Chapter 5 · Section 4Textbook pages 102–103

Principle of Floatation പ്ലവനതത്വം

A stone sinks, a piece of wood floats. A sheet of aluminium foil floats as a boat but sinks as a crumpled ball. A steel ship floats while an iron nail sinks. On this page one simple rule – the principle of floatation – explains all of them, and finally answers the question from the opening page.

📖 What you need (pages 5–7 of this guide)

Archimedes' principle: buoyant force = weight of the fluid displaced.
Buoyant force = W₁ − W₂ = ρ_fluid × V_{under the fluid} × g.
1 kgwt = 9.8 N; 1 cm³ of water has a mass of 1 g.

1. Wood and wax in the overflow jar (Table 5.6)

Repeat the overflow-jar experiment of page 7 with a wooden block (മരക്കട്ട) and a wax block (മെഴുകുകട്ട) instead of the stone and the glass slab, and complete Table 5.6.

🧪 Virtual lab: objects that float – Table 5.6

object lower the balance

Table 5.6 – sample readings (your real readings will differ slightly)
Object വസ്തു	Weight in air W₁ (N)	Weight in water W₂ (N)	Buoyant force W₁ − W₂ (N)	Weight of displaced water (N)

Sample blocks (approx.): wood 50 g, density ≈ 650 kg/m³ (teak-like); wax 45 g, density ≈ 900 kg/m³. Once the block floats, the string goes slack and the balance reads 0.

Q. വസ്തുവിന്റെ വായുവിലെ ഭാരവും ആദേശം ചെയ്ത ജലത്തിന്റെ ഭാരവും തമ്മിലുള്ള ബന്ധം എന്താണ്? – What is the relation between the weight of the object in air and the weight of the water it displaced?

They are equal: wood 0.49 N in air, displaced water 0.49 N; wax 0.441 N and 0.441 N. Why: a floating object sinks just until the water it pushes aside weighs as much as itself – then the buoyant force balances its weight, and the spring balance has nothing left to hold (W₂ = 0).

⭐ Key idea (textbook page 102) – Principle of floatation (പ്ലവനതത്വം)

ഒരു വസ്തു ദ്രവത്തിൽ പൊങ്ങിക്കിടക്കുമ്പോൾ വസ്തുവിന്റെ ഭാരവും വസ്തു ആദേശം ചെയ്യുന്ന ദ്രവത്തിന്റെ ഭാരവും തുല്യമായിരിക്കും. ഇതാണ് പ്ലവനതത്വം.

When an object floats in a fluid, the weight of the object is equal to the weight of the fluid it displaces. This is the principle of floatation.

⚖️ Sink or float? (textbook page 102)

ഒരു ദ്രവത്തിൽ മുങ്ങിക്കിടക്കുന്ന വസ്തുവിൽ അനുഭവപ്പെടുന്ന പ്ലവക്ഷമബലം വസ്തുവിന്റെ ഭാരത്തെക്കാൾ കുറവായിരിക്കും. എന്നാൽ ദ്രവത്തിൽ പൊങ്ങിക്കിടക്കുന്ന വസ്തുവിൽ അനുഭവപ്പെടുന്ന പ്ലവക്ഷമബലം വസ്തുവിന്റെ ഭാരത്തിന് തുല്യമായിരിക്കും.

Sinking object (മുങ്ങുക): buoyant force < weight (even when fully immersed).
Floating object (പൊങ്ങിക്കിടക്കുക): buoyant force = weight (it is only partly under, just enough).

2. Float-or-sink lab – how much stays under?

For a floating object, buoyant force = weight: ρ_liquid × V_under × g = ρ_object × V × g. Cancel g:

fraction under the liquid = V_under ÷ V = ρ_object ÷ ρ_liquid

If ρ_object is bigger than ρ_liquid, even the whole volume cannot displace enough liquid – the object sinks.

🧪 Drop a 1000 cm³ block into a liquid

density of the block kg/m³ liquid

Values marked ≈ are approximate. Try ice in water (about 92 % under – icebergs!), wax in kerosene, and iron in mercury (it floats!).

3. Activity – the aluminium foil boat (Fig 5.7)

Take a piece of aluminium foil about 15 cm long and 10 cm wide, shape it like a boat and put it on the water surface. What do you observe? Put a 100 g weight in the boat. Why doesn't the boat sink? Then crumple the same foil into a tight ball and put it on the water.

🎬 Foil boat and foil ball, step by step

Sample values (approx.): kitchen foil 0.016 mm thick, so the 15 cm × 10 cm sheet has a volume of 0.24 cm³ and a mass of about 0.65 g. The boat is folded to a 10 cm × 5 cm base with 2.5 cm high sides.

Textbook questions (page 102)

What do you observe when the foil boat is put on the water?
ബോട്ട് മുങ്ങാത്തത് എന്തുകൊണ്ടായിരിക്കും? Why doesn't the boat sink even with the 100 g weight?
What happens to the same foil crumpled into a ball? Why?

1. It floats, almost entirely above the water.
2. Shaped like a boat, the foil displaces a weight of water equal to its own weight. With the weight inside, it sinks a little deeper (about 2 cm here) and displaces water equal to the total weight of the boat and the weight (about 100.65 g of water) – so it still floats.
3. It sinks. Crumpled, it can push aside only about its own metal volume (≈ 0.24 cm³ of water, weighing ≈ 0.24 gwt) – much less than its weight (≈ 0.65 gwt). The buoyant force is less than the weight. Why: the volume of water displaced by the boat-shaped foil is much greater than that displaced by the crumpled foil.

🚢 The opening question answered – nail vs ship

ഇരുമ്പാണി ജലത്തിൽ താഴ്ന്നുപോകുമെങ്കിലും ഇരുമ്പ് കൊണ്ടുണ്ടാക്കിയ കപ്പൽ സമുദ്രജലത്തിൽ പൊങ്ങിക്കിടക്കുന്നതിന് കാരണം വിശദീകരിക്കാമല്ലോ. – Explain why an iron nail sinks but a ship made of iron floats on the sea.

A 5 g iron nail has a volume of only about 0.64 cm³, so even fully under water it displaces just 0.64 g of water: buoyant force (0.64 gwt) < weight (5 gwt) → it sinks. A ship is the foil boat on a giant scale: its steel is shaped into a hollow hull full of air, so it can push aside an enormous volume of water. It settles until the weight of the sea water displaced equals the ship's whole weight – then buoyant force = weight and it floats (principle of floatation).

4. Loading a ship – fresh water and sea water

🧪 Load the cargo ship (simplified box-shaped hull)

cargo loaded tonnes

Model (approx.): hull 200 m long, 30 m wide, 15 m high, empty mass 20 000 tonnes. Fresh water 1000 kg/m³, sea water 1025 kg/m³. The depth of the hull under water is called the draught.

Think. Why does a ship rise a little when it sails from the river into the sea? And why does it rise when its cargo is unloaded at Kochi port?

In both cases the ship must displace a weight of water equal to its own weight. Sea water is denser, so a smaller volume of it has that weight → the ship rises. After unloading, the ship's weight is smaller, so it needs to displace less water → it rises.

🌴 Kerala connection

INS Vikrant, built at Cochin Shipyard, has a mass of about 43 000 tonnes. Floating, it displaces about 43 000 tonnes of sea water – roughly 42 000 m³ (43 000 000 kg ÷ 1025 kg/m³), the volume of about 17 Olympic swimming pools.
The house boats (കെട്ടുവള്ളം) of Vembanad lake and Alappuzha float deeper when more tourists come aboard – the same principle of floatation. Overloading pushes the hull dangerously low, which is why boats carry a passenger limit.
Every ferry and Water Metro boat carries life jackets (ലൈഫ് ജാക്കറ്റ്): a light, large-volume jacket helps you and it together displace enough water to float with your head up.

⚠ Never lean over a well or play near deep water; do water experiments in a bucket or tub, with an adult nearby. On any boat, wear the life jacket and never stand on the edge.

5. Textbook questions (page 103)

Q1. തടാകത്തിൽ സ്ഥിതിചെയ്യുന്ന ഒരു ബോട്ട് 6000 kg ജലം ആദേശം ചെയ്യുന്നു. ബോട്ടിൽ അനുഭവപ്പെടുന്ന പ്ലവക്ഷമബലം എത്രയായിരിക്കും? – A boat on a lake displaces 6000 kg of water. What is the buoyant force on the boat?

Archimedes: buoyant force = weight of the water displaced. Weight = mass × g (or simply “6000 kg of water weighs 6000 kgwt”).

🎬 Solution in exam layout

Answer: buoyant force = weight of 6000 kg of water = 6000 kgwt = 6000 × 9.8 = 58 800 N. (The boat floats, so its own weight is also 6000 kgwt.) More solved questions: page 10 ▶

Q2. വായുവിൽ 0.45 kgwt ഭാരമുള്ള ഒരു വസ്തു മുഴുവനായും ജലത്തിൽ മുങ്ങിയിരിക്കുമ്പോഴുള്ള ഭാരം 0.31 kgwt ആണ്. എങ്കിൽ താഴെ കൊടുത്തവ കണ്ടെത്തുക. – An object weighs 0.45 kgwt in air and 0.31 kgwt when fully immersed in water. Find (a) ഭാരനഷ്ടം the loss of weight, (b) പ്ലവക്ഷമബലം the buoyant force, (c) ആദേശം ചെയ്ത ജലത്തിന്റെ ഭാരം the weight of the displaced water.

Loss = W₁ − W₂. Then use page 5 (buoyant force = loss of weight) and page 7 (buoyant force = weight of displaced water).

🎬 Solution in exam layout

Answer: (a) loss of weight = 0.45 − 0.31 = 0.14 kgwt; (b) buoyant force = 0.14 kgwt; (c) weight of displaced water = 0.14 kgwt (= 0.14 × 9.8 = 1.372 N). More: page 10 ▶

🌐 Explore online needs internet · opens in a new tab

📄 Sinking and Floating The Physics Classroom
Compare weight with buoyant force to predict sink, float or hang; includes the ice-cube example.
📄 Ships and boats: How do they float? Explain that Stuff
Why a giant steel ship floats while a steel nail sinks.
📄 How do submarines work? Explain that Stuff
Ballast tanks let a submarine fill with water to dive and blow it out to rise.
📄 What is the Plimsoll line? Lloyd's Register Foundation Heritage Centre
History and meaning of the load-line marks painted on every ship's side.
🖼️ Load line (watercraft) Wikipedia
Diagram of the Plimsoll mark: TF, F, T, S, W lines for fresh, tropical and sea water.
📄 CSL delivers Indigenous Aircraft Carrier, Project-71 (Vikrant) to the Indian Navy Cochin Shipyard Ltd
Official Cochin Shipyard news on handing over INS Vikrant, built in Kochi.
📄 PM commissions India's first indigenous aircraft carrier INS Vikrant in Kochi Press Information Bureau, Govt of India
Government release on INS Vikrant, a ship of about 43,000 tonnes that floats by displacing sea water.
📄 Hot Air Balloon NASA Glenn Research Center
Buoyancy in air: hot, less-dense air makes a balloon rise.

6. Check yourself

🧭 Summary

Principle of floatation: a floating object displaces fluid whose weight equals its own weight (wood 0.49 N = 0.49 N).
Sinking: buoyant force < weight. Floating: buoyant force = weight; the spring balance reads 0.
Fraction under = ρ_object ÷ ρ_liquid; if ρ_object > ρ_liquid, it sinks.
Shape matters: a hollow boat or ship displaces much more water than the same metal crumpled up.
Boat displacing 6000 kg of water → buoyant force 6000 kgwt = 58 800 N; 0.45 → 0.31 kgwt → 0.14 kgwt.

Next: Relative density, hydrometer and lactometer ▶