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Physical Quantities and Measurement - Questions & Answers

EXERCISE 2 (A)

1. Define the term density.

Density of a substance is defined as the mass per unit volume of the substance. i.e., Density = Mass / Volume.

2. Name the S.I. unit of density. How is it related to g cm⁻³?

The S.I. unit of density is kg m⁻³ (kilogram per cubic metre). The relationship is: 1 g cm⁻³ = 1000 kg m⁻³.

3. The density of brass is 8.4 g cm⁻³. What do you mean by this statement?

This statement means that the mass of 1 cm³ volume of brass is 8.4 g.

4. How does the density of a substance change with the rise in temperature?

When a substance is heated, its volume increases due to expansion while its mass remains constant. Since density is inversely proportional to volume (for a constant mass), the density of a substance decreases with the rise in temperature.

5. State the density of water at 4°C in (i) S.I. units and (ii) C.G.S. units.

(i) In S.I. units, the density of water at 4°C is 1000 kg m⁻³. (ii) In C.G.S. units, it is 1 g cm⁻³.

6. Explain the method of measuring the density of an irregular solid (denser than water and insoluble in it) using a measuring cylinder.

1. Note the mass (M) of the solid using a beam balance. 2. Take a measuring cylinder and fill it partly with water. Note the initial volume of water as V₁. 3. Tie the solid with a fine thread and lower it gently into the water until it is completely immersed. 4. Note the new level of water as V₂. 5. The volume of the solid is V = V₂ - V₁. 6. Calculate the density using the formula: Density = M / (V₂ - V₁).

7. Describe the method of measuring the density of a liquid using a density bottle.

1. Weigh the clean and dry density bottle with its stopper (M₁). 2. Fill the bottle with the given liquid and insert the stopper. Wipe the liquid that overflows and weigh it (M₂). 3. The mass of the liquid is M = M₂ - M₁. 4. Since the volume of the density bottle (V) is known (usually marked on it), the density is calculated as: Density = (M₂ - M₁) / V.

8. MULTIPLE CHOICE QUESTIONS

(i) The S.I. unit of density is:

kg m⁻³

(ii) The density of water is:

1000 kg m⁻³

(iii) A block of wood of density 0.8 g cm⁻³ has a volume of 60 cm³. The mass of the block is:

48 g

9. FILL IN THE BLANKS

1. The density of water at 4°C is 1.0 g cm⁻³.

2. 1 g cm⁻³ = 1000 kg m⁻³.

3. Density of a substance decreases with the rise in temperature.

4. The density of a liquid is measured by using a density bottle.

10. MATCH THE FOLLOWING

(a) kg m⁻³(iii) S.I. unit of density
(b) Density of water(iv) 1000 kg m⁻³
(c) Density bottle(ii) measures density of a liquid
(d) g cm⁻³(i) C.G.S. unit of density

EXERCISE 2 (B)

1. Define the term relative density.

Relative density (R.D.) of a substance is the ratio of the density of the substance to the density of water at 4°C.

2. State the unit of relative density.

Relative density is a ratio of two similar quantities; therefore, it has no unit.

3. Differentiate between density and relative density.

Density is the mass per unit volume and has units like kg m⁻³ or g cm⁻³. Relative density is the ratio of the density of a substance to the density of water at 4°C and has no unit.

4. How is the density of a substance related to its relative density?

Density of a substance (in g cm⁻³) = Relative Density × 1 g cm⁻³. Density of a substance (in kg m⁻³) = Relative Density × 1000 kg m⁻³.

5. A body of density ρ is placed in a liquid of density ρL. State the condition when the body will (i) float, (ii) sink in the liquid.

(i) The body will float if its density is less than or equal to the density of the liquid (ρ ≤ ρL). (ii) The body will sink if its density is greater than the density of the liquid (ρ > ρL).

6. State the law of floatation.

The law of floatation states that a floating body displaces a weight of the liquid equal to its own weight.

7. An iceberg floats on fresh water with a part of it outside the water surface. Calculate the fraction of the volume of the iceberg above the water surface. (Density of ice = 917 kg m⁻³, density of fresh water = 1000 kg m⁻³).

Fraction submerged = Density of Ice / Density of Water = 917 / 1000 = 0.917. Fraction above water = 1 - 0.917 = 0.083.

8. Why does a ship made of iron float on water, while an iron nail sinks in it?

An iron nail is solid and its density is greater than water, so it sinks. A ship, though made of iron, is hollow and contains a lot of air. Its average density becomes much less than the density of water, allowing it to float.

9. What is a submarine? How can it be made to dive or rise to the surface of water?

A submarine is a watercraft capable of independent operation underwater. It has large ballast tanks. To dive, the tanks are filled with water to increase its average density. To rise, compressed air is used to force the water out, decreasing the average density.

10. FILL IN THE BLANKS

1. The relative density of a substance is the ratio of its density to the density of water at 4°C.

2. Relative density has no unit.

3. A body sinks in a liquid if its density is more than the density of the liquid.

4. An iceberg floats in water with 1/12th (or approx. 0.083) of its volume above the surface.

EXERCISE 2 (C)

1. The density of copper is 8.9 g cm⁻³. Calculate its density in kg m⁻³.

Density in kg m⁻³ = Density in g cm⁻³ × 1000 = 8.9 × 1000 = 8900 kg m⁻³.

2. A carboy holds 35 kg of water. What is the volume of the carboy?

Mass of water = 35 kg. Density of water = 1000 kg m⁻³. Volume = Mass / Density = 35 / 1000 = 0.035 m³.

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

(a) Density = Mass / Volume = 150 / 200 = 0.75 g cm⁻³. (b) Density in S.I. unit = 0.75 × 1000 = 750 kg m⁻³.

4. The density of iron is 7.8 g cm⁻³. Find its relative density.

Relative Density = Density of substance in g cm⁻³ / Density of water in g cm⁻³ = 7.8 / 1 = 7.8.

5. Calculate the mass of a body whose volume is 2 m³ and relative density is 0.52.

Relative Density = 0.52. Density = 0.52 × 1000 kg m⁻³ = 520 kg m⁻³. Mass = Density × Volume = 520 × 2 = 1040 kg.

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Multiple Choice Questions - Test your understanding with these MCQs. Click "Show Answer" to reveal the correct answer.

Question 1What is the definition of density?

Correct Answer: Mass per unit volume

Question 2Which symbol is commonly used to represent density?

Correct Answer: d

Question 3What is the S.I. unit of density?

Correct Answer: kg m⁻³

Question 4What is the C.G.S. unit of density?

Correct Answer: g cm⁻³

Question 5What is the relationship between 1 g cm⁻³ and kg m⁻³?

Correct Answer: 1 g cm⁻³ = 1000 kg m⁻³

Question 6If the mass of a substance increases while its volume remains constant, what happens to its density?

Correct Answer: It increases

Question 7Does the density of a substance change if its shape or size is changed?

Correct Answer: No, it does not change

Question 8What generally happens to the density of a substance when it is heated?

Correct Answer: Decreases

Question 9Why does the density of a substance generally decrease on heating?

Correct Answer: Volume increases

Question 10Water exhibits anomalous expansion between which temperatures?

Correct Answer: 0°C to 4°C

Question 11At what temperature is the density of water maximum?

Correct Answer: 4°C

Question 12What is the maximum density of water in S.I. units?

Correct Answer: 1000 kg m⁻³

Question 13What is the maximum density of water in C.G.S. units?

Correct Answer: 1 g cm⁻³

Question 14How do equal masses of lead and cotton compare in volume?

Correct Answer: Cotton has larger volume

Question 15Why does iron have more mass than an equal volume of wood?

Correct Answer: Iron particles are closely packed

Question 16Which formula is used to calculate the volume of a regular cube?

Correct Answer: side³

Question 17Which formula is used to calculate the volume of a sphere?

Correct Answer: 4/3 π r³

Question 18Which instrument is used to measure the mass of a solid?

Correct Answer: Beam balance

Question 19What method is used to measure the volume of an irregular solid?

Correct Answer: Displacement method

Question 20What instrument can be used to measure the volume of an irregular solid by displacement?

Correct Answer: Measuring cylinder

Question 21What is the specific feature of a Eureka can?

Correct Answer: It has a spout

Question 22When using a measuring cylinder, 1 mL is equal to how many cubic centimeters?

Correct Answer: 1 cm³

Question 23Which vessel is used to transfer a fixed volume of liquid like milk or oil?

Correct Answer: Measuring beaker

Question 24How is the volume of a liquid displaced by a solid related to the solid's volume?

Correct Answer: It is equal to the solid's volume

Question 25What is a density bottle primarily used for?

Correct Answer: Determining density of liquids

Question 26Why does the stopper of a density bottle have a narrow hole?

Correct Answer: To allow excess liquid to drain out

Question 27What ensures that a density bottle always contains the same volume of liquid?

Correct Answer: The narrow hole in the stopper

Question 28If a density bottle holds 50g of water, what is its volume capacity?

Correct Answer: 50 mL

Question 29What is the formula for Relative Density (R.D.)?

Correct Answer: Density of substance / Density of water

Question 30What is the unit of Relative Density?

Correct Answer: No unit

Question 31Relative Density is also defined as the ratio of the mass of a substance to the mass of an equal volume of what?

Correct Answer: Water

Question 32If the Relative Density of iron is 7.8, how many times heavier is it than an equal volume of water?

Correct Answer: 7.8 times

Question 33What was the older name for Relative Density?

Correct Answer: Specific Gravity

Question 34Which state of matter typically has the highest density?

Correct Answer: Solid

Question 35Which state of matter typically has the lowest density?

Correct Answer: Gas

Question 36Which common substance is an exception where its solid state is less dense than its liquid state?

Correct Answer: Water (Ice)

Question 37What is the approximate density of ice?

Correct Answer: 0.92 g cm⁻³

Question 38Why does a piece of cork float on water?

Correct Answer: Its density is less than water

Question 39Why does an iron nail sink in water?

Correct Answer: Its density is greater than water

Question 40Will a solid iron ball float or sink in mercury?

Correct Answer: Float

Question 41What is the approximate density of Mercury?

Correct Answer: 13.6 g cm⁻³

Question 42What is the buoyant force?

Correct Answer: The upward force exerted by a liquid

Question 43Buoyant force is also known as what?

Correct Answer: Upthrust

Question 44According to the Principle of Floatation, the weight of a floating body is equal to what?

Correct Answer: Weight of the liquid displaced by its immersed part

Question 45What is the apparent weight of a floating body?

Correct Answer: Zero

Question 46If the Weight (W) of a body is greater than the Buoyant Force (F_B), what happens?

Correct Answer: The body sinks

Question 47If the Weight (W) of a body is equal to the Buoyant Force (F_B) when fully submerged, what happens?

Correct Answer: It floats just inside the liquid surface

Question 48If the density of a solid is less than the density of a liquid, what will the solid do?

Correct Answer: Float partially submerged

Question 49Why does an iron ship float while an iron nail sinks?

Correct Answer: The ship is hollow, reducing its average density

Question 50Why is it easier to swim in sea water than in river water?

Correct Answer: Sea water is denser due to salt
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True or False Questions - Determine whether each statement is true or false. Click "Show Answer" to reveal the correct answer.

Statement 1Density is defined as mass per unit volume.

Correct Answer: True

Statement 2The S.I. unit of density is g cm⁻³.

Correct Answer: False

Statement 31 g cm⁻³ is equal to 1000 kg m⁻³.

Correct Answer: True

Statement 4The density of a substance changes with its shape.

Correct Answer: False

Statement 5Equal masses of different substances always have the same volume.

Correct Answer: False

Statement 6The density of water is maximum at 4°C.

Correct Answer: True

Statement 7Water contracts when heated from 0°C to 4°C.

Correct Answer: True

Statement 8The density of water at 4°C is 1000 kg m⁻³.

Correct Answer: True

Statement 9Generally, the density of a substance increases with an increase in temperature.

Correct Answer: False

Statement 10Iron is denser than wood.

Correct Answer: True

Statement 11The volume of a cube is calculated as (side)³.

Correct Answer: True

Statement 12A beam balance is used to measure the volume of an object.

Correct Answer: False

Statement 13A measuring cylinder is used to measure the volume of liquids.

Correct Answer: True

Statement 141 mL is equal to 1 cm³.

Correct Answer: True

Statement 15A Eureka can is used to measure the mass of a solid.

Correct Answer: False

Statement 16The volume of a cylinder is calculated as πr²h.

Correct Answer: True

Statement 17A measuring beaker is used to measure a fixed volume of liquid.

Correct Answer: True

Statement 18The displacement method is used to measure the volume of irregular solids.

Correct Answer: True

Statement 19When immersing a solid in a measuring cylinder, one should drop it quickly.

Correct Answer: False

Statement 20Density = Volume / Mass.

Correct Answer: False

Statement 21A density bottle is used to determine the density of a liquid.

Correct Answer: True

Statement 22A density bottle has a stopper with a narrow hole to ensure a fixed volume.

Correct Answer: True

Statement 23Relative Density is defined as the ratio of density of a substance to the density of water.

Correct Answer: True

Statement 24The unit of Relative Density is g cm⁻³.

Correct Answer: False

Statement 25Relative Density is a dimensionless quantity.

Correct Answer: True

Statement 26Relative Density was formerly known as Specific Gravity.

Correct Answer: True

Statement 27Density in kg m⁻³ = 1000 × Relative Density.

Correct Answer: True

Statement 28Gases are generally denser than solids.

Correct Answer: False

Statement 29Ice is denser than water.

Correct Answer: False

Statement 30Mercury is a liquid with a density of 13.6 g cm⁻³.

Correct Answer: True

Statement 31Iron floats on mercury.

Correct Answer: True

Statement 32A cork floats on water because its density is less than that of water.

Correct Answer: True

Statement 33A body sinks if its density is greater than the density of the liquid.

Correct Answer: True

Statement 34Buoyant force acts vertically downwards.

Correct Answer: False

Statement 35Buoyant force is also known as upthrust.

Correct Answer: True

Statement 36If the weight of a body is greater than the buoyant force, the body will float.

Correct Answer: False

Statement 37A floating body has an apparent weight of zero.

Correct Answer: True

Statement 38Buoyant force is equal to the weight of the liquid displaced.

Correct Answer: True

Statement 39An iron ship floats because it is hollow and contains air.

Correct Answer: True

Statement 40The average density of an iron ship is greater than that of water.

Correct Answer: False

Statement 41Sea water is denser than river water.

Correct Answer: True

Statement 42It is easier to swim in river water than in sea water.

Correct Answer: False

Statement 43A piece of ice floats with 9/10th of its volume inside water.

Correct Answer: True

Statement 44A submarine uses water tanks to change its average density.

Correct Answer: True

Statement 45To rise to the surface, a submarine fills its tanks with water.

Correct Answer: False

Statement 46Whales use a swim bladder to rise or sink in water.

Correct Answer: True

Statement 47Hydrogen balloons rise because hydrogen is denser than air.

Correct Answer: False

Statement 48Density of aluminium is 2.7 g cm⁻³.

Correct Answer: True

Statement 49Turpentine oil is denser than water.

Correct Answer: False

Statement 50Volume of a sphere is 4/3 πr³.

Correct Answer: True
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Fill in the Blanks - Complete the sentences by filling in the missing words. Click "Show Answer" to check your response.

Question 1The density of a substance is defined as its mass per unit ______.

Correct Answer: volume

Question 2The S.I. unit of density is ______.

Correct Answer: kg m^-3

Question 3The C.G.S. unit of density is ______.

Correct Answer: g cm^-3

Question 41 g cm^-3 is equal to ______ kg m^-3.

Correct Answer: 1000

Question 5The density of water is maximum at ______ degrees Celsius.

Correct Answer: 4

Question 6A substance is generally most dense in its ______ state.

Correct Answer: solid

Question 7The density of a substance ______ with an increase in temperature if it expands on heating.

Correct Answer: decreases

Question 8Relative density is defined as the ratio of the density of a substance to the density of ______.

Correct Answer: water

Question 9Relative density has ______ unit.

Correct Answer: no

Question 10A body ______ in a liquid if its density is less than the density of the liquid.

Correct Answer: floats

Question 11A body ______ in a liquid if its density is greater than the density of the liquid.

Correct Answer: sinks

Question 12The buoyant force acting vertically upwards on an immersed body is also called ______.

Correct Answer: upthrust

Question 13The buoyant force is equal to the ______ of the liquid displaced by the immersed part of the body.

Correct Answer: weight

Question 14When a body floats, its apparent weight is ______.

Correct Answer: zero

Question 15A ______ can is a vessel with a side opening called a spout used to measure volume.

Correct Answer: Eureka

Question 16The volume of an irregular solid is measured using the ______ method.

Correct Answer: displacement

Question 17A specially designed bottle used to determine the density of a liquid is called a ______ bottle.

Correct Answer: density

Question 18The density of iron is ______ g cm^-3.

Correct Answer: 7.8

Question 19The density of mercury is ______ kg m^-3.

Correct Answer: 13600

Question 20An iron nail sinks in water but floats on ______.

Correct Answer: mercury

Question 21A ship made of iron floats because it is ______ and contains air, making its average density less than water.

Correct Answer: hollow

Question 22It is easier to swim in ______ water than in river water due to higher density.

Correct Answer: sea

Question 23Ice floats on water with ______ of its volume submerged.

Correct Answer: 9/10

Question 24Large pieces of ice floating on sea water are called ______.

Correct Answer: icebergs

Question 25A ______ is a water-tight boat that can travel under water by changing its average density using water tanks.

Correct Answer: submarine

Question 26Whales use a special organ called a ______ to sink or rise in water.

Correct Answer: swim bladder

Question 27A balloon filled with ______ gas rises in air because its density is less than air.

Correct Answer: hydrogen

Question 28The density of water in S.I. units is ______ kg m^-3.

Correct Answer: 1000

Question 29The density of water in C.G.S. units is ______ g cm^-3.

Correct Answer: 1

Question 30In the ______ system, the unit of volume is m^3.

Correct Answer: S.I.

Question 31In the ______ system, the unit of volume is cm^3.

Correct Answer: C.G.S.

Question 32Equal volumes of different substances have different ______.

Correct Answer: masses

Question 33Equal masses of different substances have different ______.

Correct Answer: volumes

Question 34The particles of lead are more ______ packed than those of cotton.

Correct Answer: closely

Question 35Mass = Volume x ______.

Correct Answer: Density

Question 36Volume = Mass / ______.

Correct Answer: Density

Question 37The density of a substance does not change with its ______ or size.

Correct Answer: shape

Question 38Almost all substances ______ on heating and contract on cooling.

Correct Answer: expand

Question 39Water is an exception; it ______ on heating from 0°C to 4°C.

Correct Answer: contracts

Question 40The volume of a cube is equal to (______)^3.

Correct Answer: side

Question 41The volume of a sphere is (4/3) x π x (______)^3.

Correct Answer: radius

Question 42A ______ balance is used to measure the mass of a solid.

Correct Answer: beam

Question 43A measuring cylinder is graduated in ______ with the zero mark at the bottom.

Correct Answer: millilitres

Question 44The capacity of a density bottle is often 25 mL or ______ mL.

Correct Answer: 50

Question 45The stopper of a density bottle has a ______ through it to allow excess liquid to drain.

Correct Answer: narrow hole

Question 46Density of water is 1 g cm^-3, so the mass of water filling a bottle in grams is equal to its volume in ______.

Correct Answer: mL

Question 47Relative density of a substance is also the ratio of the mass of any volume of the substance to the mass of an ______ volume of water.

Correct Answer: equal

Question 48Relative density is a ______ quantity because it is a ratio of similar quantities.

Correct Answer: dimensionless

Question 49The density of ice is ______ g cm^-3.

Correct Answer: 0.92

Question 50The density of ______ is 13.6 g cm^-3.

Correct Answer: mercury
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Short Answer Questions - Practice concise answers to these questions. Click "Show Answer" to reveal the response.
Question 1

What physical quantity is defined as mass per unit volume?

Answer:
Density
Question 2

What is the formula for density?

Answer:
Mass / Volume
Question 3

What is the S.I. unit of density?

Answer:
kg m⁻³
Question 4

What is the C.G.S. unit of density?

Answer:
g cm⁻³
Question 5

How many kg m⁻³ are equal to 1 g cm⁻³?

Answer:
1000
Question 6

Does the density of a substance change with its shape?

Answer:
No
Question 7

What happens to the density of most substances when heated?

Answer:
It decreases
Question 8

At what temperature is the density of water maximum?

Answer:
4°C
Question 9

What is the value of the maximum density of water in kg m⁻³?

Answer:
1000
Question 10

Which vessel is used to determine the density of a liquid?

Answer:
Density bottle
Question 11

What vessel has a spout to allow excess liquid to overflow?

Answer:
Eureka can
Question 12

What method is used to measure the volume of an irregular solid?

Answer:
Displacement method
Question 13

What instrument is used to measure the mass of a body?

Answer:
Beam balance
Question 14

What is the ratio of the density of a substance to the density of water called?

Answer:
Relative Density
Question 15

What is the unit of Relative Density?

Answer:
No unit
Question 16

What is the symbol for Relative Density?

Answer:
R.D.
Question 17

What is the density of water in g cm⁻³?

Answer:
1
Question 18

Which state of matter usually has the highest density?

Answer:
Solid
Question 19

Which state of matter has the lowest density?

Answer:
Gas
Question 20

What is the density of ice in g cm⁻³?

Answer:
0.917
Question 21

Does ice float or sink in water?

Answer:
Float
Question 22

What is the density of mercury in g cm⁻³?

Answer:
13.6
Question 23

Will a piece of iron float or sink in mercury?

Answer:
Float
Question 24

What upward force acts on a body immersed in a liquid?

Answer:
Buoyant force
Question 25

What is another name for buoyant force?

Answer:
Upthrust
Question 26

If a body's weight is greater than the buoyant force, what happens?

Answer:
It sinks
Question 27

If a body's density is less than the liquid's density, what happens?

Answer:
It floats
Question 28

What is the apparent weight of a floating body?

Answer:
Zero
Question 29

Why does an iron ship float while an iron nail sinks?

Answer:
The ship is hollow
Question 30

Is it easier to swim in sea water or river water?

Answer:
Sea water
Question 31

Why is it easier to swim in sea water?

Answer:
Higher density of sea water
Question 32

What part of a floating iceberg is seen above water?

Answer:
1/10th
Question 33

How does a submarine dive underwater?

Answer:
By filling tanks with water
Question 34

What organ allows whales to change their density?

Answer:
Swim bladder
Question 35

Why do hydrogen-filled balloons rise?

Answer:
Hydrogen is less dense than air
Question 36

What is the density of Aluminium in g cm⁻³?

Answer:
2.7
Question 37

What is the density of Iron in g cm⁻³?

Answer:
7.8
Question 38

What is the formula for volume of a cube?

Answer:
Side³
Question 39

What is the formula for volume of a cuboid?

Answer:
Length × Breadth × Height
Question 40

Which liquid is denser: water or glycerine?

Answer:
Glycerine
Question 41

Which liquid is less dense: water or alcohol?

Answer:
Alcohol
Question 42

Does relative density depend on the mass of the sample?

Answer:
No
Question 43

What is the S.I. unit of volume?

Answer:
Cubic metre (m³)
Question 44

What is the C.G.S. unit of volume?

Answer:
Cubic centimetre (cm³)
Question 45

How many grams are there in 1 kg?

Answer:
1000
Question 46

What is the density of gold roughly (heavy metal example)?

Answer:
19.3 g cm⁻³
Question 47

What is the approximate density of cork?

Answer:
0.25 g cm⁻³
Question 48

What is the approximate density of wood?

Answer:
0.7 to 0.9 g cm⁻³
Question 49

Does the buoyant force depend on the volume of the immersed body?

Answer:
Yes
Question 50

Does the buoyant force depend on the density of the liquid?

Answer:
Yes
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Long Answer Questions - Practice detailed answers to these comprehensive questions. Click "Show Answer" to reveal the response.
Question 1

Define density and explain its relationship with mass and volume. Also, state its S.I. and C.G.S. units.

Answer:
Density of a substance is defined as its mass per unit volume. It explains why equal masses of different substances have different volumes and equal volumes have different masses. The formula for density is Density equals Mass divided by Volume (d = M / V). The S.I. unit of density is kilogram per cubic metre (kg m-3), and the C.G.S. unit is gram per cubic centimetre (g cm-3). The relationship between them is 1 g cm-3 equals 1000 kg m-3.
Question 2

Explain how the density of a substance changes with temperature. Are there any exceptions?

Answer:
Generally, substances expand on heating and contract on cooling, while their mass remains unchanged. Since density is mass divided by volume, an increase in volume due to heating leads to a decrease in density. Conversely, cooling increases density. An exception to this is water. Water contracts when heated from 0 degrees Celsius to 4 degrees Celsius, causing its density to increase. Above 4 degrees Celsius, water expands, and its density decreases. Thus, the density of water is maximum at 4 degrees Celsius.
Question 3

Describe the process of measuring the density of a regular solid, such as a cube or sphere.

Answer:
To measure the density of a regular solid: 1. Measure the mass (M) of the solid using a beam balance. 2. Calculate the volume (V) using the appropriate geometric formula. For a cube, volume is side cubed. For a sphere, volume is 4/3 pi times radius cubed. For a cylinder, volume is pi times radius squared times height. 3. Once mass and volume are known, calculate density using the formula d = M / V.
Question 4

Describe an experiment to determine the density of an irregular solid using a measuring cylinder.

Answer:
1. Measure the mass (M) of the irregular solid using a beam balance. 2. Take a measuring cylinder and fill it partly with water. Note the initial water level (V1). 3. Tie the solid with a thread and gently lower it into the water until it is completely immersed, ensuring no water splashes out. 4. Note the new water level (V2). 5. The volume of the solid is the difference in levels (V = V2 - V1). 6. Calculate density using the formula Density = M / V.
Question 5

How would you determine the density of an irregular solid using a Eureka can?

Answer:
1. Measure the mass (M) of the solid using a beam balance. 2. Place a Eureka can on a table and place a measuring cylinder under its spout. 3. Fill the Eureka can with water until it overflows through the spout, then wait for the dripping to stop. 4. Empty and dry the measuring cylinder and place it back under the spout. 5. Gently immerse the tied solid into the Eureka can. Water equal to the volume of the solid will displace and collect in the measuring cylinder. 6. Note the volume of water collected (V). 7. Calculate density using Density = M / V.
Question 6

Explain the procedure to determine the density of a liquid using a measuring cylinder and a beaker.

Answer:
1. Measure the mass of an empty clean beaker (M1) using a beam balance. 2. Pour a specific volume of the liquid (V), for example, 50 mL, into a measuring cylinder. 3. Transfer this liquid into the beaker and measure the mass of the beaker with the liquid (M2). 4. Calculate the mass of the liquid by subtracting M1 from M2 (M = M2 - M1). 5. Calculate the density using the formula Density = M / V.
Question 7

What is a density bottle? Describe its construction and specific use.

Answer:
A density bottle is a specially designed small glass bottle used to determine the density or relative density of a liquid. It typically has a capacity of 25 mL or 50 mL. It comes with a glass stopper that has a narrow hole (capillary) running through it. When the bottle is filled with liquid and the stopper is inserted, excess liquid rises through the hole and drains out. This ensures that the bottle always contains exactly the same volume of liquid whenever it is filled, allowing for accurate relative measurements.
Question 8

Differentiate between Density and Relative Density.

Answer:
1. Density is the mass per unit volume of a substance, whereas Relative Density is the ratio of the density of a substance to the density of water at 4 degrees Celsius. 2. The S.I. unit of Density is kg m-3 (or g cm-3 in C.G.S.), while Relative Density has no unit because it is a ratio of two similar quantities. 3. Density represents an intrinsic physical property with dimensions, while Relative Density is a dimensionless comparison value.
Question 9

Describe the experiment to determine the relative density of a liquid using a density bottle.

Answer:
1. Weigh the empty, dry density bottle (M1). 2. Fill the bottle completely with water, insert the stopper, wipe the outside dry, and weigh it again (M2). 3. Empty and dry the bottle, then fill it completely with the liquid, insert the stopper, wipe dry, and weigh it (M3). 4. Calculate the mass of water as (M2 - M1) and the mass of the liquid as (M3 - M1). 5. Since the volume is constant, the Relative Density is the ratio of the mass of the liquid to the mass of the water: R.D. = (M3 - M1) / (M2 - M1).
Question 10

Why does a piece of iron sink in water while a ship made of iron floats?

Answer:
A solid piece of iron sinks because its density (7.8 g cm-3) is greater than the density of water (1.0 g cm-3), making its weight greater than the buoyant force. However, an iron ship is hollow and contains a large amount of air. This makes the average density of the ship (iron plus air) less than the density of water. Consequently, the weight of the water displaced by the submerged part of the ship equals the total weight of the ship, allowing it to float.
Question 11

Explain the Principle of Floatation.

Answer:
The Principle of Floatation states that for a body to float in a liquid, the weight of the floating body must be equal to the weight of the liquid displaced by its immersed part. In this state, the apparent weight of the floating body is zero because the upward buoyant force balances the downward weight of the body. If the density of the body is less than or equal to the liquid, it floats; otherwise, it sinks.
Question 12

Why is it easier to swim in sea water than in river water?

Answer:
Sea water contains dissolved salts, which increases its density compared to fresh river water. According to the law of floatation, a body floats when the weight of displaced liquid equals the body's weight. Because sea water is denser, a smaller volume of it needs to be displaced to support the swimmer's weight. This means less of the swimmer's body needs to be submerged to stay afloat, making swimming easier.
Question 13

How does a submarine dive and rise to the surface?

Answer:
A submarine is equipped with ballast tanks. To dive, these tanks are filled with water. This increases the total mass and average density of the submarine. When the average density becomes greater than that of sea water, the submarine sinks. To rise, compressed air is used to force the water out of the tanks. This decreases the average density of the submarine until it is less than that of sea water, causing it to rise to the surface.
Question 14

Why are icebergs dangerous for ships?

Answer:
The density of ice (roughly 0.9 g cm-3) is slightly less than that of sea water (roughly 1.02 g cm-3). According to the principle of floatation, approximately 9/10ths of the volume of an iceberg remains submerged underwater, while only 1/10th is visible above the surface. This makes it difficult for sailors to estimate the true size and underwater extent of the iceberg, leading to potential collisions with the submerged portion.
Question 15

Explain how whales are able to sink or rise in the sea.

Answer:
Whales have a special organ called a swim bladder. To rise to the surface, they fill this bladder with air, which decreases their average density, making them lighter than the water displaced. To sink or dive, they empty the bladder, which increases their average density, allowing them to descend. This mechanism enables them to control their buoyancy at will.
Question 16

Compare the densities of matter in solid, liquid, and gaseous states using the molecular model.

Answer:
In solids, molecules are closely packed with strong intermolecular forces, resulting in the highest density. In liquids, molecules are less closely packed and have more freedom of movement, leading to a lower density than solids (with exceptions like ice/water). In gases, molecules are very loosely packed with large intermolecular spaces, resulting in the lowest density. Therefore, generally: Density of Solid > Density of Liquid > Density of Gas.
Question 17

A block of glass is 30 cm long, 25 cm wide, and 2 cm thick. Its mass is 7.5 kg. Calculate its density in g cm-3.

Answer:
1. Calculate volume: V = length x breadth x thickness = 30 cm x 25 cm x 2 cm = 1500 cm3. 2. Convert mass to grams: M = 7.5 kg = 7500 g. 3. Calculate density: Density = M / V = 7500 g / 1500 cm3 = 5 g cm-3.
Question 18

A piece of iron has a volume of 30 cm3 and a mass of 234 g. Calculate its density in g cm-3 and kg m-3.

Answer:
1. Given Mass M = 234 g and Volume V = 30 cm3. 2. Calculate density in C.G.S.: Density = 234 / 30 = 7.8 g cm-3. 3. Convert to S.I. units: Since 1 g cm-3 = 1000 kg m-3, multiply by 1000. Density = 7.8 x 1000 = 7800 kg m-3.
Question 19

An empty density bottle weighs 30 g. When filled with water, it weighs 60 g. When filled with a liquid, it weighs 54 g. Calculate the density of the liquid.

Answer:
1. Mass of empty bottle (M1) = 30 g. 2. Mass of bottle + water (M2) = 60 g. 3. Mass of water = M2 - M1 = 60 - 30 = 30 g. Since density of water is 1 g cm-3, volume of bottle = 30 cm3. 4. Mass of bottle + liquid (M3) = 54 g. 5. Mass of liquid = M3 - M1 = 54 - 30 = 24 g. 6. Density of liquid = Mass / Volume = 24 g / 30 cm3 = 0.8 g cm-3.
Question 20

Explain why hydrogen or helium-filled balloons rise in the air.

Answer:
Hydrogen and helium are gases with densities significantly lower than that of air. When a balloon is filled with these gases, the weight of the air displaced by the balloon is greater than the weight of the balloon itself (including the gas). This creates a net upward buoyant force (upthrust) that is greater than the downward weight, causing the balloon to rise.
Question 21

State the three possibilities when a body is immersed in a liquid based on the forces acting on it.

Answer:
1. If the weight of the body (W) is greater than the buoyant force (Fb), the body sinks. This happens when the body's density is greater than the liquid's. 2. If the weight of the body (W) is equal to the buoyant force (Fb), the body floats just below the surface (or anywhere inside if densities are perfectly equal). This happens when the body's density equals the liquid's. 3. If the weight of the body (W) is less than the buoyant force (Fb) for full immersion, the body rises and floats partially submerged. This happens when the body's density is less than the liquid's.
Question 22

What is meant by the statement 'Relative density of iron is 7.8'?

Answer:
The statement 'Relative density of iron is 7.8' means that a piece of iron of any volume is 7.8 times heavier than an equal volume of water. It implies that the density of iron is 7.8 g cm-3 or 7800 kg m-3.
Question 23

Describe the factors that determine the buoyant force acting on a body immersed in a liquid.

Answer:
The buoyant force (or upthrust) depends on two main factors: 1. The volume of the body immersed in the liquid: The larger the submerged volume, the greater the volume of liquid displaced, and thus the greater the buoyant force. 2. The density of the liquid: The higher the density of the liquid, the greater the weight of the displaced liquid, resulting in a stronger buoyant force.
Question 24

A body floats on liquid A but sinks in liquid B. Compare the densities of the body and the liquids.

Answer:
Since the body floats on liquid A, the density of the body is less than or equal to the density of liquid A. Since the body sinks in liquid B, the density of the body is greater than the density of liquid B. Therefore, the density of liquid A is greater than the density of the body, which is greater than the density of liquid B (Density A > Density Body > Density B).
Question 25

Calculate the volume of a wood piece of mass 6000 kg if the density of wood is 0.8 g cm-3.

Answer:
1. Convert density to S.I. units: 0.8 g cm-3 = 800 kg m-3. 2. Given Mass M = 6000 kg. 3. Use the formula Volume = Mass / Density. 4. Volume = 6000 kg / 800 kg m-3 = 7.5 m3.
Question 26

What is the Law of Floatation? How is it related to apparent weight?

Answer:
The Law of Floatation states that a floating body displaces a weight of liquid equal to its own weight. Mathematically, Weight of floating body = Weight of displaced liquid. Because the upward buoyant force (equal to weight of displaced liquid) exactly balances the downward weight of the body, the resultant force is zero. Therefore, the apparent weight of a floating body is zero.
Question 27

Explain the experiment to demonstrate that a body floats with more portion outside in a denser liquid.

Answer:
1. Take two identical wooden blocks. 2. Place one in a beaker of water and the other in a beaker of glycerine (which is denser than water). 3. Observe the level of submersion. 4. You will notice that the block in glycerine floats with a larger portion above the surface compared to the block in water. 5. This demonstrates that a denser liquid exerts a greater buoyant force for the same submerged volume, so less volume is needed to support the body's weight.
Question 28

Convert a density of 8.4 g cm-3 to kg m-3 and explain the conversion factor.

Answer:
To convert g cm-3 to kg m-3, we consider that 1 kg = 1000 g and 1 m = 100 cm. Therefore, 1 kg m-3 = 1000 g / (100 cm)^3 = 1000 g / 1,000,000 cm3 = 1/1000 g cm-3. Conversely, 1 g cm-3 = 1000 kg m-3. So, for 8.4 g cm-3: 8.4 x 1000 = 8400 kg m-3.
Question 29

Why does the density of a substance not change if it is cut into smaller pieces?

Answer:
Density is an intensive property, meaning it depends on the nature of the substance, not the amount. If a substance is cut into smaller pieces, both its mass and its volume decrease in the same proportion. Since density is the ratio of mass to volume, the ratio remains constant. For example, half the mass will occupy half the volume, yielding the same density.
Question 30

A piece of zinc of mass 438.6 g has a volume of 86 cm3. Calculate its density.

Answer:
1. Identify Mass M = 438.6 g. 2. Identify Volume V = 86 cm3. 3. Apply formula d = M / V. 4. Calculation: 438.6 / 86 = 5.1. 5. The density of zinc is 5.1 g cm-3.
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Quick Review Flashcards - Click to flip and test your knowledge!
Question
What is the definition of density?
Answer
Density of a substance is its mass per unit volume.
Question
What is the formula for calculating density (d), given mass (M) and volume (V)?
Answer
$d = \frac{M}{V}$
Question
What is the S.I. unit of density?
Answer
Kilogram per cubic metre ($kg~m^{-3}$).
Question
What is the C.G.S. unit of density?
Answer
Gram per cubic centimetre ($g~cm^{-3}$).
Question
What is the relationship between the S.I. and C.G.S. units of density?
Answer
$1~g~cm^{-3} = 1000~kg~m^{-3}$.
Question
What is the density of water in C.G.S. units?
Answer
$1~g~cm^{-3}$.
Question
At what temperature is the density of water at its maximum?
Answer
4°C.
Question
How does the density of most substances change upon heating?
Answer
The density decreases because the substance expands while its mass remains constant.
Question
What is the first step in determining the density of a regular solid?
Answer
Measure the mass (M) of the solid using a beam balance.
Question
What is the formula for the volume of a cuboid with given length, breadth, and height?
Answer
$Volume = length \times breadth \times height$.
Question
What is the formula for the volume of a sphere with radius 'r'?
Answer
$Volume = \frac{4}{3} \pi (radius)^3$.
Question
What is a Eureka can used for?
Answer
It is used to measure the volume of an irregular solid by displacement.
Question
What principle is used to measure the volume of an irregular solid immersed in a liquid?
Answer
An immersed solid displaces a volume of liquid equal to its own volume.
Question
In measuring the volume of an irregular solid with a measuring cylinder, what does the difference between the final water level ($V_2$) and initial water level ($V_1$) represent?
Answer
It represents the volume of the solid ($V = V_2 - V_1$).
Question
What is a density bottle?
Answer
A specially designed glass bottle used to determine the density of a liquid, as it holds a fixed volume.
Question
How does a density bottle ensure it always contains the same volume of liquid?
Answer
It has a ground glass stopper with a narrow hole, allowing excess liquid to drain out when the stopper is inserted.
Question
How can the volume of a density bottle be determined using water?
Answer
Since the density of water is $1~g~cm^{-3}$, the mass in grams of the water needed to fill the bottle is numerically equal to its volume in $cm^3$ (or mL).
Question
What is the definition of relative density (R.D.) of a substance?
Answer
It is the ratio of the density of the substance to the density of water.
Question
What is the formula for relative density (R.D.) in terms of densities?
Answer
$R.D. = \frac{\text{Density of the substance}}{\text{Density of water}}$.
Question
Relative density can also be defined as the ratio of the mass of any volume of a substance to the mass of an _____ volume of water.
Answer
equal
Question
What is the unit of relative density?
Answer
Relative density is a dimensionless quantity and has no unit.
Question
What is the modern name for relative density?
Answer
Specific gravity.
Question
If the density of iron is $7.8~g~cm^{-3}$, what is its relative density?
Answer
7.8.
Question
If the relative density of a substance is 10.3, what is its density in $kg~m^{-3}$?
Answer
$10300~kg~m^{-3}$ (since density of water is $1000~kg~m^{-3}$).
Question
Among solid, liquid, and gas states of a substance, which state is typically the most dense?
Answer
The solid state.
Question
What is the exception to the rule that the solid state is denser than the liquid state for a substance?
Answer
Water is an exception, as ice (solid) is less dense than liquid water.
Question
What is the density of ice in $g~cm^{-3}$?
Answer
$0.917~g~cm^{-3}$.
Question
Under what condition will a body sink in a liquid?
Answer
A body will sink in a liquid if its density is greater than the density of the liquid.
Question
Under what condition will a body float on a liquid?
Answer
A body will float on a liquid if its density is less than or equal to the density of the liquid.
Question
What are the two forces that act on a body when it is immersed in a liquid?
Answer
Its weight acting downwards and the buoyant force (upthrust) of the liquid acting upwards.
Question
What is the name for the upward force exerted by a liquid on an immersed body?
Answer
Buoyant force or upthrust.
Question
According to the principle of floatation, what happens if the weight of a body is greater than the buoyant force?
Answer
The body will sink to the bottom of the liquid.
Question
According to the principle of floatation, what happens if the weight of a body is equal to the buoyant force?
Answer
The body will float just inside the surface of the liquid.
Question
According to the principle of floatation, what happens if the weight of a body is less than the buoyant force when fully immersed?
Answer
The body will rise and float partially submerged on the surface.
Question
What is the Law of Floatation?
Answer
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.
Question
According to the law of floatation, what is the apparent weight of a floating body?
Answer
The apparent weight is zero.
Question
Why does an iron nail sink in water while a large iron ship floats?
Answer
The ship is hollow, so its average density (iron + air) is less than water, while the solid nail's density is greater than water.
Question
Why is it easier for a person to swim in sea water than in river water?
Answer
Sea water is denser than river water due to dissolved salts, so it exerts a greater buoyant force.
Question
What fraction of an iceberg's volume is typically submerged in sea water?
Answer
Approximately nine-tenths ($9/10$) of its volume is submerged.
Question
Why are icebergs dangerous for ships?
Answer
Because a large portion of the iceberg is submerged and invisible from the surface.
Question
How does a submarine dive into the water?
Answer
It fills its water tanks with water, increasing its average density to become greater than that of sea water.
Question
How does a submarine rise to the surface of the water?
Answer
It empties its water tanks, decreasing its average density to become less than that of sea water.
Question
What special organ do whales use to rise or sink in the water?
Answer
A swim bladder.
Question
Why does a hydrogen or helium-filled balloon rise in the air?
Answer
The density of these gases is less than the density of air, so the buoyant force of the air is greater than the weight of the balloon.
Question
A body floats in a liquid with more of its volume submerged. What does this indicate about the liquid's density compared to another liquid where less volume is submerged?
Answer
The liquid is of lower density.
Question
What is the buoyant force on a body equal to?
Answer
The weight of the liquid displaced by the immersed part of the body.
Question
The buoyant force on an immersed body depends on two factors: the volume of the body immersed and the _____ of the liquid.
Answer
density
Question
Using a density bottle, if $M_1$ is the mass of the empty bottle, $M_2$ is the mass with water, and $M_3$ is the mass with another liquid, what is the formula for the relative density of the liquid?
Answer
$R.D. = \frac{M_3 - M_1}{M_2 - M_1}$
Question
The density of mercury is $13.6~g~cm^{-3}$ and the density of iron is $7.8~g~cm^{-3}$. Will a piece of iron float or sink in mercury?
Answer
It will float, because the density of iron is less than the density of mercury.
Question
A block of wood has a density of $0.8~g~cm^{-3}$. Will it float or sink in water (density $1.0~g~cm^{-3}$)?
Answer
It will float, because its density is less than the density of water.
Question
When a body floats, the buoyant force _____ the total weight of the body.
Answer
balances (or is equal to)
Question
A piece of cork (density $0.25~g~cm^{-3}$) and an iron nail (density $7.8~g~cm^{-3}$) are placed on the surface of water. Describe what happens to each.
Answer
The cork floats because its density is less than water, and the iron nail sinks because its density is greater than water.
Question
Given two liquids, A and B, a body sinks in A but floats in B. What can you conclude about the densities of the liquids relative to the body?
Answer
The density of liquid A is less than the body's density, and the density of liquid B is greater than the body's density.
Question
A piece of wood floats in water with some part outside the surface. How does the buoyant force experienced by it compare to its weight?
Answer
The buoyant force is equal to the weight of the wood piece.
Question
How can you express the mass of a substance if you know its density (d) and volume (V)?
Answer
$Mass = Density \times Volume$ ($M = d \times V$).
Question
A piece of iron when immersed in water in a Eureka can displaces 25 mL of water. What is the volume of the iron piece in $cm^3$?
Answer
25 $cm^3$ (since 1 mL = 1 $cm^3$).
Question
The mass of 10 $cm^3$ of silver is 103 g. What is the density of silver in $g~cm^{-3}$?
Answer
$10.3~g~cm^{-3}$.
Question
An empty density bottle has a mass of 25 g. When filled with water, its mass is 55 g. What is the volume of the density bottle?
Answer
30 $cm^3$ or 30 mL.
Question
Equal masses of different substances have different _____.
Answer
volumes
Question
Equal volumes of different substances have different _____.
Answer
masses