2. PHYSICAL QUANTITIES AND MEASUREMENT

DENSITY

RELATIVE DENSITY

FLOATING AND SINKING

LAWS OF FLOATATION

• Volume: Amount of space

covered by an object.

• SI unit is m3 (cubic meter). It can

also be measured in cm3(cubic

centimeter) ,mm3(cubic

millimeter)

• Mass: The amount of matter or

substance that makes up an

object.

• Its S.I unit is kilogram (kg). It can

also be measured in gram(g),

milligram(mg) etc.

REVISION OF CONCEPTS

DENSITY

“Each body has certain mass and volume.

If mass increases, volume also increases and vice -versa.”

1. EQUAL VOLUME OF DIFFERENT SUBSTANCES HAVE DIFFERENT MASSES.

• Consider two solid cube box.• One is filled with iron and other with cotton.• Though they both have same volume, but their masses can be

different. • Reason is, molecules of iron are tightly packed as compared to

molecules of cotton. So, iron have more mass than cotton. Hence ,iron is more denser than cotton.

DENSITY - 2

2. EQUAL MASSES OF DIFFERENT SUBSTANCES HAVE DIFFERENT VOLUME

Consider that we have 1kg of lead and 1kg of cotton.

Though both have same mass but their volume will be certainly different.

• Reason is, molecules of lead are tightly packed. So, their volume will be

less. Whereas, volume of cotton will be more.

• Hence, we can say that lead is more denser than cotton.

What do you mean by density?

Density of substance is mass(M) per unit volume(V).Represented by D.

FORMULA

• Density of substance = 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒

• So units can be derived as • D=Mass(kg)/volume(𝑚3)• So, its S.I unit is kg/m3

• Or in C.G.S unit,• g/c𝑚3.

1. MEASUREMENT OF DENSITY

RELATIONSHIP BETWEEN S.I AND C.G.S. UNIT

• As 1 kg/m3 = 1 𝑘𝑔

1𝑚3= 1000 𝑔

100×100×100 𝑐𝑚3

= 1

1000Τ𝑔 𝑐𝑚3

• Thus,

1 kg m-3 = 10-3 g cm-3

or, 1 g cm-3 = 1000 kg m-3

For better understanding refer to :https://www.youtube.com/watch?v=QXoQbWoIiRE

DENSITY OF REGULAR SOLID

HOW TO MEASURE DENSITY OF A REGULAR OBJECT?

1. Measure the mass of the object using beam balance.

2. As it is regular solid, using various formula we can find its volume.

( by finding length, breadth , radius, height etc.)

• Knowing both the quantities, using the formula, we can find the density.

• For better understanding refer to: https://www.youtube.com/watch?v=ovdE_-FCWpc

VESSELS FOR MEASURING VOLUME

This vessels are only used for finding volume of the liquid.

1.MEASURING CYLINDER : It is usually made up of glass or plastic graduated in units of milliliter (mL). Starting from bottom( 0mL) , increases gradually in upward direction.

2.MEASURING BEAKER: It is made up of glass, plastic or even metal. it is used find fix volume of liquids. ( 50mL, 100mL, 1 L). Mostly used by milkman, groceries shop etc.

• EUREKA CAN: A beaker made of usually glass with a side opening near its mouth, called as SPOUT. the excess liquid flows out through the spout.

MEASUREMENT OF DENSITY OF AN IRREGULAR OBJECT

1. Using measuring cylinder

Using beam balance, we can easily find the mass of an object.( ex: 20g)

To find volume: Using measuring cylinder, fill the water up to some level( lets say 100ml)

Insert the object inside the cylinder( water rises up to level 120ml)

As the liquid level increases, measure the volume by subtracting

i.e., final volume(120ml)-initial volume(100)=20ml

• So, density= mass/volume

=20g/20ml

=20g/ 20 cm3 (as, 1ml= 1cm3)

= 1 g cm-3

2.USING EUREKA CAN

DENSITY BOTTLE

• A Density bottle is specially designed bottle which determine the density of liquid.

• This glass bottle have glass stopper at its neck, so it can fill only fixed volume of liquid.

• Stopper is also provided with a hole on the top, so that excess liquid can flow out through it.

DETERMINATION OF DENSITY USING DENSITY BOTTLE

1. Wash the bottle and dry it.

2. Measure the mass of the empty bottle. Let it be M1 g.

3. Fill the bottle with the WATER and measure its mass again. Let it be M2 g.

4. Remove water from the bottle, and dry it.

5. Fill the bottle again with the liquid, whose density to be found.

6. Measure the mass and let it be M3.

7. Now, calculate the mass of water (M2- M1)

8. Mass of liquid as ( M3-M1)

9. As the density of water is 1 g cm-3 , the mass contained in bottle gives volume of the liquid.

10. So , mass of liquid = M3-M1

volume of the liquid= M2-M1

Therefore, density of liquid = 𝑀

3−𝑀

1

𝑀2−𝑀1

𝑔

𝑐𝑚3

For better understanding refer to: https://www.youtube.com/watch?v=hgfqiRflIoM&t=210s

RELATIVE DENSITY • The ratio of density of substance to the density of water is defined as relative

density.

• In simple words it is a comparison of density of any substance with the density of water

• R.D= 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

As , both numerator and denominator has same quantity, its UNITLESS.

It can also be expressed as,

R.D= 𝑀𝑎𝑠𝑠 𝑜𝑓 1𝑐𝑚3 𝑡ℎ𝑒 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒

𝑚𝑎𝑠𝑠 1𝑐𝑚3 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

• It can also be defined as, ratio of mass of any volume of the substance to the mass of equal volume of water.

• For better understanding, refer : https://www.youtube.com/watch?v=omRMpPYh_vw

DENSITY IN DIFFERENT STATES

• There are mainly three states of matter: solid, liquid and gas.

• According to their states, their density differs.

• SOLID: As in solids, molecules are tightly packed with each other. So , their density is quite more.

• LIQUIDS:As molecules are a bit far away from each other, they are less dense than solids.

• GAS: As molecules are far away from each other, they are least dense as compared to solids and liquids.

• EXCEPTION : MERCURY being only liquid metal, have more density as compared to few solids.

FLOATING AND SINKING

1. If you place an ice cube on water, does it float or sink?

2. If you keep an iron nail in water, does it float or sink?

• So, the concept of floating and sinking takes place. The concept totally depend on the density of the substance and liquid.

• As the density of water is 1 g cm-3 which is more than the density of ice( 0.917 g cm-3), so the ice floats on water.

• The same concept, the density of iron is 7.874 g cm-3 , and water is 1 g cm-3. As the density of iron is more, an iron nail sinks.

• For better understanding refer to: https://www.youtube.com/watch?v=05WkCPORlj4

PRINCIPLE OF FLOATATION

• When a body is immersed in a liquid, two forces act on it:

1. The weight of the body W, acting downwards. This force has tendency to pull an object downwards.

2. The buoyant force of liquid FB acting vertically upwards. This force has tendency to move an object upwards.

THIS FORCE IS ALSO CALLED AS BUOYANT FORCE OR UPTHRUST.

APPARENT WEIGHT :

• Weight of an object in a liquid is called as APPARENT WEIGHT.

• Apparent weight= Actual weight- up thrust

There are three possibilities :

Case 1

• The weight of the body W is greater than the buoyant force FB. (W > FB)

• In this case, the density of the body is MORE as compared to the liquid. As the density of substance is more, W acts more as compared to FB.

• So, the BODY SINKS.

Case 2

• When weight of the body is same as buoyant force(FB) ( W=FB)

• In this case, the body floats just below the liquid.

• The reason is that, as the density of liquid and density of substance is SAME.

• As both the forces are equal, the resultant force will be ZERO.

Case 3

• When weight of the body is less as compared to buoyant force(FB)

( W<FB)

• In this case, the body floats on the liquid.

• The reason is that, as the density of substance is less than that of liquid.

• As a result buoyant force acts more than weight of the and body floats on liquid

LAW OF FLOATATION

• When a body is immersed in a liquid, a part of the liquid is displaced.

• So the law of floatation states that

“Weight of the floating body = weight of the liquid displaced by its immersed

part”

It means that , 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.

• In other words, the apparent weight of a floating body is ZERO.

APPLICATIONS OF FLOATATION

FLOATATION OF AN IRON SHIP

• An iron nail sinks in water, but a ship made from iron doesn’t .

• The reason is that , iron nail is solid and its density is more than that of water. So, it sinks inside.

• Whereas , a ship is hollow from inside and its empty space contains air. This makes average density of ship less than that of water.

FLOATATION OF ICE ON WATER

• Everyone knows why the great Titanic ship sank in water?

• A piece of ice on water with 9/10th part inside water and 1/10th part of it outside the water.

• Reason is that, the density of ice (0.9 g cm-

3) which is less as compared to water (1 g cm-3).

• As a result, the weight of the water displaced by 9/10th part of ice immersed inside becomes equal to total weight of the ice piece.

SUBMARINE

• A submarine can dive inside and float on the surface of the water, when desired.

• Reason is that, submarine is provided with a water tanks.

• To make submarine DIVE, the water tanks are filled. As a result, the average density of submarine is more than water, so it sinks( LAW OF FLOATION 1)

• Whereas to make submarine float, water tanks are emptied. As a result, the average density of submarine is less than the density of sea water so it rises up.

FLOATATION OF MAN

• It is easier for a person to swim in sea water as compared to river water.

• The reason is that sea water contains salt, makes it more dense as compared to river water.

• So the weight of man gets balanced by less immersed part of his body in sea water as compared to river water.

WHALES

• The whales can rise or sink according to their will.

• The reason is that, they have a special organ in their body called as SWIM BLADDER.

• In order to rise, they fill bladder with air. As a result, average density of whale decreases as compared to water and rises up.

• To dive inside, they empty their bladder and this increases the average density of whale and goes down.

AIR BALLOONS

• A hydrogen or helium filled balloons rises in air.

• The reason is that, density of these gases are less than that of the air.

• As a result, buoyant force experienced by balloon due to air becomes greater than the weight of balloon .

• So, it rises up.

WORKSHEET

QUESTION 1: Fill in the blanks.

1. The S.I unit of density is ______.

2. Mass= _______ x density.

3. 1 g cm-3 = _________ kg m-3.

4. C.G.S unit of density is ________.

5. The relative density has _______ unit.

6. _______ is the only liquid metal found.

7. The density of ice is ________ kg m-3.

8. Volume of cube=_________

9. The buoyant force acts vertically _______.

10. Weight of the body acts on ________ direction.

11. Density of _______ is usually more than liquids and gases.

12. When W> FB, body ________

13. When W= FB, body will ________.

QUESTION 2: DEFINE THE FOLLOWING

1. Density

2. Relative density

3. Law of floatation

4. Apparent weight

5. Buoyant force

QUESTION 3: ANSWER IN SHORT

1. Why a piece of ice float on water?

2. Arrange the following substances in order of their increasing density: Iron , water, mercury

SOLVED NUMERICALS

1. The density of aluminum is 2.7 g cm-3. Express in kg m-3.

SOLUTION:

as 1 g cm-3 = 1000 kg m-3

therefore,

=2.7 x 1000 kg m-3

=2700 kg m-3

2. A piece of wood of mass 150g and has a volume of 200 cm3 . Calculate the density in (a) C.G.S (b) S.I unit.

Solution : As density= 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒

= 150𝑔

200𝑐𝑚 3= 0.75 g cm-3

In S.I unit,

0.75 g cm-3 x 1000= 750 kg m-3

3. Find relative density using following:

Mass of empty bottle = 22g

Mass of bottle + water = 50g

Mass of bottle + brine water = 54g

SOLUTION: Mass of empty bottle( M1) = 22g

Mass of water(M2) = 50g

Mass of bottle + brine water(M3) = 54g

• Using formula,

Relative density = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑏𝑟𝑖𝑛𝑒

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

= 𝑀3−𝑀1

𝑀2−𝑀1

= 54−22

50−22

= 32

28

= 1.14

NUMERICALS

1. Calculate the volume of wood of mass 6000kg if the density of wood is 0.8 g cm-3 ( Ans :7.5 m3)

2. The dimension of a hall are 10m x 7m x 5m. If the density of air is 1.11 kg m-3 , find mass of air in the hall. (Ans: 388.5 kg)

SOLUTIONS

QUESTION 1.

1. kg m-3

2. Volume

3. 1000

4. g cm-3

5. No

6. Mercury

7. 900

8. (Length)3

9. Upwards

10. Vertically downwards

11. Solids

12. sinks

13. Float just below the

surface

QUESTION 2

1. Density of substance is mass(M) per unit volume(V).

2. Relative density of a substance is defined as the ratio of the density of the substance to the density of water.

3. 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.

4. Weight of an object in a liquid is called as apparent weight.

5. When a body is immersed partially or completely in a liquid, it experiences an upward force due to liquid, which Is called as buoyant force.

SOLUTIONS…cont.

QUESTION 3

Ans 1: As the density of ice(0.9 g cm3) is less than water (1 g cm3). So, the ice floats on the water.

Ans 2: water <iron < mercury.

SOLUTIONS…cont.