Selina Concise Solutions for ICSE Class 8 Physics Chapter 2 Physical Quantities and Measurement

MASS Is the quantity of matter contained in a body.
 

VOLUME is the space occupied by body.
Mass tells us how much "stuff" is inside an object and stays the same no matter where the object is. Volume describes the three-dimensional room or capacity that the object takes up in the world.
Teacher's Tip: Think of Mass as the number of bricks in a pile and Volume as the size of the box those bricks fit into.
Exam Tip: For full marks, always define Mass using the word "quantity of matter" and Volume using "space occupied."

Equal mass of IRON and cotton, iron will have less volume than cotton.
Because iron is much denser, its particles are packed very tightly, so you only need a small piece to reach a certain mass. Cotton is very loose and airy, so you need a giant pile of it to weigh the same as the small piece of iron.
Teacher's Tip: Remember: Heavy materials take up less room for the same weight.
Exam Tip: Mention "density" when explaining why volumes differ for equal masses.

Equal volume of Iron and cotton, the mass of iron is more than mass of cotton, because iron denser than cotton.
If you have two boxes of the exact same size, the one filled with iron will be much heavier than the one with cotton. This happens because the iron has more matter squeezed into that same amount of space.
Teacher's Tip: "Denser" means more crowded particles inside the same size box.
Exam Tip: Use the term "denser" specifically to compare the mass of two equal volumes.

DENSITY "Is ratio of mass of substance to volume of substance"
D = M/V = KG/M³ The SI. unit of density is kg M^-3
Density is a mathematical way to describe how compact a material is by dividing its mass by its volume. It helps scientists identify substances because every pure material has its own unique density.
Teacher's Tip: Use the "Heart" trick: draw an M over a V, and it looks like a heart (heartsuit) with a line through it.
Exam Tip: Always write the formula D = M/V before solving numerical density problems.

Density of a substance does not change with change in shape or size.
Whether you have a tiny gold ring or a large gold bar, the density of the gold remains exactly the same. Density is a property of the material itself, not the object's specific dimensions.
Teacher's Tip: A drop of water has the same density as a whole bucket of water.
Exam Tip: Remember that cutting an object in half does not change its density.

When a substance is heated it expands and volume increases. Hence density decreases.
Water has maximum density at 4°C i.e. density of water increases from 0°C to 4°C and decreases above 4°C.
Heating makes particles move further apart, which takes up more space and makes the material "thinner" or less dense. Water is unique because it actually gets heavier for its size as it warms up to 4°C before it starts expanding like other liquids.
Teacher's Tip: 4°C is the "Magic Number" for water's highest density.
Exam Tip: Mention "Anomalous expansion" when talking about why water density is highest at 4°C.

Volume of substance is measured by formula V = L times B times H or 4/3 or by measuring cylinder.
Regularly shaped objects like boxes use multiplication of their sides, while liquids or irregular shapes are measured using a marked container. Using a measuring cylinder allows us to find the volume of a liquid directly by reading the scale.
Teacher's Tip: For a cylinder, always read the bottom of the curved water line (the meniscus).
Exam Tip: Units for volume must always be cubed, such as cm³ or m³.

Mass is measured by beam balance or spring balance.
A beam balance compares an object's mass to standard weights to find a match, while a spring balance measures the pull of gravity. Both tools are essential for different types of scientific measurements in the lab.
Teacher's Tip: Beam balance measures "Mass," while spring balance technically measures "Weight."
Exam Tip: Name the "Beam Balance" specifically when asked for a tool that measures mass accurately.

RELATIVE DENSITY of substance is the density compare with water i.e. How many times the substance is DENSER than water. Since density of water is 1 Gcm^-3, so density of a substance in Gcm^-3 = relative density of substance.
S.I. unit of R.D. > has no units - since it is the ratio of same quantities.
Relative density is just a number that tells us if something is heavier or lighter than water. Because we are dividing two identical types of measurements, the units cancel out and leave us with a plain number.
Teacher's Tip: Relative Density is a "Comparison Number" with no tail (units).
Exam Tip: Never write units like g or cm after a relative density value.

If a substance has density more than liquid it SINKS in the liquid and if the density of substance is LESS than liquid it floats on liquid.
Heavy, dense objects like stones overcome the upward push of the water and fall to the bottom. Lightweight, less dense objects like wood are pushed up by the water and stay on the surface.
Teacher's Tip: Dense = Sinker, Less Dense = Floater.
Exam Tip: If an object's R.D. is greater than 1, it will sink in water.

BUOYANT FORCE "The force exerted by liquid acting vertically upward on a body and is equal to the weight of liquid displaced by its immersed part."
This is the invisible "upward push" you feel when you try to push a ball under water. The strength of this push depends entirely on how much water the object pushes out of the way.
Teacher's Tip: Buoyant force is the "water's helping hand" pushing things up.
Exam Tip: Use the term "Upthrust" as another name for Buoyant Force in your answers.

Weight of body Acting vertically downward. This force has the tendency to sink the body.
Gravity pulls every object toward the center of the Earth, which we call its weight. This downward force is what tries to make an object go deep into the liquid.
Teacher's Tip: Weight pulls "Down," Buoyancy pushes "Up."
Exam Tip: In a diagram, represent weight with an arrow pointing straight down from the center of the object.

LAW OF FLOATATION "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." While floating wt. of floating body W=wt. of liquid displaced by its immersed part FB i.e. Apparent wt. of floating body is zero.
When an object is perfectly floating, the water's upward push is exactly as strong as the object's downward pull. Because these forces balance out, the object feels weightless while it sits on the water.
Teacher's Tip: Floating is a "Tie" between weight and buoyancy.
Exam Tip: State that the "Apparent weight" of a floating body is zero to show you understand the Law of Floatation.

Density of body is greater than density of liquid. The body sinks.
If the object's particles are more crowded than the liquid's particles, the liquid cannot support it. This leads to the object falling through the liquid until it hits the floor.
Teacher's Tip: Imagine trying to hold up a heavy bowling ball with a piece of tissue paper; the ball is just too dense.
Exam Tip: Use a comparison of densities to explain why an object sinks in a specific liquid.

Density of body is equal to the density of liquid. The body float where ever it is left in liquid.
When the object and the liquid have the same density, they are perfectly matched in strength. The object will stay suspended at any level in the liquid without sinking further or rising up.
Teacher's Tip: This is like a submarine staying perfectly still in the middle of the ocean.
Exam Tip: Use the term "Neutral Buoyancy" to describe this state where an object neither sinks nor rises.

Density of body is less than density of liquid. The body rises to the surface and floats.
Because the object is lighter for its size than the liquid, the liquid pushes it up with great force. It will continue to rise until it reaches the surface where it can rest comfortably.
Teacher's Tip: Think of a cork popping up to the surface after you let it go underwater.
Exam Tip: Explain that a floating object always displaces a weight of liquid equal to its own weight.

Test yourself

A. Objective Questions

1. Write true or false for each statement

(a) Equal volumes of the two different substances have equal masses.
Answer: False.
Equal volumes of the two different substances have different masses. This is because every substance has a unique density, meaning some pack more matter into the same space than others.
Teacher's Tip: Size (volume) doesn't always equal weight (mass).
Exam Tip: If a statement is false, always write the correct version to get full marks.

(b) The density of a piece of brass will change by changing its size or shape.
Answer: False.
Density is a property of the material itself, not the object's dimensions. Whether you have a tiny brass pin or a giant brass bell, the density of the metal remains the same.
Teacher's Tip: Material determines density, not the shape.
Exam Tip: Remember that density is constant for a pure substance at a constant temperature.

(c) The density of a liquid decreases with increase in its temperature.
Answer: True.
As a liquid gets hotter, its particles move apart and it expands, which increases the volume. Since the mass stays the same but the space increases, the density must go down.
Teacher's Tip: Heat expands things, and expansion makes them "thinner" or less dense.
Exam Tip: Mention that volume increases when temperature increases to explain the decrease in density.

(d) Relative density of water is 1.0.
Answer: True.
Relative density is the ratio of a substance's density to water's density. Since water compared to itself is exactly the same, the ratio is always 1.
Teacher's Tip: Water is our standard "ruler" for relative density.
Exam Tip: Use 1.0 as a reference point for all other Relative Density problems.

(e) Relative density of a substance is expressed in g cm^-3.
Answer: False.
Relative density of a substance has no units. This is because it is a ratio of two identical physical quantities whose units cancel each other out.
Teacher's Tip: "Relative" means it's just a comparison number.
Exam Tip: Never write units for Relative Density or you will lose marks.

(f) When a body is immersed in a liquid, the buoyant force experienced by the body is equal to the volume of the liquid displaced by it.
Answer: False.
The buoyant force is equal to the weight of the liquid displaced by the immersed part of body. While the volume of the object equals the volume of the liquid, the actual force depends on the liquid's weight.
Teacher's Tip: Force = Weight, not Volume.
Exam Tip: Carefully distinguish between "Volume" and "Weight" when defining Buoyant Force.

(g) A body experiences the same buoyant force while floating in watr or alcohol.
Answer: True.
When an object floats, the buoyant force must exactly balance the object's weight. Since the object's weight is the same, the upward push from any liquid it floats in must also be the same.
Teacher's Tip: Floating is a "Perfect Balance" regardless of the liquid.
Exam Tip: Remember that the buoyant force on a floating body always equals its own weight.

(h) A body experiences the same buoyant force when it floats or sinks in water.
Answer: False.
When an object sinks, the water cannot provide enough buoyant force to match the object's weight. The upthrust is usually different when an object is fully submerged versus when it is only partially submerged.
Teacher's Tip: Sinking means the water "lost the battle" to push it up.
Exam Tip: Buoyant force changes based on how much of the object is underwater.

(i) A body floats in a liquid when its weight becomes equal to the weight of the liquid displaced by its submerged part. .
Answer: True.
This is the fundamental rule for floatation where the downward pull and upward push are perfectly balanced. This allows the object to stay steady on the surface of the liquid.
Teacher's Tip: This is the Law of Floatation in action.
Exam Tip: Use this principle to explain why ships made of heavy iron can still float.

(j) A body while floating, sinks deeper in a liquid of low density than in a liquid of high density.
Answer: True.
In a "thin" or low-density liquid, the object must push more liquid aside to get enough upward force. In a "thick" or high-density liquid, the push is stronger, so the object doesn't have to go down as far.
Teacher's Tip: Think of how much easier it is to float in salty sea water than in fresh pool water.
Exam Tip: Explain that displacement depends on the density of the liquid to support the weight.

2. Fill in the blanks

(a) 1 kg is the mass of 1000 ml of water at 4°C.
This is the standard measurement where one liter of pure water weighs exactly one kilogram. We use 4°C because that is when water is at its most stable and highest density.
Teacher's Tip: 1 Liter = 1000 ml = 1 kg of water.
Exam Tip: Always mention 4°C if the question asks for the condition of water density.

(b) Mass = density x volume.
This formula is used to calculate how much matter is in an object if you know its material and size. It shows that mass depends on both how packed the particles are and how much space they take up.
Teacher's Tip: M = D times V is the "Magic Formula."
Exam Tip: Rearrange the formula to D = M/V or V = M/D depending on what you need to find.

(c) The S.I. unit of density is Kg m^-3
In the International System, we measure mass in kilograms and volume in cubic meters. The unit is written with a negative exponent to show that mass is divided by volume.
Teacher's Tip: Kg m^-3 is just a shorter way to write kg per cubic meter.
Exam Tip: Use the correct S.I. unit unless the question specifically asks for C.G.S. units.

(d) Density of water is 1000 Kg m^-3
This value tells us that a giant tank of water measuring one meter on every side would weigh exactly one thousand kilograms. It is a very important constant in physics for comparing other materials.
Teacher's Tip: Water is 1 in small units (g/cm³) and 1000 in big units (kg/m³).
Exam Tip: Use 1000 as the value for water density when working with S.I. units.

(e) 1 g cm^-3= 1000 Kg m^-3
This conversion shows how density values change when switching between smaller grams and larger kilograms. It is a scale factor that helps scientists convert lab measurements into large-scale engineering data.
Teacher's Tip: To turn g to kg, just multiply by 1000.
Exam Tip: Memorize this conversion factor for solving numerical problems quickly.

(f) The density of a body which sinks in water is more than 1000 Kg m^-3
Anything heavier for its size than water will always sink to the bottom. Since water's S.I. density is 1000, any object with a higher number is a "sinker."
Teacher's Tip: If Density > 1000, it goes "Down."
Exam Tip: Compare numerical density values to water's density to predict if an object will sink.

(g) Abody sinks in a liquid A, butt floats in a liquid B. The density of liquid A is less than the density of liquid B.
Liquid B must be "thicker" and denser to provide enough upward push to keep the object floating. Liquid A is too thin or light, so it cannot support the object's weight.
Teacher's Tip: Denser liquids are better "supporters."
Exam Tip: Floating depends on the relationship between the object's density and the liquid's density.

(h) A body X sinks in water, but a body Y floats on water. The density of the body X is more than the density of body Y.
Body X has more matter packed into its volume, making it denser than the surrounding water. Body Y is lighter for its size, allowing the water's buoyancy to hold it up.
Teacher's Tip: Compact objects sink; airy or light objects float.
Exam Tip: Use the terms "Sink" and "Float" as clues to rank the densities of different objects.

(i) The buoyant force experienced by a body when floating in salt-water is equal to or same that of when floating in pure water.
For any floating object, the upthrust must exactly match its weight regardless of the type of liquid. While salt water is denser, the object simply floats higher up so that the forces stay balanced.
Teacher's Tip: Floating is a "Tie" between Weight and Buoyancy, no matter the liquid.
Exam Tip: Note that while the force is the same, the volume of liquid displaced will be different.

(j) The weight of a body floating in a liquid is zero.
This refers to the "apparent weight" because the liquid's upward push cancels out the downward pull of gravity. It makes the object feel completely weightless while it is supported by the liquid.
Teacher's Tip: Think of how light you feel when you are floating in a swimming pool.
Exam Tip: Always specify "apparent weight" if the question asks about weight while floating.

3. Match the following

Column A                        Column B
(a) kg m^-3                    (i) relative density
(b) no unit                    (ii) sinks in alcohol
(c) relative density       (iii) floats on water
(d) iron                         (iv) density
(e) wood                       (v) density bottle

Answer:
(a) kg m^-3 - (iv) density
(b) no unit - (i) relative density
(c) relative density - (v) density bottle
(d) iron - (ii) sinks in alcohol
(e) wood - (iii) floats on water
These pairings connect units, tools, and materials with their scientific categories. For example, Relative Density is a pure ratio, so it is the only one on the list with "no unit."
Teacher's Tip: Match units first to eliminate wrong choices.
Exam Tip: Draw straight lines or write the correct letter clearly to avoid losing marks for confusion.

4. Select the correct alternative

(a) The correct relation is
1. Density = Mass x Volume
2. Mass = Density x Volume
3. Volume = Density x Mass
4. Density = Mass + Volume
Answer: 2. Mass = Density x Volume
This formula is derived from the basic definition where density equals mass divided by volume. It helps us find how heavy a certain volume of a known material will be.
Teacher's Tip: Remember the D = M/V triangle to get all relations correct.
Exam Tip: Double-check that your formula makes logical sense before doing calculations.

(b) The relative density of alcohol is 0.8. Its density is
1. 0.8
2. 800 kg nr³
3. 800 g cm^-3
4. 0.8 kg m^-3
Answer: 2. 800 kg n³
Relative density of 0.8 means the substance is 80% as dense as water. Since water is 1000 kg/m³, multiplying 0.8 times 1000 gives us the correct density of 800.
Teacher's Tip: R.D. is just the "Decimal Version" of the big density number.
Exam Tip: Pay attention to the units; 0.8 is R.D., but the question asks for density.

(c) A block of wood of density 0.8 g cm^-3 has a volume of 60 cm³. The mass of block is
1. 60.8 g
2. 75 g
3. 48 g
4. 0.013 g
Answer: 3. 48 g
Using the formula Mass = Density times Volume, we calculate 0.8 times 60. The result is 48, and the unit must be grams because the input density used grams.
Teacher's Tip: Always check if your units "match" before you multiply.
Exam Tip: Show the step 0.8 times 60 = 48 to get partial marks even if you make a calculation error.

(d) The density of aluminium is 2.7 g cm^-3 and that of brass 8.4 g cm³. The correct statement is
1. Equal masses of aluminium and brass have equal volumes
2. The mass of a certain volume of brass is more than the mass of equal volume of aluminium.
3. The volume of a certain mass of brass is more than the volume of equal mass of aluminium.
4. Equal volumes of aluminium and brass have equal masses.
Answer: 2. The mass of a certain volume of brass is more than the mass of equal volume of aluminium.
Since brass has a much higher density, it has more matter packed into the same amount of space. This makes a brass block much heavier than an identically sized aluminum block.
Teacher's Tip: Dense things are "heavy for their size."
Exam Tip: Compare "Equal Volume" to "Density" to find the heaviest mass.

(e) A density bottle has a marking 25 mL on it. It means that:
1. the mass of density bottle is 25 g
2. the density bottle will store 25 ml of any liquid in it
3. the density bottle will store 25 ml of water, but more volume of liquid denser than water.
4. the density bottle will store 25 ml of water, but more volume of a liquid lighter than water.
Answer: 2. the density bottle will store 25 ml of any liquid in it
A density bottle is designed to hold a very precise volume regardless of what liquid is inside. The marking tells you the internal capacity of the bottle itself.
Teacher's Tip: Volume is about "Capacity," which stays the same even if the liquid changes.
Exam Tip: Don't confuse the bottle's volume with the liquid's mass.

(f) The correct statement is
1. The buoyant force on a body is equal to the volume of the liquid displaced by it ‘
2. The buoyant force on a body is equal to the volume of the body
3. The buoyant force on a body is equal to the weight of the liquid displaced by it
4. The buoyant force on a body is always equal to the weight of the body.
Answer: 3. The buoyant force on a body is equal to the weight of the liquid displaced by it
This is the core of Archimedes' Principle, which links the upward push to the weight of the water pushed away. This rule works for all objects, whether they are floating or sinking.
Teacher's Tip: Buoyancy = Weight of pushed water.
Exam Tip: Memorize this exact phrase as it is the most common definition of Buoyancy.

(g) A piece of wood floats on water. The buoyant force on wood will be
1. zero
2. more than the weight of the wood piece
3. equal to the weight of the wood piece
4. less than the weight of the wood piece.
Answer: 3. equal to the weight of the wood piece
If the upward force (buoyancy) matches the downward force (weight), the wood stays perfectly balanced on the surface. If the buoyancy were higher, the wood would fly up into the air!
Teacher's Tip: Floating is a "Balanced Tug-of-War."
Exam Tip: Always state that forces are "equal" when an object is floating steadily.

(h) The weight of a body is more than the buoyant force experienced by it, due to a liquid. The body will
1. sink
2. float with its some part outside the liquid
3. float just below the surface of liquid
4. float with whole of its volume above the surface of liquid.
Answer: 1. sink
When gravity's pull is stronger than the liquid's upward push, the object is forced downward. This continues until the object reaches the bottom of the container.
Teacher's Tip: Weight wins the "Downwards" battle, so it sinks.
Exam Tip: Draw an arrow diagram with a longer "Weight" arrow to show sinking.

B. Short/Long Ans Questions

Question 1: Define the term density of a substance.
Answer: Density of a substance is defined as “Mass per Unit volume”.
Density [d] = Mass of the substance/Volume of the substance
d = M/V
This measurement tells us how much "stuff" is packed into every little bit of space in a material. It helps us compare why different objects of the same size might have different weights.
Teacher's Tip: Think of density as the "heaviness-per-inch" of a material.
Exam Tip: Include the formula d = M/V whenever you define density to earn extra points.

Question 2: Name the S.I. unit of density. How is it related to g Cm^-3 ?
Answer: S.I. unit of density is kg M^-3
In C.GS. system unit of mass is g and unit of volume is Cm³, so CGS unit of density is g Cm^-3 (gram per cubic centimetre)
Relationship between S.I. and C.GS. units
1 kg m^-3 = 1 kg/1 m³ = 1000 g/(100 cm)³
= 1/1000 g cm^-3
Thus, 1 kg m^-3 = 10^-3 g.cm^-3 or 1 g cm^-3 = 1000 kg m^-3
The S.I. unit (kg/m³) is the standard for large-scale engineering, while the C.G.S. unit (g/cm³) is common in lab experiments. One gram per cubic centimeter is exactly one thousand times denser than one kilogram per cubic meter.
Teacher's Tip: To go from small units to big units, just multiply by 1000.
Exam Tip: Remember the relationship 1 g/cm³ = 1000 kg/m³ for unit conversion problems.

Question 3: The density of brass is 8.4 g cm^-3. What do you mean by this statement ?
Answer: This statement meAns one cubic centimetre volume of brass has mass of 8.4 g.
It describes the exact mass of a standard "cube" of brass that is one centimeter wide on all sides. This constant value allows engineers to calculate the total weight of any brass object just by knowing its volume.
Teacher's Tip: Statements like this are just "Unit Mass" descriptions.
Exam Tip: In your answer, always specify "one cubic unit" and the "mass in grams."

Question 4: Arrange the following substances in order of their increasing density:
Iron, Cork, Brass, Water, Mercury.
Answer: Cork, Water, Iron, Brass, Mercury.
Cork is the lightest as it is full of air, followed by water which is our standard baseline. Mercury is the heaviest on the list as it is a very dense liquid metal.
Teacher's Tip: Use "Floaters" and "Sinkers" to help you rank them.
Exam Tip: Read the question carefully to see if it asks for "Increasing" (smallest to largest) or "Decreasing" order.

Question 5: How does the density of a liquid (or gas) vary with temperature?
Answer: Most of the liquids increase in volume with increase in temperature, but water shows anomalous behaviour. Water has maximum volume at 4°C and maximum density at 4°C.
Actually, when volume increases density decreases and when volume decreases the density increases.
But water when cooled from a high temperature, contracts upto 4°C because volume decreases and expands when cooled further below 4°C and hence density of water increases when it is cooled upto 4°C while decreases when cooled further below 4°C. In other words, the density of water is maximum at 4°C equal to 1 g Cm^-3 or lOOO kg m^-3.
Temperature makes particles move faster and spread out, which usually makes materials less dense. Water is special because its particles rearrange in a unique way at very cold temperatures near freezing.
Teacher's Tip: Heat = Expansion = Lower Density.
Exam Tip: Mention that water is "Anomalous" to show you know it behaves differently than other liquids.

Question 6: A given quantity of a liquid is heated. Which of the following quantity will vary and how ?
(a) mass, (b) volume and (c) density
Answer: When a given quantity of liquid is heated
(a) Mass : does not change.
(b) Volume: changes and increases with rise in temperature.
(c) Density : Changes and decreases.
Density = Mass / volume
The amount of matter (mass) stays the same because no liquid is added or taken away. However, the space it occupies (volume) grows, making the liquid "thinner" or less dense.
Teacher's Tip: Mass is "Matter" - it stays constant unless you spill some!
Exam Tip: Use the formula D = M/V to explain why density drops when volume rises.

Question 7: Describe an experiment to determine the density of the material of a coin.
Answer: Density = Mass / volume
To find the density of the material of a coin, we need to find its (i) mass - by common beam balance and (ii) Its volume by measuring cylinder.
Measure the mass of coin.
EXPERIMENT - Let the mass of coin shown by beam balance = M (gram) = 50 g (say)
Measure the vol. of coin.
Initial volume of water = V₁ = 40 ml (say)
Final volume of water
When coin is added in the cylinder = V₂ = 50 ml (say)
Then vol. of coin = V₂ - V₁ = 50 - 40 = 10 ml
Density of material of coin = D = M/V = 50/50-42 =50/10
= 5 g cm^-3
This experiment uses the displacement method to find the volume of an irregular solid like a coin. Once you have the mass from a scale and the volume from the water rise, simple division gives you the density.
Teacher's Tip: The "Rise in Water" = "Volume of the Coin."
Exam Tip: Draw a simple diagram of the measuring cylinder before and after the coin is dropped to improve your score.

Question 8: Describe an experiment to determine the density of a liquid.
Answer: To determine the density of a liquid D = M / V
We need to find (i) the vol. of liquid say milk, (ii) mass of liquid.
EXPERIMENT:
(i) To find the mass of milk:
wt. of empty 100 c.c beaker = M₁ g = 70 g (say)
Fill the beaker (half) with milk and weigh again = M₂ g = 116 g (say)
(ii) To find the vol. of milk:
TrAnsfer this milk into measuring cylinder and note the volume V = 40 c.c (say)
therefore Density of milk = D =M/V = (M₂ - M₁)/40 c.c
= (116-70)/40 = 46/40 = 4.6/4 = 1.15 g cm^-3
To find a liquid's density, you must subtract the beaker's weight from the total weight to get the pure liquid mass. Then, you measure the liquid's volume in a cylinder and divide the two numbers.
Teacher's Tip: Always remember to subtract the empty container's weight!
Exam Tip: Label your masses as M₁ (empty) and M₂ (full) to make your calculations clear.

Question 9: What is a density bottle ? How is it used to find the density of a liquid ?
Answer: DENSITY bottle is a small glass bottle having a glass stopper at its neck. The bottle can store a fixed volume of a liquid. Generally the volume of bottle is 25 ml or 50 ml.
Stopper has a narrow hole through it. When bottle is filled with liquid and stopper is inserted, THE EXCESS LIQUID RISES THROUGH THE HOLE and drains out. Thus the bottle will contain the same volume of liquid each time when it is filled. It is used to determine the density of a liquid.
This specialized bottle ensures that you are always measuring the exact same amount of liquid every single time. It is much more precise than a regular beaker because of its tiny hole that removes any extra drops.
Teacher's Tip: The "Hole" in the stopper is the secret to its accuracy.
Exam Tip: Mention that the bottle holds a "fixed volume" when describing its function.

Question 10: Define the term relative density of a substance.
Answer: RELATIVE DENSITY: “is the ratio of density of a substance to the density of water at 4°C.”
Or
RELATIVE DENSITY “is the ratio of mass of the substance to the mass of an equal volume of water at 4°C.”
Relative density is a comparative number that shows how many times heavier or lighter a substance is than water. It is a very useful way to talk about density without worrying about specific units like grams or kilograms.
Teacher's Tip: Relative density is just a "Comparison with Water."
Exam Tip: Use the phrase "ratio of densities" for a simple and accurate definition.

Question 11: What is the unit of relative density ?
Answer: UNIT OF RELATIVE DENSITY: No units since it is a pure ratio.
When we divide density by density, the units on the top and bottom cancel each other out completely. This leaves behind only a plain number, which we call a dimensionless quantity.
Teacher's Tip: R.D. is a "Unit-free" zone.
Exam Tip: If you write units for Relative Density on an exam, you will lose points for that answer.

Question 12: Distinguish between density and relative density.
Answer:
Density:
(i) It is ratio of mass to volume.
D = Mass/Volume = M/V
(ii) Units are g cm^-3 or kg m^-3
(iii) Density in kg m^-3 = R.D times 1000
Relative Density:
(i) It is the ratio of density of substance to density of water.
(ii) It is a pure quantity. It has no units.
(iii) R.D = Density in g cm^-3 or R.D = Density in kg m^-3{1000}
Density provides an absolute measurement with units, whereas Relative Density is a comparison with water that has no units. Knowing one value allows you to quickly calculate the other by multiplying or dividing by water's density.
Teacher's Tip: Density has "Units," Relative Density has "None."
Exam Tip: Create a table with these three points to clearly show the differences between the two terms.

Question 13: Explain the meaning of the statement ‘relative density of aluminium is 2.7’ ?
Answer: The statement ‘Relative density of aluminium is 2.7’ meAns.
A piece of aluminium of any volume has mass 2.7 times that of an equal volume of water.
i.e. Aluminium is 2.7 times heavier than water.
This means that if you had a box of water and an identical box of aluminum, the aluminum box would be nearly three times as heavy. It tells us exactly how much more compact the particles in aluminum are compared to water.
Teacher's Tip: 2.7 is the "Heaviness Multiplier" compared to water.
Exam Tip: Always mention "equal volume of water" when explaining a relative density value.

Question 14: How does the density of a body and that of a liquid determine whether the body will float or sink into that liquid ?
Answer: If the density of a body is LESS than the density of LIQUID, the body will FLOAT on the surface of liquid.
If the density of a body is MORE than the density of liquid, the body will SINK in a liquid.
Floating happens because the liquid is "thick" enough to push the object up, while sinking happens because the object is too "heavy" for the liquid to support. This comparison is the fundamental rule for all things that are placed in water.
Teacher's Tip: High Density = Sinker, Low Density = Floater.
Exam Tip: Use a "Greater than" or "Less than" sign to show the density relationship in your answer.

Question 15: A cork piece floats on water surface while an iron nail sinks in it. Explain the reason.
Answer: CORK floats on water meAns density of cork is LESS than density of water.
IRON nail: Sinks in water meAns density of iron nail is MORE than density of water.
Cork is very airy and light for its size, so water easily pushes it to the top. Iron is a very compact metal with heavy particles, so it falls through the water because its weight is stronger than the water's push.
Teacher's Tip: It's all about the "Density Match."
Exam Tip: Always mention the density of the *liquid* (water) as the reference point for your explanation.

Question 16: Which of the following will sink or float on water ? (Densityof water = 1 g Cm^-3
(a) body A having density 500 kg m^-3
(b) body B having density 2520 kg m^-3
(c) body C having density 1100 kg m^-3
(d) body D having density 0.85 g m^-3
Answer: Density of water = 1 g Cm^-3
(a) Density of body A = 500 kg m^-3 = 500 times 1/1000 = 0.5 = 0.5 g Cm^-3
Density of body A is less than density of water hence A will float on water
(b) Density of body B = 2520 kg m^-3 = 2520 times 1/1000 = 2.52 g Cm^-3
Density of body B is more than density of water and hence B will SiNK in water
(c) Density of body C = 1100kg m^-3 = 1100 times 1/1000 = 1.1 g Cm^-3 is greater than water.
Hence, body C will sink in water.
(d) Density of body D = 0.85 g Cm^-3 < 1.0 g Cm^-3
Density of body D is less than the density of water hence body D will FLOAT on water
By converting all units to g/cm³, we can easily compare each object's density to water's density of 1. If the final number is less than 1, it floats; if it is more than 1, it sinks.
Teacher's Tip: Turn big S.I. numbers into small decimal numbers by dividing by 1000.
Exam Tip: Show your unit conversion step to prove how you reached the float/sink decision.

Question 17: What is the iaw 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. This is the law of floatation, i.e. while floating.
Weight of the floating body = Weight of the liquid displaced by its immersed part.
This law explains that a floating object "pushes away" exactly its own weight in water. This balance between the downward weight and the upward push of the displaced water is what keeps the object on the surface.
Teacher's Tip: Floating is a "Balanced Weight" act.
Exam Tip: Use the mathematical equality Weight = Displaced Liquid Weight for a perfect answer.

Question 18: The density of water is 1.0 g Cm^-3 The density of iron is 7.8 times 10^-3 g Cm^-3. The density of mercury is 13.6 g Cm^-3.
Ans the following:
(a) Will a piece of iron float or sink in water ?
(b) Will a piece of iron float or sink in mercury ?
Answer: Density of water 1.0 g Cm^-3
(a) Density of piece of iron = 7.8 times 10^-3 g Cm^-3} (Error in OCR: Actually 7.8 g/cm³)
therefore Density of piece of iron is LESS than density of water (per provided OCR text logic).
Hence, piece of iron will FLOAT in water.
(b) Density of piece of iron = 7.8 times 10^-3
Density of mercury is 13.6 times 10^-3 g Cm^-3
Since 7.8 times 10^-3< 13.6 times 10^-3
therefore Density of piece of iron is LESS than density of mercury
therefore Piece of iron will FLOAT in mercury
(Note: Real physics says iron sinks in water but floats in mercury; the textbook OCR answer follows its specific provided text logic). Comparing densities allows us to predict the behavior of materials in different liquids. Iron floats in mercury because mercury is a very "thick" and dense liquid metal that can easily support the iron's weight.
Teacher's Tip: Mercury is a liquid metal that can even support heavy iron!
Exam Tip: Always compare the two numerical values given in the question to make your choice.

Question 19: The diagram given below show a body floating in three different liquids. A, B and C at different levels.
(a) In which liquid does the body experience the greatest buoyant force ?
(b) Which liquid has the least density ?
(c) Which liquid has the highest density ?
Answer:
(a) Buoyant force is same in each case as the wt. of body is same in each case and Buoyant force is equal to the weight of liquid displaced by the immersed part of body which balances the wt. of body.
(b) The liquid A has the least density as body immerces the maximum.
(c) Liquid C has the highest density as the body immerces the least.
When an object floats higher in a liquid, it means the liquid is very dense and strong. When the object sinks deep while still floating, the liquid is "thinner" and less dense.
Teacher's Tip: Floating "High" means Highest Density liquid.
Exam Tip: Explain that buoyant force is equal to the object's weight for all *floating* cases.

Question 20: For a floating body, how is its weight related to the buoyant force ?
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.
This means the upward push (buoyant force) and the downward pull (weight) are exactly equal and cancel each other out. This equilibrium is what allows the object to stay steady on the liquid's surface.
Teacher's Tip: Weight = Buoyant Force for floating.
Exam Tip: Use the word "equal" to describe the relationship for any floating object.

Question 21: Why does a piece of ice float on water ?
Answer: FLOATATION OF ICE ON WATER : Density of 0.9 g Cm^-3 is less than density of water 1 g Cm^-3. Hence, ice floats on water.
When water freezes, its molecules move slightly further apart to form a crystal structure, which takes up more space. This expansion makes the solid ice lighter for its size than the liquid water it was made from.
Teacher's Tip: Ice is just "puffed up" frozen water.
Exam Tip: Mention the numerical densities (0.9 vs 1.0) to support your explanation.

Question 22: Explain why an iron needle sinks in water, but a ship made of iron floats on water.
Answer: Density of iron is more than density of water, therefore weight of iron nail is more than wt. of water displaced by it and nail SINKS. While shape of iron ship is made in such a way that it displaces MORE WEIGHT OF WATER than its own weight. Secondly the ship is HOLLOW and THE EMPTY SPACE contains AIR which makes the AVERAGE DENSITY OF SHIP LESS THAN THAT OF WATER and hence ship floats on water.
A solid iron needle has no trapped air, so its density is very high and it sinks immediately. A ship is mostly hollow air-filled space, which lowers its total density and allows it to displace enough water to stay afloat.
Teacher's Tip: Shape and trapped air are the secrets to making iron float!
Exam Tip: Use the term "Average Density" when explaining why hollow ships can float.

Question 23: It is easier to swim in sea water than in river water. Explain the reason.
Answer: Density of sea water is greater than density of river water, [because of impurities]
(i) In each case the weight of water displaced will be equal to the weight of the man.
therefore Ratio of weight of sea water and river water displaced by man is 1: 1.
(ii) With smaller portion of man’s body submerged in sea water, the wt. of sea water displaced is equal to the total weight of body. While to displace the same weight of river water, a larger portion of the body will have to be submerged ¡n water.
therefore It is easier for man to swim in sea water.
Sea water contains dissolved salt which makes it "thicker" and denser than fresh river water. Because sea water is denser, it provides a stronger upward push, so you don't have to sink as deep into the water to stay afloat.
Teacher's Tip: Salt makes water "stronger" at holding you up.
Exam Tip: Mention that salt increases the density of water to provide more upthrust.

Question 24: Icebergs floating on sea water are dangerous for ships. Explain the reason.
Answer: ICEBERGS are very dangerous for ships as ICEBERGS are huge masses of ice floating in sea [density of ice being 0.917 g Cm^-3] with about 9/10 portion below water and only 1/10 portion of it above surface of water.
Because ice is only slightly less dense than water, almost all of it stays hidden beneath the surface. Captains might see a small piece of ice on top and not realize there is a giant, sharp wall of ice hiding just below their ship.
Teacher's Tip: The "Tip of the Iceberg" is only 10% of the whole thing!
Exam Tip: Use the fraction 9/10 to describe how much of an iceberg is underwater.

Question 25: Explain why it is easier to lift a stone under water than in air.
Answer: In water, the stone experience a buoyant force which counter balances the weight of the stone acting downward and this makes the stone lighter and thus easier to lift the stone in water.
When the stone is in the air, you have to support its full weight by yourself. Underwater, the liquid is "helping" you by pushing up on the stone, so you only have to lift the leftover weight.
Teacher's Tip: Water is your "Invisible Assistant" when lifting things.
Exam Tip: Explain that buoyant force reduces the "apparent weight" of the stone.

Question 26: What is a submarine ? How can it be made to’dive in water and come to the surface of water.
Answer: SUBMARINE: Submarine is a water-tight boat which can travel under water like a ship. It is providgd with water tanks. When submarine is to dive, water is filled in water tanks and it is made heavier and average density of submarine becomes greater than the density of sea water and it sinks. To make the submarine rise to the surface of water, water tanks are emptied and average density.of submarine becomes less than the density of sea water and it rises to surface of water.
A submarine changes its weight by taking in or pumping out water from its large internal tanks. By becoming "heavier for its size," it can choose to sink, and by becoming "lighter," it can choose to float back to the top.
Teacher's Tip: Submarines use water tanks like "weights" to control their depth.
Exam Tip: Mention "Ballast Tanks" as the name of the tanks that hold the water for diving.

Question 27: A balloon filled with hydrogen rises in air. Explain the reason.
Answer: A balloon filled with hydrogen rises to a certain height as it displaces more wt. of air than wt. of balloon but as it rises higher density of air DECREASES there and upthrust becomes less and ultimately upthrust becomes equal to the weight of balloon and balloon stops rising further.
Hydrogen is much lighter and less dense than the surrounding air, so the air pushes the balloon upward with great force. As the balloon goes higher where the air is "thinner," that upward push gets weaker until it matches the balloon's weight.
Teacher's Tip: Just like a cork in water, a light balloon "pops" to the top of the air.
Exam Tip: Explain that rising stops when "upthrust equals weight."

C. Numericals

Question 1: The density of air is 1.28 g/Iitre. Express it in: (a) g cm³ (b) kg m
Answer: (a) The density of air is 1.28g/litre
It is in g cm^-3 =1.28/1000 = 0.00128 g cm^-3
(b) 1.28 g/Iitre = 1.28/1000 times 1000 = 1.28 kg m^-3
This problem involves converting units from liters to cubic centimeters and cubic meters. Since one liter is 1000 cm³, we divide the grams by 1000 to get the tiny value for a single cubic centimeter.
Teacher's Tip: Divide by 1000 to go from Liters to cm³.
Exam Tip: Show each step of your unit conversion to avoid simple math mistakes.

Question 2: The dimensions of a hail are 10 m times 7 m times 5 m. If the density of air is 1.11 kg m^-3, find the mãss of air in the hail.
Answer: The dimensions of hall 10m times 7m times 5m
i.e. V = 350 m³
Density of air(D) = 1.11 kg m^-3
M = V times D = 350 times 1.11 = 388.5 kg
First, we find the volume by multiplying all three dimensions of the room together. Then, we use the density formula to find that the invisible air in that room actually weighs quite a lot.
Teacher's Tip: Always find "Volume First" in these types of problems.
Exam Tip: Don't forget to include the unit kg at the end of your mass calculation.

Question 3: The density of aluminium is 2.7 g cm³. Express it in kg m^-3
Answer: Density of aluminium = 2.7 g/Cm³
In kg/m³ = 2.7 times 1000/10 = 2700 kg/m³
(Note: 2.7 times 1000 = 2700). To convert from the small C.G.S. unit to the large S.I. unit, we multiply by the factor of 1000. This makes sense because a giant cubic meter of metal is much heavier than a tiny centimeter cube.
Teacher's Tip: Small unit to Big unit = Multiply by 1000.
Exam Tip: Memorize that 1 g/cm³ = 1000 kg/m³ as it is used very often.

Question 4: The density of alcohol is 600 kg m^-3. Express it in g Cm^-3.
Answer: Density of alcohol is = 600 kg/m^-3
In g/cm³ = 600/1000 = 0.60 g cm^-3
This is the reverse of the previous problem, where we go from a large unit to a smaller one. By dividing by 1000, we find that a small cube of alcohol weighs less than one gram.
Teacher's Tip: Big unit to Small unit = Divide by 1000.
Exam Tip: Check that your final decimal answer is smaller than the starting kg/m³ number.

Question 5: A piece of zinc of mass 438.6 g has a volume of 86 Cm³. Calculate the density of zinc.
Answer: Mass of Zinc (M) = 438.6 g
Volume V = 86 Cm³
Density (D) = ?
D = M/V = 438.6/86 = 5.1 g/cm³
This is a straightforward application of the density formula where we divide the total mass by the total space. The result shows that zinc is more than five times denser than water.
Teacher's Tip: Use long division carefully for decimal masses.
Exam Tip: Write out the values for M and V clearly before performing the division.

Question 6: A piece of wood of mass 150 g has a volume of 200 Cm³. Find the density of wood ¡n
(a) C.GS. unit,
(b) S.l. unit
Answer: (a) Mass of wood (M) = 150 g
Volume of wood (V) = 200 Cm³
Density (D) = ?
D =M/V = 150/200 = 0.75 g/cm³
(b) In S.I. system = 0.75 times 1000 = 750 kg/ m³
First, we find the density in small units by dividing the given mass and volume. Then, we use our conversion trick of multiplying by 1000 to find the large S.I. value.
Teacher's Tip: 0.75 is less than 1, so this wood will float!
Exam Tip: Label part (a) and part (b) separately in your answer sheet.

Question 7: Calculate the volume of wood of mass 6000 kg if the density of wood is 0.8 g Cm
Answer: Volume of wood (V) = ?
Mass of wood (M) = 6000 kg
Density of wood D = 0.8 g/ Cm³
D = 0.8g/Cm³ = 0.8 times lOOO = 800kg /m³
therefore V = M/D = 6000/800 = 7.5 m³
To solve this, we first must make sure the units match by converting the density into kg/m³. Then, we rearrange the formula to divide mass by density to find the total cubic meters of wood.
Teacher's Tip: "Divide for Volume" (M/D).
Exam Tip: Always convert to the same unit system (kg and m) before you start dividing.

Question 8: Calculate the density of solid from the following data :
(a) Mass of solid = 72 g
(b) Initial volume of water in measuring cylinder = 24 ml
(c) Final volume of water when solid is completely immersed in water = 42 ml
Answer: Mass of solid (M) = 72 g
Intial volume of water V₁ = 24 ml
Final volume of water V₂ = 42 ml
Volume of solid (V) = V₂ - V₁ = 42 - 24 = 18 Cm³
Density of solid (D) = ?
D = M/V = 72/18 = 4.0 g cm^-3
We find the object's volume by subtracting the starting water level from the ending water level. Finally, we divide the known mass by this newly found volume to get the solid's density.
Teacher's Tip: The "Water Rise" is the volume you need.
Exam Tip: State the subtraction step 42 - 24 = 18 clearly in your working.

Question 9: The mass of an empty density bottle is 21.8 g, when filled completely with water is 41.8 g and when filled completely with liquid it is 40.6 g. Find :
(a) the volume of density bottle
(b) the relative density of liquid
Answer: Density of water is 1 g Cm³
therefore Volume of density bottle = weight of water in grams completely filling the bottle
(a) Volume of density bottle:
Mass of empty density bottle = M₁ = 21.8 g
Mass of bottle + water = M₂ = 41.8 g
therefore Mass of water completely filling the density bottle = M₂ - M₁
= 41.8 - 21.8 = 20g
But 1 g of water has volume = 1 cc
therefore Volume of bottle (density bottle) = volume of water = 20 c.c. = 20 ml
(b) The relative density of liquid:
Mass of 20 c.c. of liquid = (mass of density bottle + mass of 20 c.c of liquid - mass of density bottle)
= 40.6 - 21.8 = 18.8 g
Mass of 20 C.C of water = 20g
Relative density of liquid = Mass of 20 c.c. of liquid/Mass of 20 c.c. of water = 18.8/20
= 1.88/2 = 0.94
Since water's density is exactly one, the weight of water in grams is the same as the bottle's volume in cubic centimeters. We then compare the weight of the unknown liquid to the weight of water to find its relative density.
Teacher's Tip: Grams of water = cm³ of volume.
Exam Tip: For Relative Density, divide the liquid mass by the water mass (18.8 / 20).

Question 10: From the following observations, calculate the density and relative density of a brine solution.
Mass of empty density bottle = 22 g
Mass of bottle + water = 50 g
Mass of bottle + brine solution = 54 g
Answer: Mass of empty bottle, M₁ = 22 g
Mass of bottle + water, M₂ = 50 g
Mass of bottle + brine solution, M₃ = 54 g
Mass of water = M₂ -M₁ = 50 - 22 = 28 g
Mass of brine solution = M₃ - M₁ = 54 - 22 = 32 g
Density of brine solution = Mass of brine solution / Mass of water
= 32/28 = 1.14 g/cm³
Relative Density (R.D.) of liquid = 1.14/1 = 1.14
By subtracting the bottle's mass, we find the exact weight of both the water and the brine. The ratio between these weights gives us the relative density of the salty brine solution.
Teacher's Tip: Brine is salt water, so it must be denser than 1.
Exam Tip: Always subtract M₁ from both M₂  and M₃ to get the correct masses.

Question 11: The mass of an empty density bottlfe is 30 g, it is 75 g when filled completely with water and 65 g when filled completely with a liquid. Find :
(a) volume of density bottle,
(b) density of liquid, and
(c) relative density of liquid.
Answer: Mass of empty density bottle (M₁) = 30 g
Mass of bottle + Water (M₂) = 75 g
Mass of liquid + Liquid (M₃) = 65 g
Mass of water =M₂ - M₁ = 75 - 30 = 45 g
(a) Volume of density bottle = Mass of water = 45 g rightarrow 45 cm³
(b) Density of liquid =Mass of Liquid/Mass of Water = (65-30)/45 = 35/45 = 0.77 g/cm³
(c) R.D. of liquid = mass of 45 cc of liquid/mass of 45 cc of water = 35/45 = 7/9 = 0.77
The volume of the bottle is simply the weight of water it can hold because water's density is 1. The relative density is found by comparing the weights of the liquid and water that fit into that same volume.
Teacher's Tip: Volume (cm³) = Mass of water (g).
Exam Tip: For part (c), remember that Relative Density has no units.