This initial chapter lays the groundwork for understanding the physical world by homing in on two pivotal concepts: physical quantities and measurement. At its core, a physical quantity is any observable attribute of an object or event that can be expressed numerically – think of its length, weight, or temperature. Measurement, on the other hand, is presented as a comparative process, where an unknown quantity is evaluated against a known, consistent benchmark.
The text emphasizes the critical role of standardized units in ensuring accuracy and clarity, both in scientific pursuits and in daily life. The International System of Units (SI units), the globally accepted standard, is introduced, along with its fundamental components: the meter for length, the kilogram for mass, the second for time, and the Kelvin for temperature. The chapter further clarifies how “derived units” are constructed by combining these basic units to describe more intricate quantities, with speed (a combination of length and time) serving as a prime example.
Practical aspects of measurement are also addressed. The chapter offers an overview of common measuring tools such as scales for weight, cylinders for volume, thermometers for temperature, and clocks for time, alongside advice on their correct application for precise readings. To deepen our grasp of measurement precision, two crucial concepts are briefly explained: “least count,” which signifies the smallest division an instrument can accurately measure, and “significant figures,” representing the trustworthy digits in a measurement. In essence, this introductory chapter furnishes the essential knowledge needed to quantify and characterize the properties of our physical environment.
Test yourself
A. Objective Questions
1. Write true or false for each statement
(a) Equal volumes of the two different substances have equal masses.
Ans: False.
Equal volumes of the two different substances have different masses.
(b) The density of a piece of brass will change by changing its size or shape.
Ans: False.
(c) The density of a liquid decreases with increase in its temperature.
Ans: True.
(d) Relative density of water is 1.0.
Ans: True.
(e) Relative density of a substance is expressed in g cm-3.
Ans: False.
Relative density of a substance has no units.
(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.
Ans: False.
The buoyant force is equal to the weight of the liquid displaced by the immersed part of the body.
(g) A body experiences the same buoyant force while floating in water or alcohol.
Ans: True.
(h) A body experiences the same buoyant force when it floats or sinks in water.
Ans: False.
(i) A body floats in a liquid when its weight becomes equal to the weight of the liquid displaced by its submerged part. .
Ans: True.
(j) A body while floating, sinks deeper in a liquid of low density than in a liquid of high density.
Ans: True.
2. Fill in the blanks
(a) 1 kg is the mass of _______ml of water at 4°C
Ans: 1000
(b) Mass = density x__________.
Ans: volume
(c) The S.I. unit of density is _________
Ans: Kg m-3
(d) The density of water is __________Kg m-3.
Ans: 1000
(e) 1 g cm-3 = ________ Kg m-3.
Ans: 1000
(f) The density of a body which sinks in water is ______ than 1000 Kg m-3.
Ans: more
(g) A body sinks in a liquid A, but floats in a liquid B. The density of liquid A is _________than the density of liquid B.
Ans: less
(h) A body X sinks in water, but a body Y floats on water. The density of body X is ____________ than the density of body Y.
Ans: more
(i) The buoyant force experienced by a body when floating in saltwater is __________ to or same that of when floating in pure water.
Ans: equal
(j) The weight of a body floating in a liquid is_____.
Ans: zero
3. Match the following
4. Select the correct alternative
(a) The correct relation is
- Density = Mass x Volume
- Mass = Density x Volume
- Volume = Density x Mass
- Density = Mass + Volume
Ans: Mass = Density x Volume
(b) The relative density of alcohol is 0.8. Its density is
- 0.8
- 800 kg nr3
- 800 g cm-3
- 0.8 kg m-3
Ans: 800 kg nr3
(c) A block of wood of density 0.8 g cm-3 has a volume of 60 cm3. The mass of block is
- 60.8 g
- 75 g
- 48 g
- 0.013 g
Ans: 48 g
(d) The density of aluminium is 2.7 g cm-3 and that of brass 8.4 g cm’3. The correct statement is
- Equal masses of aluminium and brass have equal volumes
- The mass of a certain volume of brass is more than the mass of equal volume of aluminium.
- The volume of a certain mass of brass is more than the volume of equal mass of aluminium.
- Equal volumes of aluminium and brass have equal masses.
Ans: The mass of a certain volume of brass is more than the mass of equal volume of aluminium.
(e) A density bottle has a marking 25 mL on it. It means that:
- the mass of density bottle is 25 g
- the density bottle will store 25 ml of any liquid in it
- the density bottle will store 25 ml of water, but more volume of liquid denser than water.
- the density bottle will store 25 ml of water, but more volume of a liquid lighter than water.
Ans: the density bottle will store 25 ml of any liquid in it
(f) The correct statement is
- The buoyant force on a body is equal to the volume of the liquid displaced by it ‘
- The buoyant force on a body is equal to the volume of the body
- The buoyant force on a body is equal to the weight of the liquid displaced by it
- The buoyant force on a body is always equal to the weight of the body.
Ans: The buoyant force on a body is equal to the weight of the liquid displaced by it
(g) A piece of wood floats on water. The buoyant force on wood will be
- zero
- more than the weight of the wood piece
- equal to the weight of the wood piece
- less than the weight of the wood piece.
Ans: equal to the weight of the wood piece
(h) The weight of a body is more than the buoyant force experienced by it, due to a liquid. The body will
- sink
- float with its some part outside the liquid
- float just below the surface of liquid
- float with the whole of its volume above the surface of liquid.
Ans: sink
B. Short/Long Ans Questions
1)Define the term density of a substance.
Ans: Density quantifies the amount of matter within a specific volume. Calculated as mass divided by volume (D=m/V), it’s typically expressed in units like g/cm$^3$ for solids and liquids, or g/L and kg/m$^3$ for gases. A key characteristic is its intensive nature, meaning density remains constant irrespective of the sample size, making it a valuable tool for material identification.
2)Name the S.I. unit of density. How is it related to g Cm-3 ?
Ans: To convert density from SI (kg/m$^3$) to CGS (g/cm$^3$), use the relationship 1 kg/m3=0.001 g/cm3. Conversely, to convert from CGS to SI, 1 g/cm3=1000 kg/m3.
3)The density of brass is 8.4 g cm-3. What do you mean by this statement ?
Ans: The statement that the density of brass is 8.4 g cm$^{-3}$ means that for every cubic centimeter of brass, you would find 8.4 grams of mass.
In simpler terms, it tells us how much “stuff” (mass) is packed into a given amount of space (volume) for brass. Imagine you have a small, perfectly shaped cube of brass, exactly one centimeter on each side. If you were to weigh that tiny cube, its mass would be 8.4 grams.
This value is a characteristic property of brass. It doesn’t matter if you have a tiny brass screw or a large brass statue; the ratio of its mass to its volume will always be 8.4 g cm$^{-3}$ (assuming it’s pure brass and at a standard temperature and pressure). Materials with higher densities have more mass packed into the same volume compared to materials with lower densities.
4)Arrange the following substances in order of their increasing density:
Iron, Cork, Brass, Water, Mercury.
Ans: Cork, Water, Iron, Brass, Mercury.
5)How does the density of a liquid (or gas) vary with temperature?
Ans: Water’s density increases as it cools, reaching its maximum at 4°C. Uniquely, below this point, it expands, causing its density to decrease until it freezes at 0°C. This unusual property is why ice is less dense than liquid water and floats.
6)A given quantity of a liquid is heated. Which of the following quantities will vary and how ?
(a) mass, (b) volume and (c) density
Ans:(a) Mass remains unchanged; heating adds energy, not material.
(b) Volume increases as particles gain energy and spread out.
(c) Density decreases since the same mass now occupies a larger space.
7)Describe an experiment to determine the density of the material of a coin.
Ans: To find the density of a coin, you’ll need its mass and volume. First, use a digital balance to measure the coin’s mass accurately. Next, determine its volume using water displacement. Fill a measuring cylinder with enough water to submerge the coin and note the initial water level. Carefully drop the coin into the cylinder and record the new water level. The difference between the final and initial levels is the coin’s volume. Finally, calculate the density by dividing the mass (in grams) by the volume (in milliliters or cubic centimeters).
8)Describe an experiment to determine the density of a liquid.
Ans: Experiment to Find Density of Milk
1. Mass of Milk:
- Weight of empty beaker (M1) = 70 g
- Weight of beaker + milk (M2) = 116 g
- Mass of milk (M) = M2−M1=116 g−70 g=46 g
2. Volume of Milk:
- Measured volume (V) = 40 cc (cubic centimeters)
3. Density Calculation:
The formula for density is: D=VM
Substituting the measured values: D=40 cc46 g=1.15 g/cm3
Result:
The density of milk is 1.15 g/cm³.
9)What is a density bottle ? How is it used to find the density of a liquid ?
Ans: A density bottle, usually 25 or 50 ml, is a glass flask with a unique stopper. This stopper has a fine hole, allowing any extra liquid to overflow when sealed, guaranteeing the bottle always contains an exact volume. This precise design makes it perfect for determining the density of liquids accurately.
10)Define the term relative density of a substance.
Ans: Relative density, often called specific gravity, is a straightforward comparison. It’s simply how dense a substance is compared to water at its densest point (4°C). You can think of it as either comparing their densities directly, or by seeing how the mass of a substance stacks up against the mass of the same amount of water at that specific temperature.
11)What is the unit of relative density ?
Ans: Relative density has no unit. It is a dimensionless quantity because it is the ratio of two densities, and the units cancel each other out.
12)Distinguish between density and relative density.
Ans:
13)Explain the meaning of the statement ‘relative density of aluminium is 2.7’ ?
Ans: The statement “Relative density of aluminium is 2.7” simply means aluminum is 2.7 times denser than water. Consequently, the same volume of aluminum will have 2.7 times the mass of that volume of water.
14)How does the density of a body and that of a liquid determine whether the body will float or sink into that liquid ?
Ans: An object’s fate in a liquid is determined by its density. Lighter objects float due to the liquid’s buoyant force, while heavier objects sink when their weight exceeds this force, a principle derived from Archimedes’ findings.
15)A cork piece floats on the water surface while an iron nail sinks in it. Explain the reason.
Ans: An object’s fate in water—whether it floats or sinks—is determined by how its density stacks up against water’s. If it’s lighter for its size than water, it’ll bob on the surface; if it’s heavier, it’ll plunge to the bottom.
16)Which of the following will sink or float on water ? (Density of 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
Ans:(a) Body A has a density of 0.5 g cm−3, which is less than water’s density. Therefore, Body A will float.
(b) Body B, with a density of 2.52 g cm−3, is denser than water. Consequently, Body B will sink.
(c) Body C’s density is 1.1 g cm−3, exceeding that of water. Thus, Body C will sink.
(d) Body D, at 0.85 g cm−3, is less dense than water. As a result, Body D will float.
17)What is the law of floatation ?
Ans: When an object floats, the buoyant force from the displaced fluid perfectly balances its weight. This means the weight of the fluid pushed aside by the submerged portion of the object is equal to the object’s total weight. Consequently, a floating object always displaces an amount of fluid equal to its own weight.
18)The density of water is 1.0 g Cm-3. The density of iron is 7.8 × 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 ?
Ans: (a)The density of iron (7.8 g/cm³) is higher than water (1.0 g/cm³), so iron will sink in water.
(b)The density of iron (7.8 g/cm³) is less than mercury (13.6 g/cm³), so iron will float in mercury.
19)The diagram given below shows 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 ?
Ans:(a) The buoyant force is identical in all cases because the object is floating, meaning the buoyant force always equals the object’s weight.
(b) Liquid A is the least dense since the object sinks deepest into it to achieve flotation.
(c) Liquid C is the most dense as the object floats highest, displacing the least volume of liquid.
20)For a floating body, how is its weight related to the buoyant force ?
Ans: When a body floats, the buoyant force, which is the weight of the liquid displaced by the submerged portion, perfectly balances the total weight of the body. This is a direct consequence of Archimedes’ principle, ensuring equilibrium.
21)Why does a piece of ice float on water ?
Ans: Ice floats because it’s less dense than water. As water freezes, its molecules spread out into an open, crystalline structure. This expansion means a given mass of ice occupies more volume than the same mass of liquid water, making ice lighter and buoyant.
22)Explain why an iron needle sinks in water, but a ship made of iron floats on water.
Ans: An iron needle sinks due to its concentrated mass, making it denser than water. A ship, conversely, floats because its design incorporates a large air-filled volume, significantly reducing its average density and enabling it to displace enough water for buoyancy.
23)It is easier to swim in sea water than in river water. Explain the reason.
Ans:(i) Ratio of Weights of Displaced Water: The ratio is 1:1. A floating person always displaces a weight of water equal to their own weight, regardless of the water’s density.
(ii) Ease of Swimming in Seawater vs. River Water: Swimming is easier in seawater. Seawater is denser, providing greater buoyancy, so less of the body needs to be submerged to float. River water, being less dense, offers less buoyant force, making it slightly harder to stay afloat.
24)Icebergs floating on sea water are dangerous for ships. Explain the reason.
Ans: Icebergs, with a density of 0.917 g cm−3, are dangerous to ships because approximately nine-tenths of their mass remains submerged. Only about one-tenth is visible above the waterline, making them a significant hidden hazard for navigation.
25)Explain why it is easier to lift a stone under water than in air.
Ans: Lifting a stone in water feels easier because water exerts an upward buoyant force, which directly opposes part of the stone’s downward weight. This reduction in effective weight makes the stone feel significantly lighter compared to lifting it in air.
26)What is a submarine ? How can it be made to’ dive in water and come to the surface of water?
Ans: SUBMARINE: Submarines are sealed craft built for underwater travel. They manage buoyancy by taking on water to dive (increasing density) and expelling it to surface (decreasing density). Crew use a periscope for surface viewing when submerged.
27)A balloon filled with hydrogen rises in the air. Explain the reason.
Ans: As a hydrogen balloon rises, decreasing atmospheric density diminishes the buoyant force. It stops ascending when this reduced lift equals its total weight.
C. Numericals
1)The density of air is 1.28 g/ Iitre. Express it in:
(a) g cm3 (b) kg m
Ans:
(a) The density of air is I .28g/litre
2)The dimensions of a hail are 10 m × 7 m × 5 m. If the density of air is 1.11 kg m-3, find the mãss of air in the hail.
Ans: The dimensions of hall 10m × 7m × 5m
i.e. V350 m3
Density of air(D)= 1.11 kg m-3
M = V × D 350 × 1.11 =388.5 kg
3)The density of aluminium is 2.7 g cm3. Express it in kg m-3
Ans: Density of aluminium = 2.7 g/Cm3
4)The density of alcohol is 600 kg m-3. Express it in g Cm-3.
Ans: Density of alcohol is = 600 kg/m-3
5)A piece of zinc of mass 438.6 g has a volume of 86 Cm3. Calculate the density of zinc.
Ans: Mass of Zinc (M) = 438.6 g
Volume V = 86 Cm3
Density (D) = ?
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
Ans:(a) Mass of wood (M) = 150 g
Volume of wood (V) = 200 Cm3
Density (D) =?
(b) In S.I. system = 0.75 × 1000 750 kg/ m3
7)Calculate the volume of wood of mass 6000 kg if the density of wood is 0.8 g Cm-3
Ans: Volume of wood (V) = ?
Mass of wood (M) = 6000 kg
Density of wood D = 0.8 g/ Cm3
D= O.8g/Cm3=o.8 × IOOO = 800 kg /m3
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
Ans: Mass of solid (M) = 72 g
Initial 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) = ?
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
Ans: Density of water is 1 g Cm3
∴ 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
∴ Mass of water completely fih1ig the density bottle = M2 — M1
=41.8 —21.8
20g
But 1 g of water has volume = 1 cc
∴ 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
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
Ans: 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
11)The mass of an empty density bottle 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.
Ans: Mass of empty density bottle (M1) =30 g
Mass of bottle + Water (M2) 75 g
Mass of liquid + Liquid x (M3)= 65 g
Mass of water=M2—M1=75—30=45 g
(a) Volume of density bottle = Mass of water 45 g
(b) Density of Liquid x = ?
(c) Mass of water in the density bottle =75 — 30 = 45 g
∴ Volume of water in density bottle = 45 cc
and mass of equal volume of liquid in density bottle 65—30 = 35g
