SUBMITTED TO: Dr. Jawad Sarwar

2017 -ME -289

Problem solving Techniques
1. Problem Statement:
A beaker of 100ml is Half filled with Water up to the mark of 50ml.We have to find
the density of water Theoretically and further we have to find the density of Beaker
and density of System.

2. Schematic Explanation:

I. First we Take 100ml empty beaker 4 Then we calculate it mass with help
of weight Machine

Empty 100ml beake r

II. After That we fill half of the beaker with Water and calculate its mass As


Weight Machine

3. Assumptions and Approximation:
The exact density of water is
997kg/m 3 and the Density of Beaker made up of Glass is 27 00 kg/m 3 so the
calculation we do theoretically to find the density of water and Beaker must be
near to their ideal values. Further experiment is done in Room temperature at 20 oC
and the instrument use to weight and Measure parameter of beaker are free of
4. Explanation with laws of Physics:
As we know Density is the Ratio of mass and Volume so it depend directly to the
mass and indirectly to the volume. It is the measure of compactness. It’s a scaler
Quantity and has No direction.
;#3627409222; =

The SI unit of density is Kilogram per cubic meter Kg/m 3
The Volume of Hollow cylinder depend on the height of beaker and Difference of
squares of External radius to Internal radius. Volume also varies with the change
of Temperature.
;#55349;;#56445; = ;#3627409221;;#55349;;#56457; (;#3627408505; ;#55349;;#57296;-;#3627408531;;#55349;;#57296;)
Where R is the External radius and r is internal radius. The SI unit of Volume is
m 3.
5. Properties:
Water is defined as a colorless, transparent, odorless, liquid
which forms the seas, lakes, rivers, and rain and is the basis of the fluids of living
organisms . It is by far the most studied chemical compound and is described as
the “universal solvent” and the “solvent of life”. It is the most abundant substance
on Earth and the only common substance to exist as a solid, liquid, and gas on
Earth 2 .
Its hydrogen bonding causes its many unique properties, such as having a
solid form less dense than its liquid form, a relatively high boiling point of 100 °C
for its molar mass, and a high heat capacity’s surface. It is also the third mos t
abundant molecule in the universe 3.

Water have 5 important properties.
i. Its attraction to polar molecules
ii. High -specific heat
iii. High heat of vaporization
iv. The lower density of ice
v. High polarity
Glass is defined as a hard, brittle substance, typically transparent or translucent,
made by fusing sand with soda and lime and cooling rapidly. It is used to ma ke
windows, drinking containers and Experiment containers etc. Properties of Glass
are following 1 .

i. It can take up a high polish and may be used as s ubstitute for every costly
ii. It has no definite crystalline structure.
iii. It has no sharp melting point.
iv. It is affected by alkalies.
v. It is an excellent electrical insulator at elevated temperatures due to the fact
that glass can be considered as an ionic liquid. The ions are not easily moved
at room temperature because of the high viscosity. But when the
temperature rises the ions are permitted to flow and thus they will sustain
an electric current.
vi. It behaves more as a solid than most solids in the sense that it is elastic.
But when the elastic limit is exceeded, it fractures instead of deforming.
vii. It is capable of being worked n many ways. It can be blown, drawn or
pressed. But it is strange to note that it is difficult to cast in large pieces.
viii. It is extre mely brittle.
ix. It is not usually affected by air or water.
x. It is not easily attacked by ordinary chemical reagents.
6. Calculations:

• Mass of beaker = m b = 44.98 g = 0.44 kg
• Mass of water = m w = 52.6 g = 0.52 kg
• Mass of beaker and water = m b+w = 97.58 g = 0.97 kg
• Volume of water = 50cm 3 = 0.0050 m 3
• Height of beaker = 6.35 cm = 0.063 m
• External Radius of beaker = 23.15 mm = 2.315 c m
• Internal Radius of Beaker = 21.25 m = 2.125 cm

• Volume of beaker = 12.6 cm3 = 0.0000126 m3
• Volume of select ed system = 16.8 cm3 = 0.0000168 m3

• Density of water = ���� ��� �����
������� ��� ����� = 51 .6
50 = 1. 03 g/cm 3

• Density of Beaker = ���� ��� ������
������� ��� ������ = 44 .98
12 .6 = 2.687 g/ cm 3

• Density of System = ���� ��� �������
������� ��� ������� = 97 .58
16 .8 = 1.47 g/ cm 3

7. Discussions and Reference:
After performing the experiment we came to know that experimental value of the
density of water and glass are slightly different from the actu al values. The values
are different because of human error as well Instrument, Since we had used
Weighting machine to weight the mass of beaker and Vernier caliper to find height
and Diameter of beaker the Error is inevitable to occur.
Further due to prope rties of material we use, there is also effect of change in
temperature. Since Density directly depend on mass there might lessening of water
when water was pouring into the beaker.
1 https://www.saint -gobain -sekurit.com/glossary/glass -properties .
2 https://en.wikipedia.org/wiki/List_of_physical_properties_of_glass .
3 https://owlcation.com/stem/5 -Properties -of -Water
4 http://www .lekton.info/plus/b/beaker -with -water/