MAGNETISM & ELECTROMAGNETISM

Chapter – 14

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Q.1: What is flux density and how is it related to the number of lines of induction expressed in Webers?
Ans: Magnetic flux density $B$ is the magnetic flux per unit area $(B = \Phi / A)$. The unit of flux density is Weber per $m^2$ (or tesla, $T$). Magnetic flux is the total number of magnetic lines of induction passing perpendicularly through an area $(\Phi = B \times A)$. Its SI unit is ‘Weber’ $(1 Wb = 1 T \cdot m^2)$. Hence magnetic flux density refers to the number of lines of induction (in Webers) per square meter.

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Q.2: Charged particles fired in a vacuum tube hit a fluorescent screen. Will it be possible to know whether they are positive or negative?
Ans: Yes, the charge on particles in motion can be found by applying a magnetic field perpendicular to the motion of the charges and by observing the deflection. A positive charge in an inward perpendicular magnetic field is deflected upward. In an electric field, a positive charge will be deflected towards the negative side (plate).

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Q.3: Beams of electrons and protons are made to move with the same velocity at right angles to a uniform magnetic field of induction. Which of them will suffer a greater deflection? What will be the effect on the beam of electrons if their velocity is doubled?
Ans: The radius of the circular path of a particle moving in a magnetic field is $r = \frac{mv}{Bq}$. Thus $r$ is proportional to $m$, but deflection is proportional to $1/m$. Thus, the electron, being lighter, will be deflected more than the proton.

Since $r \propto v$, if velocity is doubled, the radius will also be doubled; but deflection is halved.

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Q.4: A circular loop of wire hangs by a thread in a vertical plane. An electric current is maintained in the loop anti-clockwise when looking at the front face. To what direction will the front face or the coil turn in the earth’s magnetic field?
Ans: Toward the geographic north pole.

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Q.5: Imagine that the room in which you are seated is filled with a uniform magnetic field pointing vertically upward. A loop of wire, which is free to rotate about the horizontal axis is placed through its center parallel to its length, has its plane horizontal. For what direction of current in the loop, as viewed from above, will the loop be in a stable equilibrium with respect to forces and torque of magnetic origin?
Ans: Anti-clockwise.

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Q.6: Two identical loops, one of copper and the other of aluminum, are similarly rotated in a magnetic field of induction. Explain the reason for their different behavior. Is an electric generator a ‘generator of electricity’? Where is the electricity before it is generated? What do such machines generate?
Ans: Since the conductivities of copper and aluminum are different, they show different behavior with the induced e.m.f. As the conductivity of copper is higher than that of aluminum, a copper loop will have a greater induced current than an identical aluminum loop moving with the same speed in the same magnetic field. An electric generator is not a generator of electricity (i.e., quantity of charge). Electricity is present in the conducting coil of the generator before it was driven in an electrical circuit. A generator provides e.m.f. to drift the haphazardly moving electrons in the conducting coil. In fact, a generator converts mechanical energy into energy of moving charges.

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Q.7: A loosely wound helical spring of a stiff wire is mounted vertically with the lower end just touching mercury in a dish. When a current is started in the spring, it excretes a vibratory motion with its lower end jumping out and into mercury. Explain the reason for this behavior?
Ans: When a current is passed through a helical spring, whose one end is just above a mercury pool, a magnetic field is produced. The current through all the loops is in the same direction. This produces attraction between them, so its length decreases. The dipping and moving out of the mercury causes the circuit to break. Due to elasticity, the helix regains its original length. The electrical contact is established again. The process is repeated, so the helix vibrates up and down.

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Q.8: What is the mechanism of transfer of energy between the primary and secondary windings of a transformer? A certain amount of power is to be transferred over a long distance. If the voltage is stepped up 10 times, how is the transmission line loss reduced?
Ans: Electromagnetic induction is the phenomenon responsible for the transfer of energy between the primary windings (one circuit) to the secondary windings by means of a changing magnetic field which links the two coils. The mutual induction transforms the voltage or e.m.f. of large or similar value due to a different number of turns in the primary and secondary coils.

Suppose a power line has input power $P$. The same power can be carried at low current if the voltage is made high. Input current $I_1 \propto \frac{P}{V_1}$. If voltage is stepped up 10 times:

$$V_2 = 10V_1, \quad I_2 = \frac{P}{V_2} = \frac{P}{10V_1}, \quad \text{Thus } \frac{I_2}{I_1} = \frac{P / 10V_1}{P / V_1} = \frac{1}{10}$$

When the current is 10 times smaller, the power loss as heat in the wires $(I^2R)$ is $(10)^2$, i.e., 100 times smaller.

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Q.9: What is the difference between magnetic field a.c. generators? What is meant by the frequency of alternating current?
Ans: An alternating current generator that uses a permanent magnet to provide the magnetic flux rather than an electromagnet is called ‘magnetic’. It is used in systems like petrol engines, motorbikes, and motorboats. The a.c. generator that employs electromagnets is called “alternate.” It has a rotating field magnet (called rotor) and a stationary armature (called stator) or vice versa.

Alternating current (a.c.) is produced by a voltage source whose terminal polarity reverses with time. The number of cycles per second made by an a.c. is called its frequency $f$. Its unit is hertz (Hz). We have $f = 1/T$, and an a.c. reverses its polarity $2f$ times per second. An a.c. with a frequency of 50 Hz has a time period of $\frac{1}{50} = 0.02$ seconds. This a.c. reaches zero every 0.01 seconds.

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Q.10: In what direction are the magnetic field lines surrounding a straight wire carrying current that is flowing directly towards you?
Ans: Anti-clockwise (using the right-hand rule).

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Q.11: What kind of field or fields does or do surround a moving electric charge?
Ans: When an electric charge is in motion, it is surrounded by an electrostatic field as well as a magnetic field.

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Q.12: Can an electron at rest be set in motion with a magnet?
Ans: No. When an electron is at rest, it has no magnetic field $(F = qvB = 0 \text{ if } v = 0)$. So, in the absence of any magnetic field of its own, it cannot interact with a magnet.

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Q.13: A beam of electron is directed towards a horizontal wire in which the current flows from left or right. In what direction is the beam deflected?
Ans: If the beam is parallel to the wire, it will follow a spiral path; and if it is perpendicular to the wire, it will adopt a circular path.

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Q.14: A charged particle is moving in a circle under the influence of a uniform magnetic field. If an electric field is turned on at that point along the same direction as the magnetic field, what path will the charged particle take?
Ans: When a charged particle is moving in a circle under the influence of a uniform magnetic field; and if an electric field is applied along the same direction, it will exert lateral force on the charged particle. Consequently, the charged particle will move in a cyclic path in the form of a spiral (called helix).

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Q.15: A loop of wire is suspended between the poles of a magnet with its plane parallel to the pole faces. What happens if direct current is passed through the coil? What will happen if an alternating current is passed instead?
Ans: When d.c. passes through the loop such that its magnetic field is: (i) opposite the direction of the field of the magnet, the coil will turn round through 180° and then will stay in equilibrium. (ii) Along the field of the magnet, the coil will stay in equilibrium. However, when an a.c. is passed through the loop, it will remain in its initial position (with slight vibration).

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Q.16: A current-carrying wire is placed in a magnetic field. How must it be oriented so that the force acting on it is zero or is maximum?
Ans:

• Force will be zero if theta is equal to zero (parallel to B);
• Force will be maximum if theta is equal to 90° (perpendicular to B).

Q.17: Why is the magnetic field strength greater inside a current-carrying loop of wire?
Ans: In a loop of wire, the direction of current in the opposite sides of the loop is opposite to each other. This is analogous to two parallel conductors carrying current in opposite directions. The directions of both the magnetic fields are along the same direction in the loop. This increases the strength of the field.

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Q.18: What exactly does a transformer transform?
Ans: A transformer transforms the magnitude of alternating voltage and current.

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Q.19: Can an efficient transformer step up energy? Explain.
Ans: Transformers cannot charge energy. In an ideal transformer, the power remains constant, i.e., power input equals power output $(V_p I_p = V_s I_s)$. Thus it cannot step up energy.

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Q.20: In what three ways can a voltage be induced in a wire?
Ans:

• By moving a wire in a magnetic field.
• By moving a magnet near it.
• By changing current through a circuit near it.

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Q.21: Does the voltage output of a generator change if its speed of rotation is increased?
Ans: Yes, because induced e.m.f. = $BNA \, \text{omega} \sin \, (\text{omega} \, \text{time})$. Thus, an e.m.f. increases if the speed of rotation “Omega” is increased.

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Q.22: When a beam of electrons is shot into a certain region of space, the electrons travel a straight line through the region. Can we conclude that in the region there is no electric field? No magnetic field?
Ans: There are two possibilities:

• No electric or magnetic field is present.
• The electric and magnetic fields are at right angles to each other, and their strengths are exerting equal but opposite forces on the electron beam.

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Q.23: A copper ring is placed above a solenoid with an iron core to increase its field. When the current is turned on in the solenoid, the copper ring moves upward. Why?
Ans: When current in a solenoid (with an iron core) increases, an induced current is produced in a copper ring (held above it) in the opposite direction. This is analogous to opposite currents in two parallel wires. Thus they develop similar poles and repel each other. Consequently, the ring moves up.

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Q.24: A very long copper pipe is held vertically. Describe the motion of a bar magnet dropped lengthwise down the pipe?
Ans: Suppose a bar magnet falls through a very big copper pipe (under gravity). When the magnet is well inside the pipe, the configuration of the magnetic field remains the same. So it will fall freely with acceleration of gravity only.

Q.25: A solenoid is viewed in such a way that the solenoid current appears clockwise to the viewer. What is the direction of the field within the solenoid?
Ans: The end viewed will develop south polarity. So the direction of the magnetic field will be away from the viewer inside the solenoid.

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Q.26: A hollow copper tube carries. Why is $B = 0$ inside the tube? Is $B$ non-zero outside the tube?
Ans: The charges always reside or move on the outer of a conductor. Since inside the tube, current is zero, hence $B = 0$ (according to Ampere’s law). The outer surface of the tube behaves like a set of parallel wires carrying current down their length. The magnetic field outside the tube exists, and its direction is given by the right-hand grip rule.

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Q.27: Can a current-carrying coil be used as a compass?
Ans: A current-carrying coil behaves like a bar magnet (magnet dipole). Thus when it is suspended freely, it can be used as a compass.

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Q.28: When a charged particle enters a magnetic field, it is deflected by the magnetic force? Can the magnetic force do work on the moving charged particle?
Ans: No, magnetic force can do no work on a moving charged particle because it is always perpendicular to the velocity of the particle.

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Q.29: If both electric field (E) and magnetic field (B) act on a charged particle, what is the total force on it?
Ans: The total force is $F = qE + q (v \times B)$. This force is called the Lorenz force.

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Q.30: Can an isolated magnetic pole (monopole) exist? What is the source of the magnetic fields?
Ans: No, magnetic monopoles cannot exist. The only known source of magnetic fields are magnetic dipoles (current loops), even in magnetic materials.

Physical Quantities and Measurement

 PHYSICS 9TH - Short / Detailed Question Answers

Q.1: What is Science?

Ans: Science:
The word science refers to the study of a fact by collecting information through observation, presenting it in a mathematical way, justifying the idea with experiment, and finally making a conclusion about the fact.

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Q.2: Define Physics.

Ans: Physics:
One of the most basic and ancient sciences is Physics. It can be defined as: Physics is the branch of science which observes the nature, represents it mathematically, and concludes with the experiment.

In other words, Physics is the branch of science that deals with studies of matter, its composition, properties, and interaction with energy.

It deals with the behavior and structure of matter and the energy that derives from matter. Physics is the branch of natural science that studies matter, its motion, its behavior through space and time, and the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

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Q.3: Name and define the branches of Physics.

Ans:
Since the beginning of the universe, the structure of the universe is very straightforward. The classification of physics was not that easy, but as the physicists explained the universe, they classified Physics into many branches. These branches show the spectrum and scope of Physics around us and help scientists describe ideas in a well-organized way. The branches of Physics are classified on the basis of different areas of study with different approaches. The main branches of Physics are as follows.

Mechanics:
This branch of physics is mainly concerned with the laws of motion and gravitation.

Thermodynamics:
Thermodynamics deals with heat and temperature and their relation to energy and work.

Electricity:
Electricity is the study of the properties of charges in rest and motion.

Magnetism:
Magnetism is the study of the magnetic properties of materials.

Atomic Physics:
Atomic physics deals with the composition, structure, and properties of the atom.

Optics:
Optics studies physical aspects of light and its properties with the help of optical instruments.

Sound:
Sound is the study of production, properties, and application of sound waves.

Nuclear Physics:
Nuclear physics deals with the constituents, structure, behavior, and interaction of atomic nuclei.

Particle Physics:
Particle physics studies the elementary constituents of matter and radiation, and the interaction between them.

Astrophysics:
The study of celestial objects with the help of the laws of physics is known as Astrophysics.

Plasma Physics:
The study of the state of matter and its properties is known as Plasma Physics.

Geophysics:
The study of the internal structure of the Earth is known as Geophysics.

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Q.4: What is the importance of Physics?

Ans: Importance of Physics in Science, Technology, and Society:
Society's reliance on technology represents the importance of physics in daily life. Many aspects of modern society would not have been possible without the important scientific discoveries made in the past. These discoveries became the foundation on which current technologies were developed.

Discoveries such as magnetism, electricity, conductors, and others made modern conveniences, such as television, computers, smartphones, medical instruments, other business and home technologies possible. Moreover, modern means of transportation, such as aircraft and telecommunications, have drawn people across the world closer together, all relying on concepts of physics.

It is a matter of fact that Physics can be considered as the mother of all sciences. The beauty of physics lies in its laws that govern this whole universe, from an atom to large-scale galaxies, and in its experiments, from home to large-scale experiment labs.

Q.5: In how many categories physicists are categorized?

Ans:
Physicists are categorized into two categories: those who observe nature, solve its mysteries with available and missing information, and present their theories with a mathematical approach. They are known as theoretical physicists. Others who are more interested in testing those theories with experiments are known as experimental physicists.

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Q.6: What are physical quantities?

Ans:
Physics is much concerned with matter and energy and the interaction between them, which is explained with the help of describing the mathematical relations between various physical quantities. All physical quantities are important for describing the nature around us.

Definition:
Physics defines the mathematical relation between physical quantities. A physical quantity is a physical property of a phenomenon, body, or substance that can be quantified by measurement.

A physical quantity is a physical property of a phenomenon, body, or substance that can be quantified by measurement.

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Q.7: Define fundamental and derived physical quantities.

Ans:
Physical quantities are classified into two categories:

1. Fundamental quantities
2. Derived physical quantities

Fundamental Quantities:
Physical quantities that cannot be explained by other physical quantities are called fundamental physical quantities.

There are seven fundamental physical quantities listed in the following table along with their units:

Fundamental Quantities	S.I. Unit	Symbol of Unit
Length	meter	m
Mass	Kilogram	Kg
Time	Second	s
Electric current	Ampere	A
Temperature	Kelvin	K
Amount of substance	mole	mole
Luminous intensity	candela	cd

Derived Physical Quantities:
Physical quantities that are explained on the basis of fundamental physical quantities are called derived physical quantities.

Derived Quantities	S.I Unit	Symbol of Unit
Volume	Cubic Meter	m³
Velocity	meter per second	m/s
Force	Newton	N
Density	Kilogram per cubic meter	Kg/m³
Acceleration	meter per second square	m/s²

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Q.8: What do you know about scientific or physical instruments?

Ans:
All physical quantities are either calculated mathematically or measured through an instrument. Scientists, engineers, doctors, and others like blacksmiths, carpenters, and goldsmiths, even workers and ordinary human beings, measure those physical quantities with the help of instruments. For instance, our doctor uses a thermometer to tell our body temperature, a carpenter uses the inch-tape to measure the length of wood required for furniture.

A puncture mender uses air gauges to check the air pressure in the tire. Similarly, a chemical engineer uses a hydrometer for describing the density of a liquid.

Measuring physical quantities correctly with an instrument is not an easy task for scientists and engineers. Scientists are seriously concerned with the accuracy of the instrument and its synchronization. Moreover, the instruments they design, mostly for their own sake of research, often make their way into the commercial market. Many of the instruments we use today are inventions by pioneers of science. Usually, the basic physical quantities we use in our daily life are measured with basic and simple instruments.

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Q.9: Define least count.

Ans: Least Count:
The use of every instrument is restricted by the smallest measurement that it can perform, which is called least count.

Q.10: Define length and their units.

Ans:
If there is any measurement that has proven to be useful to humanity, it is length. For example, units of length include the inch, foot, yard, mile, meter, etc.

Definition of Length:
Length is defined as the minimum distance between two points lying on the same plane.

S.I. Unit of Length:
The meter (m) is the S.I. unit of length and is defined as: The length of the path traveled by light in a vacuum during the time interval of 1/299,792,458 of a second.

The basic measurement of length can be obtained with the help of a meter rod or an inch tape.

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Q.11: What is a meter rule? How can we use a meter rule to measure length?

Ans: Meter Rule:
A meter rule is a device used to measure the length of different objects. A meter rule of length 1 meter is equal to 100 centimeters (cm). On a meter rule, each cm is divided further into 10 divisions, which are called millimeters (mm). So, a meter rule can measure up to 1 mm as the smallest reading. It is made up of a long rigid piece of wood or steel.

The zero-end of the meter rule is first aligned with one end of the object, and the reading is taken where the other end of the object meets the meter rule.

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Q.12: What is a Vernier Caliper? How can we read it?

Ans: Vernier Caliper:
The Vernier Caliper is a precision instrument that can be used to measure internal and external distances extremely accurately. It has both an imperial and metric scale. A Vernier caliper has main jaws that are used for measuring external diameter, as well as smaller jaws that are used for measuring the internal diameter of objects. Some models also have a depth gauge. The main scale is fixed in place, while the Vernier scale is the name for the sliding scale that opens and closes the jaws.

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Q.13: What is a Micrometer Screw Gauge? How can we read it?

Ans: Micrometer Screw Gauge:
A screw gauge is extensively used in the engineering field for obtaining precision measurements. A micrometer screw gauge is used for measuring extremely small dimensions. A screw gauge can even measure dimensions smaller than those measured by a Vernier caliper.

Q.14: What do you understand by the term "the standard mass"?

Ans: The Standard of Mass:
The kilogram is the S.I. unit of mass and is equal to the mass of the international prototype of the kilogram, a platinum-iridium standard that is kept at the International Bureau of Weights and Measures.

A kilogram is a cylinder of special metal about 39 millimeters wide by 39 millimeters tall that serves as the world's mass standard. Each country that subscribed to the International Metric Convention was assigned one or more copies of the international standards; these are known as National Prototype Meter and Kilogram.

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Q.15: What is a physical balance? How does it work?

Ans: Physical Balance:
A physical balance is an instrument used for the measurement of mass. It is mostly used in a laboratory. It works on the principle of moments. It consists of a light and rigid beam of brass, a metallic pillar, a wooden base, two pans, a metallic pointer, and an ivory scale.

The plumb line indicates whether the balance is horizontal. In an ideal condition, the plumb line is aligned with the end of the knob fixed with the pillar. When the beam is horizontal, the pointer remains on the zero mark on the ivory scale. The whole box has leveling screws at the bottom to set it to horizontal. The device is enclosed in a glass box to avoid wind effects.

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Q.16: What is an electronic balance?

Ans: The Electronic Balance:
The digital mass meter is an electronic instrument configured with integrated circuits and works on the principle of balancing the forces.

The device is turned on and set to zero, then the object is placed on the plate. The reading on the screen gives the mass of the object. The electronic balance is available in different ranges of measurement, such as microgram, milligram, and kilogram, etc.

Q.17: Describe the standard of time and define the second.

Ans: The Standard of Time:
Before 1960, the standard of time was defined in terms of the mean solar day for the year 1900. The rotation of the Earth is now known to vary slightly with time, and this motion is not a good one to use for defining a time standard.

In 1960, the second was redefined to take advantage of the high precision attainable in a device known as an atomic clock, which uses the frequency of the caesium-133 atom as the "reference clock."

Second:
The second is now defined as 9,192,631,770 times the period of vibration of radiation from the caesium atom.

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Q.18: What is a stopwatch? What is meant by "human reaction time"?

Ans: Stop Watch:
A stopwatch is used to measure the time interval for two events. There are two types of stopwatches:

1. Mechanical stopwatch
2. Digital stopwatch

Mechanical / Analogue Stopwatch:
A mechanical stopwatch can measure a time interval of up to 0.1 second. It has a knob that is used to wind the spring that powers the watch. It can also be used as a start-stop and reset button. The watch starts when the knob is pressed once. When pressed the second time, the watch stops, while the third press brings the needle back to zero.

Digital Stopwatch:
A digital stopwatch can measure a time interval of up to 0.01 second. It starts to indicate the time elapsed as the start/stop button is pressed. As soon as the start/stop button is pressed again, it stops and indicates the time interval recorded by it between the start and stop of an event. A reset button restores its initial zero settings. Nowadays, almost all mobile phones have a stopwatch function.

Human Reaction Time:
As an analogue or digital watch is operated by human action, i.e., they have to be started or stopped by hand, this causes a random error in the measurement of time, called human reaction time. For most people, human reaction time is about 0.3 to 0.5 seconds. Therefore, for more accurate measurement of time intervals, light gates can be used.

Q.19: What instrument will you choose to measure the height of your friend?

Ans:
To measure the height of our friend, we can use a meter rule or inch tape. When our height is measured at the doctor's clinic, we usually stand next to a device called a stadiometer.

A stadiometer is a long ruler attached to the wall. It has a sliding horizontal headpiece that's adjusted to rest on top of our head. It's a quick way of accurately measuring our height.

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Q.20: Can you describe how many seconds there are in a year?

Ans:
One calendar common year has 365 days:

1 common year = 365 days (365 days) × (24 hours/day) × (3600 seconds/hour) = 31,536,000 seconds.

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Q.21: Which instrument will you choose to measure your mass?

Ans:
The scientific word for how much an object weighs on a scale is "mass." Here we can use the words "weight" and "mass" interchangeably because both are used in everyday language. For example, "I weigh 70 kg" or "the car’s mass is 1 tonne."

Bathroom scales are used to measure a person’s weight. They can be analogue or digital. Bathroom scales usually show units in kilograms and grams.

Q.22: Why prefixes are used for expressing units?

Ans: Prefixes:
The physical quantities are described by scientists in terms of magnitudes and units. Units play a vital role in expressing a quantity, either base or derived. Prefixes are useful for expressing units of physical quantities that are either very big or very small. A unit prefix is a specifier. It indicates multiples or fractions of the units.

Units of various sizes are commonly formed by such prefixes. The prefixes of the metric system, such as kilo and millimeters, represent multiplication by a power of ten. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognized by standards organizations.

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Table of Prefixes:

Prefix	Symbol	Meaning	Multiplier (Numerical)	Multiplier Exponential
tera	T	Trillion	1,000,000,000,000	10¹²
giga	G	Billion	1,000,000,000	10⁹
mega	M	Million	1,000,000	10⁶
kilo	K	Thousand	1,000	10³
hecto	H	Hundred	100	10²
deka	da	Ten	10	10¹
Unit	1		1
*deci	d	Tenth	0.1	10⁻¹
*centi	c	Hundredth	0.01	10⁻²
*milli	m	Thousandth	0.001	10⁻³
*micro	μ	Millionth	0.000001	10⁻⁶
*nano	n	Billionth	0.000000001	10⁻⁹
pico	p	Trillionth	0.000000000001	10⁻¹²
femto	f	Quadrillionth	0.000000000000001	10⁻¹⁵
atto	a	Quintillionth	0.000000000000000001	10⁻¹⁸

Q.23: Can you tell if the size of a nucleus is up to 1W1m, what prefix shall we use to describe its size?

Ans:
Femtometer (fm)
$10^{-15}$ meters

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Q.24: Describe scientific notation.

Ans: Scientific Notation:
Scientific notation or the standard form is a simple method of writing very large numbers or very small numbers. In this method, numbers are written as powers of ten. Thus, the calculation of very large or very small numbers becomes easy.

Numbers in Scientific Notation are made up of three parts:

1. The Coefficient: The coefficient must be equal to or (not zero) greater than one.
2. The Base: The base must be 10.
3. The Exponent: The exponent can be negative or positive.

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Q.25: Why are physicists concerned about the property of matter, which may help to define the nature of the matter in terms of its mass and space?

Ans:
The three common phases or states of matter are solid, liquid, and gas. A solid maintains a fixed shape and a fixed size, even if the same force is applied; it does not readily change its volume. A liquid does not maintain a fixed shape; it takes on the shape of its container. But, like a solid, it is not readily compressible, and its volume can be changed significantly only by a large force. However, gas has neither a fixed shape nor a fixed volume—it will expand to fill its container.

Often we find large-weight woods floating on the surface of water. However, an iron needle sinks into the water. We say iron is "heavier" than wood. This cannot really be true; rather, we should say iron is "denser" than wood. Physicists are concerned with a physical quantity, a property of matter that may help to define the nature of the matter in terms of its mass and space.

Q.26: How can we measure the volume of solids, liquids, and gases?

Ans: Measuring the Volume:
For density to be measured or calculated, we first need to find the volume of substances. Most solid shapes have formulas for their volume, which are obtained through different parameters such as radius, height, depth, width, base, and length. For irregular objects, liquids, and gases, this approach is unusual. The volume of liquids can be measured with the help of cylinders and beakers.

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Q.27: How can we use a measuring cylinder to measure the volume of liquids?

Ans: Measuring Cylinder:
A measuring cylinder is a glass or plastic cylinder with a scale graduated in cubic centimeters or milliliters (ml). It is used to find the volume of liquids. When a liquid is poured, it rises to a certain height in the cylinder. The level of liquid in the cylinder is noted, and the volume of the liquid is obtained. To read the volume correctly, we should keep the eye level with the bottom of the meniscus of the liquid surface.

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The Volume of Liquid:
A volume of about a liter or so can be measured using a measuring cylinder. When the liquid is poured into the cylinder, the level on the scale gives the volume. Most measuring cylinders have scales marked in milliliters (ml) or cubic centimeters (cm³). It should be noted that while recording the value from the cylinder, the eyes should maintain the level with the value. Angular observation may result in a false reading of the volume.

Q.28: How can we measure the volume of a regular and irregular solid?

Ans:

Regular Solid:
If an object has a regular shape, its volume can be calculated. For instance:

• Volume of a rectangular block = length × width × height
• Volume of a cylinder = π × radius² × height

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Irregular Solid:
For an irregular solid, its volume is calculated by lowering the object in a partially filled measuring cylinder. The rise in the level on the volume scale gives the volume of that object. Thus, the volume of an irregular solid is calculated by subtracting the original volume of liquid from the raised volume of liquid.

The total volume is found. The volume of the solid is measured in a separate experiment and then subtracted from the total volume.

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Quick Lab:

• Take a measuring cylinder of 1-liter capacity at the full place and set it in a beaker.
• Fill the cylinder full with water.
• Pour a stone of irregular shape into it gradually.
• As you pour the stone into the cylinder, the water from the cylinder drops into the beaker.
• Drop the stone in the cylinder completely.
• Calculate the volume of water ejected out of the cylinder.
• The volume of water ejected is the volume of the stone.

Q.29: Define density. How can we measure density?

Ans: Density:
The term density of a substance is defined as the mass of a substance (m) per unit volume (V). It is denoted by the Greek letter ρ (rho).

$$ρ = \frac{m}{V}$$

Density is a characteristic property of any pure substance. Objects made of a particular pure substance such as pure gold can have any size or mass, but its density will be the same for each. Following the above equation, the mass of a substance can be expressed as:

$$m = ρV$$

S.I. Unit of Density:
The S.I. unit for density is kg/m³ (kgm⁻³). Sometimes, the density of substances is given in g/cm³. The density of aluminum is 2.70 g/cm³, which is equal to 2700 kg/m³.

Measuring the Density:
It is to be noted that there are two ways of finding the density of a substance, either mathematically or experimentally by taking the density of water at 4°C as a reference, which is sometimes known as relative density or specific gravity. It has no unit. It is a number whose value is the same as that of the density in g/cm³.

$$\text{Relative density} = \frac{\text{density of substance}}{\text{density of water}}$$

More Information:
In Jordan, there is a sea known as the 'Dead Sea.' The human in that sea, while swimming, does not sink! This is because the water of the sea is much more salty than normal, which raises the density of the water.

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Q.30: Can you tell how a hot air balloon works?

Ans:
As air is heated, it becomes less dense than the surrounding cooler air. The less-dense hot air has enough lifting power to cause the balloon to float and rise into the air.

Q.31: Define and describe significant figures.

Ans: Significant Figures:
Engineers and scientists around the world work with numbers representing a large or small magnitude of a physical quantity. Engineers are, however, more interested in the accuracy of a value as they mostly work on estimation, but scientists, especially physicists, are more concerned with the accuracy of these numbers. For instance, an engineer records the speed of the wind and explains it as an average. On the other hand, for the physicist, the speed of the Earth on its course, the speed of light in a vacuum, the mass or charge on an electron is not just a matter of numbers but accurate numbers.

Definition:
The numbers of reliably known digits in a value are known as significant figures.

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Rules for determining significant figures:

Rule	Example
1. All non-zeros are significant.	2.25 (3 significant figures)
2. Leading zeros are not significant.	0.0000034 (2 significant figures)
3. Trailing zeros are significant ONLY if an explicit decimal point is present.	200 (1 significant figure), 2000 (3 significant figures), 2.00 (3 significant figures)
4. Trapped zeros are significant.	0.00509 (3 significant figures), 2045 (4 significant figures)

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Q.32: A pendulum swings as shown in the given figure from X to Y and back to X again.

(i) What would be the most accurate way of measuring time for one oscillation with the help of a stopwatch?
(a) Record time for 10 oscillations and multiply by 10
(b) Record time for 10 oscillations and divide by 10
(c) Record time for one oscillation
(d) Record time for X to Y and double it

(ii) Suggest an instrument for measuring time period more accurately.

Ans:
(i) A simple way to measure the pendulum’s period fairly precisely is to start the pendulum swinging and measure the time required for a large number of full swings — 40, 50, or so. Choose the number of swings so that the total time for the measurement is 40 seconds or more.

Dividing the total time by the number of full swings will give the period.
(a) to (d) For these questions, we need readings, so you have to perform practical work to answer them.

(ii) Today, the usual measuring instruments for time are clocks and watches. For a highly accurate measurement of time, an atomic clock is used. For more accurate measurement of time intervals, light gates can be used.