This document discusses physical quantities and measurement. It begins by listing learning objectives related to measuring density of solids and liquids, expressing results with proper units, and solving problems using density formulas. It then defines density as mass per unit volume and discusses different units. Methods are provided for determining the density of regular solids, irregular solids using displacement, and liquids using a density bottle. The document also covers relative density, floating and sinking based on an object's density compared to the liquid, and the three cases of floating.

1. PHYSICAL QUANTITIES
AND MESURMENT
Arush Deep

2. Learning Objectives
■ Measure density of an irregular solid
■ Measure density of a liquid
■ Concept of floatation based on relative density
■ Express result in proper units and symbols
■ Solving numericals problems on the formula of density
■ Make careful observations including mesurments
■ Gather data using formal units
■ Make conclusition from collected data
■ Make predictions using scientific knowledge and effectively
communicating the same.

3. DENSITY

4. Density
■ Each body has a certain mass and a definite volume.
■ The volume occupied by body increases if its mass increases.
■ Similarly the mass of a body increases if its volume increases.
■ The density of a substance is the mass per unit volume of a substance.
■ Equal masses of different substances have different volumes.
■ Equal volumes of different substance have different masses.
■ Density of a substance = Mass of the substance/Volume of the substance

5. Unit of Density
■ Unit of density= Unit of mass/Unit of volume
■ In S.I. unit the unit of mass is kg and unit of volume is m3 , so S.I. unit of density is kg m-3
(kilogram per cubic metre).
■ In C.G.S. unit the unit of mass is g and the unit of volume is cm3, the C.G.S. unit of
density is g cm-3 (gram per cubic centimetre).

6. Determination of Density of Regular
Solids
■ Finding the density of a regular solid is very easy.
1. First measure the mass of the given regular solid using a beam balance.
2. To find the volume use the formula length × breadth × height.
3. Then to find the density of the substance simply divide the mass by the volume of the
substance.

7. Vessels for measuring
volume
1. MeasuringCylinder: It is made up of glass or plastic and is
graduated in milliletre (ml) with zero mark at the bottom.
2. Measuring Beaker: A measuring beaker is made up of
plastic, glass or metal like aluminium. It is used to take
fixed volume of liquids such as 50ml, 100ml, 200ml, 500ml
and 1l.
3. Eureka Can: Eureka Can is a glass, plastic or metal
container with a side opening near its mouth which is
known as the spout.Thus the container can hold a specific
amount of liquid and any excess water flows out through
the spout.
(the diagrams are respective to the following list)

8. Determination of Density of Irregular
Solid
■ To determine the density of an irregular solid, we have to measure its mass and
volume.
■ The mass of the body is determined by a beam balance.
■ To measure the volume of the body we use the displacement method.
■ Then we use the formula of density i.e. Mass/Volume
■ We will understand the method by a simple activity.

9. Activity 1
■ Now tie the given solid and dip in the
container. Be careful that no water
splashes out.
■ Note that the level of water rises and
let it beV2.
■ Find the difference ofV2 –V1. It gives
the volume of the solid.
■ Then calculate the density of the
solid by using the
formula: Mass/Volume
■ Note: 1 ml = 1 cm3
Objective: Measurment of density of an
irregular solid.
■ Take a measuring cylinder and fill it
partly with water as shown.
■ Note the level of water and let it be
V1.

10. Activity 2
Objective: Measurment of density of an
irregular solid.
■ Take an Eureka can. Place the eureka
can on a table with a measuring
cylinder under its spout. Pour water
until it starts overflowing through
the spout.
■ When the water stops dripping take
the measuring cylinder empty it, dry
it and place it under the spout.
■ Now tie the solid with a thread and
dip it in the can.The water
that overflows is the volume of the
solid.
■ Dry the solid and measure the mass
using a beam balance.
■ Using the formula of the density we
can measure the density of the solid.

11. Determination of Density of a Liquid
■ To determine the density of a liquid, its mass is measured by a common beam balance
and its volume is measured in a measuring container.
■ Then the density is calcuated by the formula mass/volume.

12. Density Bottle
■ A density bottle is a specially designed bottle which is used to determine the density
of a liquid.
■ It is a small glass bottle having a glass stopper at its neck.This bottle can hold a fixed
amount of liquid.
■ Generally the bottle is 25ml or 50ml.The bottle always contains the same amount of
liquid each time when it is filled completely.
■ Sine the density of water is 1 g cm-3, so the mass (in g) of water neede to fill the bottle
completely, will give the volume (in ml) of bottle.
■ Nowadays, it is not named as a gravity bottle.

13. Determination of Density of Liquid by
Using Density Bottle
■ First wash the bottle and dry it.Then
measure the mass of the empty
bottle. Let it be M1.
■ Remove the stopper from the bottle
and fill it with water. Replace the
stopper.Wipe the outside of the
bottle dry. Measure its mass again.
Let it be M2.
■ Empty the bottle and dry it. Now fill
it with the liquid. Replace
the stopper.Wipe the outside of
the bottle dry. Measure its mass
again. Let it be M3.
■ Calculate the mass of the water (M2-
M3) and the mas sof thr liquid (M2-
M1).
■ Since the density of the water is
1 g cm-3, the mass of the water
contained in the bottle gives the
volume of the bottle.
■ Density of liquid= Mass/Volume

14. RELATIVE
DENSITY

15. Relative Density
■ The relative density of a substance is defined as the ratio of the density of the
substance to the density of water.
■ The symbol for relative density is R.D.
■ Thus relative density of a substance can also be defined as the ratio of the mass of any
volume of the substance to the mass of an equal volume of water.

16. Unit of Relative Density
■ Relative density is just a number.
■ It has no units.
■ It is the ratio of the same quantities.
Mesurmeny of Relative
Density
■ The relative density of a liquid is
measured by a density bottle.

17. How to determine the relative density of
a liquid
■ First wash the bottle and dry it.Then
measure the mass of the empty bottle.
Let it be M1.
■ Remove the stopper from the
bottle and fill it with water. Replace
the stopper.Wipe the outside of
the bottle dry. Measure its mass
again. Let it be M2.
■ Empty the bottle and dry it. Now fill it
with the liquid. Replace the stopper.
Wipe the outside of the bottle dry.
Measure its mass again. Let it be M3.
 Mass of empty bottle=M1 g
 Mass of bottle+water=M2 g
 Mass of bottle+liquid=M3 g
 Mass of water=M2 g - M1 g
 Mass of liquid=M3 g - M1 g
Relative density= Mass of the liquid/Mass
of equal volume of water

18. FLOATING AND
SINKING

19. Floating and Sinking
■ If we place a iron piece and cork on water, we will see that iron sinks while the cork
floats.
■ This is because the density of cork is less than the density of water while iron is more
dense that water.
■ Thus a body floats on a liquid if it is less dense than the liquid, while a body sinks if it is
more dense than the liquid.

20. Principle of Flotation
When a body is immersed in a liquid, there are two forces acting upon it:
■ The weight of the bodyW acting vertically downwards.This force has tendency to sink
the body.
■ The buoyant force of the liquid FB acting vertically upwards.The buoyant force is equal
to the weight of the liquid displaced by the immersed part of the body.This force has
tendency to move the body upwards.This is also called upthrust.

21. CASES OF
FLOATING

22. Law of
Floating
When a body floats in a liquid, the weight
of the liquid displaced by its immersed
part is equal to the total weight of the
body.This is the law of floatation.
Weight of the floating body =Weight of
the liquid displaced by the immersed part
of the body
The apparent weight of a floaing body is
zero.

23. Case I
■ The weight of the bodyW is greater than the
buoyant force FB.
■ In this case, the resultant force on the body
is (W-FB) which acts downwards.
■ The body will sink in liquid .
■ This happens when the density of the object is
less than the density of the liquid.

24. Case II
■ The weight of the bodyW is equal to the
buoyant force FB.
■ In this case, the resultant force on the body
is zero i.e. the aparent weight of the body is
zero.
■ The body will float just inside the surface of the
liquid.
■ This happens when the density of the solid is
equal to the density of the liquid.

25. Case III
■ In this case the resultant force acts on the body
upwards.
■ This body will float partially above the surface
of liquid
■ Only that much portion of the body will
immerse inside the liquid by which the
weight of the liquid displaced balances FB the
total weight of the body.
■ This happens when the density of the solid is
less than the density of the liquid.

26. THANKYOU