Understanding Specific Gravity and Measurement Instruments

The question asks about the instrument used to measure the specific gravity (or relative density) of liquids. Specific gravity is a dimensionless quantity defined as the ratio of the density of a substance to the density of a reference substance (usually water for liquids). It tells us how much denser or lighter a liquid is compared to water.

Let's look at the options provided:

• Multi-meter: A multi-meter is an electronic measuring instrument that combines several measurement functions in one unit. It is used to measure electrical quantities such as voltage (volts), current (amperes), and resistance (ohms). It is not used for measuring the specific gravity of liquids.
• Hydrometer: A hydrometer is an instrument used for measuring the specific gravity (or relative density) of liquids. It is typically a sealed glass tube with a weighted bulb at one end and a narrow stem with a scale calibrated for specific gravity. When placed in a liquid, it floats at a depth that depends on the liquid's specific gravity. Denser liquids support the hydrometer higher, while less dense liquids allow it to sink lower.
• Galvanometer: A galvanometer is an electromechanical instrument used for detecting and indicating an electric current. It is a sensitive instrument primarily used in laboratories for detecting very small currents. It is not used for measuring the specific gravity of liquids.
• Thermometer: A thermometer is an instrument used for measuring temperature. It works based on the principle of thermal expansion of a substance (like mercury or alcohol) or electrical resistance changes with temperature. It is not used for measuring the specific gravity of liquids.

Based on the functions of these instruments, the instrument specifically designed to measure the specific gravity or relative density of liquids is the hydrometer.

How a Hydrometer Works

A hydrometer works on the principle of buoyancy, also known as Archimedes' principle. This principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. The hydrometer floats in the liquid, sinking to a depth where the buoyant force equals the weight of the hydrometer.

The buoyant force is given by the weight of the displaced liquid:

\(\text{Buoyant Force} = \rho_{\text{liquid}} \times V_{\text{submerged}} \times g\)

Where:

• \(\rho_{\text{liquid}}\) is the density of the liquid.
• \(V_{\text{submerged}}\) is the volume of the hydrometer submerged in the liquid.
• \(g\) is the acceleration due to gravity.

The weight of the hydrometer is constant.

\(\text{Weight}_{\text{hydrometer}} = m_{\text{hydrometer}} \times g\)

For the hydrometer to float, the buoyant force equals its weight:

\(\rho_{\text{liquid}} \times V_{\text{submerged}} \times g = m_{\text{hydrometer}} \times g\)

This simplifies to:

\(\rho_{\text{liquid}} \times V_{\text{submerged}} = m_{\text{hydrometer}}\)

Since \(m_{\text{hydrometer}}\) is constant, \(V_{\text{submerged}}\) is inversely proportional to \(\rho_{\text{liquid}}\). This means that in a denser liquid (\(\rho_{\text{liquid}}\) is higher), a smaller volume needs to be submerged (\(V_{\text{submerged}}\) is smaller) for the buoyant force to equal the hydrometer's weight. Conversely, in a less dense liquid, a larger volume must be submerged.

The scale on the stem of the hydrometer is calibrated to directly read the specific gravity based on the level at which it floats. Specific gravity (SG) is defined as:

\(\text{SG} = \frac{\rho_{\text{liquid}}}{\rho_{\text{water}}}\)

Thus, by measuring the density relative to water, the hydrometer gives the specific gravity.

Conclusion

The hydrometer is the correct instrument among the given options that is specifically used to measure the specific gravity (or relative density) of liquids.

Revision Table: Measurement Instruments

Additional Information on Specific Gravity and Density

Density (\(\rho\)) is a fundamental property of matter defined as mass per unit volume:

\(\rho = \frac{m}{V}\)

Where \(m\) is mass and \(V\) is volume. The standard SI unit for density is kilograms per cubic meter (\(\text{kg/m}^3\)), although grams per cubic centimeter (\(\text{g/cm}^3\)) is also commonly used, especially for liquids and solids. The density of pure water at \(4^\circ\text{C}\) is approximately \(1000 \text{ kg/m}^3\) or \(1 \text{ g/cm}^3\).

Specific gravity (SG) is a dimensionless ratio, meaning it has no units. It is often defined with respect to water at a specific temperature (often \(4^\circ\text{C}\) where its density is maximum and equal to \(1000 \text{ kg/m}^3\) or \(1 \text{ g/cm}^3\)). Since it's a ratio of densities, if the density of the reference substance (water) is \(1 \text{ g/cm}^3\), the numerical value of specific gravity will be the same as the numerical value of the density in \(\text{g/cm}^3\). However, specific gravity is a ratio and thus unitless.

Specific gravity is useful because it is often easier to measure than density directly and provides a convenient way to compare the densities of different substances. Different types of hydrometers exist for specific applications, such as lactometers for milk, saccharometers for sugar solutions, and alcoholometers for alcoholic beverages.