Question

If a sample of metal weigh 210g in air, 180g in water and 120g in a liquid
A. RD of metal is 3
B. RD of metal is 7
C. RD of liquid is 7
D. RD of liquid is (1/3)

Answer 1

Hint: To solve this problem we should understand about the Density, relative density and the concepts behind them including its formula. By using this information, we can easily calculate our answer and hence approach our solution.

Complete step-by-step answer:
Density- density is determined as mass per unit of volume. The average density of an object equivalent to its total mass divided by its total volume.
d =M/V
Where d is the density of substance, M is mass, and V is volume. Density is commonly expressed in units of gram per cubic centimeter.
Relative density: It is the correlation of the density and substance to the density of a given reference material. Relative density for liquids is nearly always measured with respect to water at its densest. The relative density of a substance will let you know if it will float or sink, it gives us the idea about relative mass or density.
Relative density of metal
$= \dfrac{{weight\,in\,air}}{{change\,in\,weight\,of\,water}}$
$= \dfrac{{210}}{{210 - 180}} = 7$
$\therefore$ Density of metal$= 7g/c{m^2}$
Modification in weight in a liquid upthrust in liquid
$= \left( {{V_{solid}}} \right)\left( {{\rho _{liquid}}} \right)g$
Or,$\Delta \,\omega \, \propto \,{\rho _{liquid}}$
$\therefore \dfrac{{\Delta {\omega _l}}}{{\Delta {\omega _w}}} = \dfrac{{{\rho _l}}}{{{\rho _w}}}$
${\rho _l} = \dfrac{{\Delta {\omega _l}}}{{\Delta {\omega _w}}}{\rho _w}$
$= \left( {\dfrac{{210 - 120}}{{210 - 180}}} \right)\left( 1 \right)gm/c{m^3}$
$= 3g/c{m^3}$

So, the correct answer is option A, i.e. RD of the metal is 3.

Note - Relative density informs us how heavy the substance is in comparison to water. It helps us to measure the density of a known substance. It is important in the accurate measurement of density. Relative density helps to quantify the buoyancy of a substance, used by geologists and mineralogists to help determine the mineral content of a rock or other sample.
Density is mass per unit volume; relative density is the compared to a reference substance (usually water) under standard conditions. Density is measured, while relative density is dimensionless. Density is unique for each body, while the same body can have numerous densities.