The basic principle of operation of a beam balance is------------------

Step 1: Analyze the question We need the basic principle behind how a beam balance works. A beam balance has a horizontal beam pivoted at its centre (the fulcrum), with a pan on each side. One pan holds the object and the other holds known masses.

Step 2: Explain the concept The principle of moments says that when a body is in rotational equilibrium, the sum of the clockwise moments about the pivot equals the sum of the anticlockwise moments about the same pivot.

Moment = force × perpendicular distance from the pivot

Step 3: Apply it to the beam balance

• The two pans hang at equal distances (d) from the pivot.
• The object has weight W₁ = m₁g, and the standard masses have weight W₂ = m₂g.
• The beam balances (stays horizontal) when:

Clockwise moment = Anticlockwise moment m₁g × d = m₂g × d so m₁ = m₂

When the beam is balanced, the unknown mass equals the known mass. This is the principle of moments in action.

Step 4: Check the other options

• A. Hooke's law: applies to springs (extension is proportional to load), as in a spring balance, not a beam balance.
• B. Archimedes' principle: deals with upthrust on bodies in fluids (hydrometers, floating bodies).
• C. Law of flotation: a floating body displaces its own weight of fluid (ships, hydrometers).
• D. Principle of moments: correct, as shown above.

Step 5: Answer The correct option is D. principle of moments.

Exam tip: Match the instrument to its law:

• Beam balance, see-saw, lever: moments
• Spring balance: Hooke's law
• Hydrometer, ships: flotation/Archimedes