinking a heavier or denser body loses less weight — the loss depends on volume displaced and fluid density.
• Forgetting that air also exerts a small upthrust, so even a weighing in air is slightly short of the true weight.

NDA asks what a balance reads in a liquid, or gives a weight and a displaced volume and asks for the density.

• practice — not a real PYQ

  A body weighs 50 N in air and 40 N when fully immersed in water. The upthrust on the body is

  • (a)10 N
  • (b)40 N
  • (c)50 N
  • (d)90 N

  Answer(a) 10 N — the loss in weight is exactly the upthrust, and equals the weight of the water displaced.

• practice — not a real PYQ

  The same solid block is fully immersed first in water and then in a denser liquid. Its apparent weight will be

  • (a)greater in the denser liquid
  • (b)smaller in the denser liquid
  • (c)the same in both
  • (d)zero in both

  Answer(b) smaller in the denser liquid — a denser fluid gives a larger upthrust for the same displaced volume.