Question

A solid of density $900kg{{m}^{-3}}$ floats in oil. The oil floats on water of density $1000kg{{m}^{-3}}$ .The density of oil in $kg{{m}^{-3}}$ could be:
A) 850
B) 900
C) 950
D) 1050

Answer 1

Hint: Density of a substance is the measure of mass per unit volume and it is usually represented by $\rho $ also Latin letter D is also used. Density will have the same numerical value as its mass concentration for a pure surface. The dimensional formula for density of substance is $M{{L}^{-3}}$ and density is a scalar quantity which does not show the direction.

Complete step-by-step solution:
The density of substance varies with temperature and pressure of substance. The variation of temperature and pressure will be typically small for liquids and solids but it will be greater for gases. Different substances will have different densities and density will be relevant to purity, packaging and buoyancy.
The average density of a substance is equal to total mass divided by its total volume and particle density is the number of particles per unit volume.
From the data given solid floats on oil. Therefore the density of oil (${{\rho }_{0}}$) is greater than the density of solid (${{\rho }_{S}}$).
Oil floats on water from the given data therefore the density of water (${{\rho }_{W}}$) is greater than the density of oil (${{\rho }_{0}}$).
Therefore
\[{{\rho }_{W}}>{{\rho }_{O}}>{{\rho }_{S}}\]
From the data density of solid is $900kg{{m}^{-3}}$ and density of water is $1000kg{{m}^{-3}}$
On substituting
$1000>{{\rho }_{O}}>900$
The density of oil (${{\rho }_{0}}$) in $kg{{m}^{-3}}$ is 950
The correct option is C

Note: Students density is an intensive property in which by increasing the amount of substance does not increase its density but it will increase its mass. The reciprocal of the density of substance is called its specific volume.SI unit of density of substance is kilogram per cubic meter ( $kg{{m}^{-3}}$) and density is also known as specific mass.