The question asks to identify which option is NOT based on Archimedes' Principle. Archimedes' Principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

Understanding Archimedes' Principle Applications

Let's analyze each option:

• Designing of ships and submarines: These rely heavily on buoyancy. Ships float because their overall density is less than that of water, displacing a weight of water equal to their own weight. Submarines control buoyancy to dive or surface. This is a direct application of Archimedes' Principle.
• Hydrometers: These instruments measure the specific gravity of liquids. They float in the liquid, and the depth they sink to depends on the liquid's density, following Archimedes' Principle.
• Lactometers: These are specific types of hydrometers used for milk. Their operation is based on measuring milk density using buoyancy, hence applying Archimedes' Principle.
• Designing of aeroplane wings: Aeroplane wings generate lift primarily based on aerodynamic principles, specifically Bernoulli's principle. The shape of the wing causes air to flow faster over the top surface than the bottom, creating lower pressure above and higher pressure below, resulting in an upward lift force. This is distinct from the buoyancy principle.

Identifying the Correct Option

Based on the analysis, the design of aeroplane wings operates on aerodynamic principles (lift) rather than Archimedes' Principle (buoyancy).

Therefore, the correct option is Designing of aeroplane wings.