Units & DIMENSIONS - DENSITY & RELATIVE DENSITY
SOLVED EXAMPLES
Example 1:
Take a brick of salt measuring 10.0 cm x 10.0 cm x 2.0 cm, which weighs 433 grams. Find the density of brick.
Solution:
Use the formula, which helps you to determine the amount of mass per unit volume.
\(\rho = \frac{{mass}}{{volume}} = \frac{m}{v}\)
In this example, you have the dimensions of the object.
So, you have to calculate the volume.
The formula for volume depends on the shape of the object.
Brick looks like cuboid.
v = length x width x thickness
v = 10.0 cm x 10.0 cm x 2.0 cm
v = 200.0 cm3
Now that you have the mass and volume, calculate the density, as follows:
\(\rho = \frac{m}{v}\)
\(\rho = 433g/200.0c{m^3}\)
\(\rho = \) 2.165g/cm3
Thus, the density of the salt brick is 2.165 g/ cm3.
Density is super important because it relates to whether things rise or sink. Less dense materials tend to rise above more dense materials.
Examples of dense materials include iron, lead, or platinum. Many kinds of metal and rock are highly dense. Dense materials are more likely to ‘feel’ heavy or hard.
Example 2:
A block of ice with volume 5.5m3 has a mass of 5060kg find the density of ice.
Solution:
Volume of block=5.5m3
Mass of block=5060kg
Density=mass /volume
=5060/5.5m3.
=920kg/m3.
The density of ice is 920kg/m3.
Example 3:
A silver cylindrical rod has a length of 0.5m and radius of 0.4m,find the density of the rod if its mass is 2640kg.
Solution:
Mass of cylinder=2640kg
Volume of cylinder= ðr²h=3.14 x 0.42 x 0.5=0.2512m3
Density=mass/volume=10509kg/m3
Example4:
A stone has a mass of 112.5g.when the stone totally immersed in water contained in measuring cylinder displaced water from 50cm3 to 95cm3.find the density of the stone.
Solution:
Mass of the stone=112.5g
Volume of stone=95cm3-50cm3=45cm3
Density=mass/volume=2.5g/cm3.
Example 5:
Beaker contain 262.5cm3. of a certain liquidweigh 410g,if the mass of an empty dry beaker is 200g,find the density of the liquid.
Solution:
Mass of liquid=410g-200g=210g
Volume of liquid=262.5cm3.
Density=mass/volume =0.8g/cm3.
Units & DIMENSIONS - DENSITY & RELATIVE DENSITY
SOLVED EXAMPLES
Example 1:
Find relative density of asteel ball of density20 g/cm3.
Solution:
Steel balldensity =20 g/cm3.
Relative density (RD =\(= \frac{{density\,of\,body}}{{density\,of\,water\,at\,{4^0}c}}\)
Relative density (RD)=\( = \frac{{20g/c{m^3}}}{{1g/c{m^3}}}\)= 20
Example 2:
Find relative density of airon rod of density2000 kg/m3.
Solution:
Iron roddensity =2000 kg/m3.
Relative density (RD)\(= \frac{{density\,of\,body}}{{density\,of\,water\,at\,{4^0}c}}\)
Relative density (RD)=\(= \frac{{2000kg/{m^3}}}{{1000kg/{m^3}}}\)= 2
Example 3:
A globe of steel has a mass of 12g and a volume of 15.2cm³,find its relative density.
Solution:
Mass of 15.2 g/cm3( of equal volume of water) body is m
= density of water x volume of body
=1 g/cm3x 15.2 cm3
= 15.2 g
Relative density (RD) =\( = \frac{{mass\,of\,any\,volume\,of\,body}}{{mass\,of\,an\,equal\,volume\,of\,water}}\) = \( = \frac{{12g}}{{15.2g}} = 0.79\)