Correct Option
The correct option is (a) 1 and 2 only.
Explanation
Archimedes’ Principle states that when a body is immersed fully or partially in a fluid, it experiences an upward force (buoyant force) that is equal to the weight of the fluid displaced by it. This principle governs the flotation of objects and is fundamental to instruments designed to measure the density or specific gravity of liquids.
Statement-wise Analysis
- 1. Lactometers: Correct. Lactometers are instruments used to determine the purity of milk. They work on the principle of flotation (Archimedes’ Principle). The depth to which the lactometer sinks depends on the density of the milk; denser (purer) milk exerts a greater buoyant force, causing the instrument to float higher.
- 2. Hydrometers: Correct. Hydrometers are used to measure the specific gravity (relative density) of liquids. They operate directly on Archimedes’ Principle. A hydrometer floats at different levels in liquids of different densities based on the weight of the liquid displaced.
- 3. Odometers: Incorrect. An odometer is an instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car. It functions based on mechanical or electronic counting of wheel rotations, unrelated to fluid mechanics or buoyancy.
- 4. Barometers: Incorrect. A barometer is used to measure atmospheric pressure. While it involves fluid mechanics (hydrostatic pressure), its working principle relies on balancing the weight of a mercury column against atmospheric pressure (Torricellian vacuum), rather than the buoyancy principle used for floating bodies like lactometers or hydrometers.
Key Takeaway
Archimedes’ Principle is the specific scientific basis for instruments that rely on flotation to measure fluid density, such as lactometers (for milk) and hydrometers (for liquid density).