Question

Relative density of silver is 10.8. The density of water is \(10^3 \text{ kg m}^{-3}\). Density of silver will be :

• A. \(10.8 \times 10^3 \text{ kg/m}^3\)
• B. \(10.8 \times 10^3 \text{ gm/cm}^3\)
• C. \(10.8 \times 10^6 \text{ kg/m}^3\)
• D. \(10.8 \times 10^4 \text{ kg/m}^3\)

Hint:

Relative Density = \(\frac{\text{Density of Substance}}{\text{Density of Water}}\). So, Density of Substance = Relative Density \(\times\) Density of Water. 1. Relative Density of Silver = 10.8. 2. Density of Water = \(10^3 \text{ kg/m}^3\). 3. Density of Silver = \(10.8 \times 10^3 \text{ kg/m}^3\). Make sure the units are consistent. If density of water was given as \(1 \text{ g/cm}^3\), then density of silver would be \(10.8 \text{ g/cm}^3\).

Answer 1

The Correct Option is A

Concept: Relative density (also known as specific gravity) of a substance is the ratio of its density to the density of a reference substance, which is usually water at \(4^\circ\text{C}\). Relative Density (\(RD\)) = \(\frac{\text{Density of substance}}{\text{Density of water}}\). Therefore, Density of substance = Relative Density \(\times\) Density of water. Step 1: Identify the given values
Relative density of silver (\(RD_{silver}\)) = 10.8 (This is a dimensionless quantity).
Density of water (\(\rho_{water}\)) = \(10^3 \text{ kg m}^{-3}\) (which is \(1000 \text{ kg/m}^3\)). We need to find the density of silver (\(\rho_{silver}\)). Step 2: Use the formula relating density, relative density, and density of water \[ \rho_{silver} = RD_{silver} \times \rho_{water} \] Step 3: Substitute the given values and calculate \[ \rho_{silver} = 10.8 \times 10^3 \text{ kg m}^{-3} \] The density of silver is \(10.8 \times 10^3 \text{ kg/m}^3\). Step 4: Compare with the options
(1) \(10.8 \times 10^3 \text{ kg/m}^3\): This matches our calculated value and has the correct units.
(2) \(10.8 \times 10^3 \text{ gm/cm}^3\): The numerical part might seem similar, but the unit is \(gm/cm^3\). The density of water in \(gm/cm^3\) is \(1 \text{ gm/cm}^3\). If we used that, density of silver would be \(10.8 \times 1 = 10.8 \text{ gm/cm}^3\). The value \(10.8 \times 10^3 \text{ gm/cm}^3\) is incorrect.
(3) \(10.8 \times 10^6 \text{ kg/m}^3\): Incorrect magnitude.
(4) \(10.8 \times 10^4 \text{ kg/m}^3\): Incorrect magnitude. The correct density of silver is \(10.8 \times 10^3 \text{ kg/m}^3\).