Question

(a) Out of a set of a number of spring balances of different least count used for measurement in the laboratory which one will you select for an accurate measurement?
(b) Relative density of gold is 19.3. What is its density?

Answer 1

Hint: Least count of any instrument is the smallest value that can be measured by it. Smaller the least count more is the accuracy.
Relative density of any solid or liquid is usually defined as the ratio of density of that material to the density of water.

Complete step by step answer:
(a) Least count of any measuring instrument is the smallest value that can be measured by it. If I will have to select a spring balance out of a set of number of spring balances of different least count used, I will choose the spring balance with minimum least count because spring balance with smaller least count will give more accurate measurement.
(b) Relative density of a substance is the ratio of density of that substance to the density of a standard reference material. Relative density is also known as specific gravity. Mathematically,
$RD=\dfrac{{{\rho }_{substance}}}{{{\rho }_{reference}}}$
Where RD is relative density, ${{\rho }_{substance}}$ is the density of the substance, and ${{\rho }_{reference}}$ is the density of the reference.
Specific gravity for liquids and solids is usually measured with respect to density of water at ${{4}^{{}^\circ }}C$.
We are provided that the relative density of gold is 19.3. Since, reference material is not provided we assume it as water. Therefore,
$19.3=\dfrac{{{\rho }_{gold}}}{1g/c{{m}^{3}}}\,\,\,\,\,\,\,\,(\because {{\rho }_{water}}=1g/c{{m}^{3}})$
$\Rightarrow {{\rho }_{gold}}=19.3g/c{{m}^{3}}$
Density of gold is $19.3\,\,g/c{{m}^{3}}$

Note: Relative density is a unitless quantity.
Density is defined as the volumetric mass of the material but relative density is the ratio of density of substance to density reference material.
Relative density helps to measure the buoyancy of a substance in a fluid or gas. It also helps to determine the density of an unknown substance from the known density of another.