https://www.youtube.com/watch?v=vSXTBnnx4OA
VOLUME AND DENSITY
PHYSICS PHYSICAL QUANTITIES AND MEASUREMENT
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Vessels for Measuring the Volume of Liquids
Liquids like water, milk, edible oil, etc. are measured by two
kinds of vessels:
1) Measuring cylinder, and
2)Measuring beaker.
Measuring Cylinder
It is a cylinder generally
of area 10 cm2 made up of either glass or plastic. Its 10 cm in
length with markings graduated in cm3 or ml.
PHYSICS PHYSICAL QUANTITIES AND MEASUREMEN
In order to measure the volume of a liquid, pour the liquid in an empty
cylinder.
Wait for some time to let the liquid become stationary and then
observe the meniscus of the liquid.
Read the level by keeping the eye in line with the lower meniscus.
It is shown below.
Measuring Beaker
A measuring beaker is used to measure a fixed volume of a liquid
from a large volume. It is available in different quantities such as 50 ml, 100
ml, 200 ml, 500 ml and 1 L.
In order to measure a certain volume of a liquid say 500 ml, take
a beaker measuring 500 ml. Wash it thoroughly and dry it.
Immerse the beaker in the container containing the liquid and fill
the beaker completely.
PHYSICS PHYSICAL QUANTITIES AND MEASUREMENT
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Measuring Volume of a Regular Shape
Solids of regular shapes (without curves) are called regular
solids.
Example:
Volume of a cube = side3
where, l is the side of the cube
Volume of a cuboid = l x b x h
where l, b and h are the length, breadth and height
Volume of a sphere =
ℼr3
where, r is the radius
Volume of a cylinder = ℼr2h
where, r is the radius, h
is the height
Volume of a cone =
r2h
where, r is the radius, h
is the height and
Measuring Volume of an Irregular Shape
The volume of the liquid is
measured by using a measuring cylinder by the method of displacement.The volume
of the liquid displaced is equal to the volume of the submerged object i.e. the
difference between the original volume of the liquid and the final volume of
the liquid is the volume of the irregularly shaped solid.
Example:
Take a measuring cylinder partially filled with water and note the
reading of the water level.
Tie a stone with a thread and dip it completely into water. Thus,
we see that the water level rises.
The difference in the two levels of water gives the volume of the
stone.
Initial volume of the water = 50 ml
Volume of the water when the stone is immersed = 70 ml
Volume of the water displaced = 70 ml – 50 ml = 20 ml
Volume of the stone = 20 ml = 20cm3
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Area
The space occupied by an object is called the area or the
surface area.
The area (A) of a regular plane surface such as square or
rectangle can be calculated as
Area of a square = side x side
Area of rectangle = l x b
where l is the length, b is the breadth
Unit of Area
The SI unit of area is square metre (m2).
1 m × 1 m = 1 m2
Multiple and Sub-multiple units of Area
The SI unit of area is square metre (m2).
To measure a bigger area such as a piece of land or a building
like a mall, bigger units or multiple units of area are used called acre and
hectare.
1 are = 100m2
1 hectare = 100 m x 100 m = 10,000 m2
To measure the area of a much bigger size like the area of the country,
continent or the earth, etc. a bigger unit called square kilometre (km2)
is used.
1 sq. km (km ) = 1 km x 1 km
= 1000
m x 1000 m
=
10,00,000 m2
= 106
m2
The area of smaller objects like a matchbox, book, pencil box etc.
is measured by smaller units (sub- multiple units) called square centimetre (cm2)
or square millimetre (mm2).
1 sq. cm (cm2 ) =1 cm x 1 cm
= 10 mm x 10 mm
= 100 mm2 or 102 mm2
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Measuring Area of a Regular Object
Area of a square = a2
where, “a” is the side of the square.
Area of a rectangle = l x b
where, l and b are the length and the breadth, respectively.
Area of a circle = πr2
where, r is the radius.
Surface area of a cylinder
= 2πrh
where, r is the radius, h
is the height.
Surface area of a sphere =
4πr2
where, r is the radius.
Measuring Area of an Irregular Object
To estimate the area of an irregular object (a lamina), a graph
paper is to be used.
A graph paper is a sheet of paper on which horizontal and vertical
lines are ruled at a regular interval of 1 mm.
After each 1 cm space the line is made thick such that area of one
small square formed becomes 1
mm × 1 mm = 1 mm2 and that of the big square becomes 1
cm × 1 cm = 1 cm2.
Place the lamina on the graph paper and draw its boundary with a
pencil.
Count the number of complete squares and the squares more than
half within the
Area of the lamina is the sum of areas of squares mentioned above.
Numericals:
1. A measuring cylinder contains some
water. When a stone is put in the water, the level rises.
What is the volume of the stone?
a. 50cm3 b.
70cm3 c. 75cm3 d. 125cm3
Density: It is defined as the mass per unit
volume of a substance.
Its SI unit is kgm-3. The CGS
unit is gcm-3 or g/cc.
The
density of a substance is one of its characteristic properties and used to
determine the
purity of any substance. The density of a substance does not change with change
in its shape or size.
1kg/m3 = 1000g/cc
Determination of Density of a Solid Heavier than Water
To determine the density of a stone which is heavier than water:
First, determine the mass of the stone with the help of a physical balance. Let the mass of the stone
be M.
Take a measuring cylinder which is partially filled with water and a stone tied with a string.
Measure the initial reading V1 of water in the measuring cylinder.
Now immerse the stone into the cylinder which contains water and note the reading of the new water
level, i.e. V2.
From (V2 – V1), we obtain the volume of the stone.
Thus, by substituting the values of M, V2 and V1, we obtain the density of the stone.
Speed
The distance covered or travelled by a body in one second is called the speed of the body.
It is denoted by symbol ‘v’.
Units of Speed
The SI unit of speed is metre per second (m s−1)
The other unit of speed is kilometre per hour (km h−1)
Questions on Volume and Density
1.
A
person measures the length, width, height and mass of a rectangular metal
block. Which of these measurements are needed in order to calculate the density
of the metal?
A.
mass only B. height and mass only
C.
length, width and height only D.
length, width, height and mass
2) Find the density of ethyl alcohol if 63.3 g occupies 80 mL.
3) The density of gold is 19 g/cc. Find the volume of
(i) 38 g, (ii) 95 g of gold.
4.
What
apparatus is needed to determine the density of a regularly-shaped block?
A.
a balance and a ruler B. a balance and a spring balance
C.
a measuring cylinder and a ruler D.
a measuring cylinder and a beaker
5. A piece of iron have a volume 20 cm3 and a mass of 156 g. What is its density in SI unit and C.G.S unit?
6.
Which
of the following is a unit of density?
A
cm3 /g B g/cm2 C g/cm3 D kg/m2
7.
A
measuring cylinder contains 60 cc of water. When a stone is put in the water,
the level rises to 100 cc. What is the volume of the stone?
8.
A
wooden post has a volume of 0.025 m3 and a mass of 20 kg. Calculate
its density in kg/m3.
9.
A
measuring cylinder contained a volume of 120 cm3 of a certain
liquid. The liquid was then poured into an empty beaker of mass 51 g. The total
mass of the beaker and the liquid was then found to be 145 g.
a.
Calculate the mass of the liquid in grams.
b.
Calculate the density of the liquid in g/cm3.
10.
A
rectangular concrete slab is 0.80 m long, 0.60 m wide and 0.05 m thick.
a. Calculate its volume in m3.
b. The mass of the concrete slab is 60 kg.
Calculate its density in kg/m3.
11. a.If the density of wood is 0.5 g/cm3 , what is the mass of (i) 1 cm3, (ii) 2 cm3, (iii)10 cm3 ?
12. .What is the density of a substance of
(i) mass 100 g and volume 10 cm3,
(ii) volume 3 m3 and mass 9 kg?
13. When a golf ball is lowered into a measuring cylinder of water, the water level rises by 30 cm3 when the ball is completely submerged. If the ball weighs 33 g in air, find its density.
14. What is the mass of air in a room measuring 10 m × 5.0 m × 2.0 m, if the density of air is 1.3 kg/m3?
16.
A
piece of steel has a volume of 12 cm3 and a mass of 96 g. What is
its density in
a)
g/cm3, b) kg/m3?
17.
What
is the mass of 5 m3 of cement of density 3000 kg/m3?
SPEED
20.
What
is the average speed of a
a)
car that travels 400 m in 20 s,
b)
an athlete who runs 1500 m in 4 minutes?1) The average speed of a bus is 36 km/h. How much would it be in m/s?
22. How long does it take a bird traveling at 35 km/h to go 120 km?
23) A tunnel has a length of 50 km. A car takes 20 min to travel between the two ends of the tunnel. What is the average speed of the car?
24) A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go?
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