Understanding Archimedes Principle in Instruments 

The question asks to identify which of the given instruments operates based on Archimedes principle. Let's first understand what Archimedes principle is.

What is Archimedes Principle?

Archimedes principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether wholly or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Mathematically, the buoyant force (\(F_B\)) can be expressed as:

\[F_B = \rho_f \cdot V_{disp} \cdot g\]

Where:

• \(\rho_f\) is the density of the fluid
• \(V_{disp}\) is the volume of the displaced fluid
• \(g\) is the acceleration due to gravity

This principle explains why objects float or sink in fluids. An object floats if the buoyant force is equal to its weight, which happens when the object's density is less than or equal to the fluid's density. It sinks if the buoyant force is less than its weight, which happens when the object's density is greater than the fluid's density.

Analyzing the Instruments

Let's look at the principles behind each of the given instruments:

Galvanometer: A galvanometer is an instrument used for detecting and indicating an electric current. Its operation is based on the principle of electromagnetism, specifically the torque experienced by a current-carrying coil placed in a magnetic field.

Hydrometer: A hydrometer is an instrument used for measuring the specific gravity (or relative density) of liquids. It typically consists of a sealed glass tube with a weighted bulb at one end, causing it to float upright in the liquid. The depth to which the hydrometer sinks depends on the density of the liquid. In a denser liquid, the hydrometer sinks less, and in a less dense liquid, it sinks more. This behavior is a direct application of Archimedes principle, as the buoyant force supporting the hydrometer is equal to the weight of the liquid it displaces, and this displaced volume changes with the liquid's density to maintain equilibrium with the constant weight of the hydrometer.

Ohmmeter: An ohmmeter is an instrument used for measuring electrical resistance. Its operation is based on Ohm's Law, which relates voltage, current, and resistance in an electrical circuit.

Voltmeter: A voltmeter is an instrument used for measuring the electrical potential difference between two points in a circuit. It works based on electromagnetic principles, similar to a galvanometer, calibrated to measure voltage.

Identifying the Instrument Based on Archimedes Principle

Based on the analysis above, the hydrometer is the instrument whose function relies directly on Archimedes principle. It measures liquid density by floating at a depth determined by the buoyant force balancing its weight, where the buoyant force is dictated by the density of the fluid and the volume displaced.

Let's summarize the instruments and their principles:

Therefore, the instrument based on Archimedes principle is the Hydrometer.