Long type questions,ch5 Floatation

Buoyancy and Floating Bodies – Q&A

1. A body is held immersed in a liquid.
(i) Name the two forces acting on body and draw a diagram to show these forces.
(ii) State how do the magnitudes of two forces mentioned in part (i) determine whether the body will float or sink in liquid when it is released.
(iii) What is the net force on body if it (a) sinks, (b) floats?

(i) The two forces are:
- Weight (W) acting vertically downward from the center of gravity.
- Upthrust (U) or buoyant force acting vertically upward from the center of buoyancy.

(ii) If Upthrust > Weight → body floats
If Weight > Upthrust → body sinks

(iii)
(a) If it sinks: Net force = Weight - Upthrust (downward)
(b) If it floats: Net force = 0 (Weight = Upthrust)

2. Draw a diagram to show the forces acting on a body floating in water with its some part submerged. Name the forces and show their points of application. How is the weight of water displaced by the floating body related to the weight of the body itself?

- Forces: Weight (W) acts downward from center of gravity. Upthrust (U) acts upward from center of buoyancy.
- In equilibrium (floating), Weight = Upthrust.
- According to Archimedes' Principle: Weight of water displaced = Weight of the body.
(Diagram: Show a floating object partially submerged with arrows for W and U.)

3. A body of volume V and density ρ_s floats with volume v inside a liquid of density ρ_L. Show that V / ρ_s = v / ρ_L.

Weight of body = ρ_s × V × g
Upthrust = Weight of displaced liquid = ρ_L × v × g
For floating body: Weight = Upthrust
⇒ ρ_s × V × g = ρ_L × v × g
Cancelling g: ρ_s × V = ρ_L × v
⇒ V / ρ_L = v / ρ_s or V / ρ_s = v / ρ_L

4. Explain the following:

1. Icebergs floating in sea are dangerous for ships.
2. An egg sinks in fresh water, but floats in a strong salt solution.
3. A toy balloon filled with hydrogen rises to the ceiling, but if filled with carbon dioxide sinks to the floor.
4. As a ship in harbour is being unloaded, it slowly rises higher in water.
5. A balloon filled with hydrogen rises to a certain height and then stops rising further.
6. A ship submerges more as it sails from sea water to river water.

(a) Only a small part of iceberg is visible above water. Most of it is submerged, so ships may hit the hidden part.

(b) Fresh water has less ρ than salt water. In salt solution, greater ρ gives more upthrust, making egg float.

(c) Hydrogen is lighter than air, so balloon rises. CO₂ is heavier than air, so balloon sinks.

(d) Unloading reduces ship's weight, reducing its displacement. So it rises higher in water.

(e) Balloon stops rising when ρ of air becomes equal to ρ of hydrogen inside the balloon.

(f) Sea water is denser (ρ high), so more upthrust. In river (less dense), upthrust decreases, ship sinks more.