Important Scientific Laws and Theories

Archimedes’ Principle

1. Archimedes’ Principle: It states that a body wholly or partially immersed in a liquid experiences an upward thrust, which is equal to the weight of the liquid displaced by it. Thus, the body appears to lose a part of its weight. This loss in weight is equal to the weight of the liquid  displaced by the body.

 Aufbau Principle

2. Aufbau Principle: It states that, in an unexcited atom, electrons reside in the lowest energy orbitals available to them.

Avogadro’s Law

3. Avogadro’s Law: It states that equal volumes of all gases under similar conditions of temperature and pressure contain equal number of molecules.

 Brownian Motion

4. Brownian Motion: It is a zigzag, irregular motion exhibited by small solid particles when suspended in a liquid or gas due to irregular bombardment by the liquid or gas molecules.

Bernoulli’s Principle

5. Bernoulli’s Principle: It states that as the speed of a moving fluid,liquid, or gas increases, the pressure within the fluid decreases. The aerodynamic lift on the wing of an aeroplane is also explained in part by this principle.

Boyle’s Law

6. Boyle’s Law: It states that temperature remaining constant, volume of a given mass of a gas varies inversely with the pressure of the gas.

Thus, PV = K (constant), where, P = Pressure and V = Volume.

Charles’s Law

7. Charles’s Law: It states that pressure remaining constant, the volume of a given mass of gas increases or decreases by 1/273 part of its volume at 0 degree celsius for each degree celsius rise or fall of its temperature.

Coulomb’s Law

8. Coulomb’s Law: It states that force of attraction or repulsion between two charges is proportional to the amount of charge on both charges and inversely proportional to the square of the distance between them.

Heisenberg Principle (Uncertainty principle)

9. Heisenberg Principle (Uncertainty principle): It is impossible to accurately determine with accuracy, both the position and the momentum of a particle such as electron simultaneously.

Gay-Lussac’s Law of Combining Volumes

10. Gay-Lussac’s Law of Combining Volumes: Gases react together in volumes which bear simple whole number ratios to one another and also to the volumes of the products, if gaseous—all the volumes being measured under similar conditions of temperature and pressure.

Graham’s Law of Diffusion

11. Graham’s Law of Diffusion: It states that the rates of diffusion of gases are inversely proportional to the square roots of their densities under similar conditions of temperature and pressure.

Physical Quantity |Science in Everyday Life

Physical Quantity

❖❖ It is the physical property of a body, substance, or of a phenomenon, that can be quantified by measurement.

Measurement of a Physical Quantity

❖❖ It is done by assigning a value to a physical quantity by comparing itwith a standard value (calibrated value) of that physical quantity whichis called unit.

❖❖ To know the value (or magnitude) of a physical quantity, we generally measure it in different systems of units.

System Units

❖❖ Physical quantities are measured in four systems of units:

●● CGS (Centimetre, Gram, Second): In this system of units, Length,

Mass, and Time are measured in Centimetre, Gram, and Second,

respectively. CGS system is also called the Metric or French System

of Units.

●● FPS (Foot, Pound, Second): In this system of units, Length, Mass, and

Time are measured in Foot, Pound, and Second. FPS system is also

called British System of Units.

●● MKS (Metre, Kilogram, Second): In this system of units, Length,

Mass, and Time are measured in Metre, Kilogram, and Second.

●● SI system (International System of Units) of units was adopted and

accepted on the basis of a comprehensive consensus. In fact, the

SI system is an extended and modified form of the MKS system.

Fundamental Quantities in SI System

S. No. Fundamental Quantity Fundamental unit Symbol

1. Length Metre m

2. Mass Kilogram kg

3. Time Second s

4. Electric current Ampere A

5. Temperature Kelvin K

Unit of Length

❖❖ The SI unit of length is metre (m). One metre is the distance travelled by

light in vacuum in 1 /299792458 of a second.

Facts to Know!

❖❖ A vector is a quantity that has magnitude as well as direction, e.g., force, position, etc.

❖❖ A scalar quantity has only magnitude and no direction, e.g., temperature,

mass, etc.

Other Units of Length

❖❖ Light year: The distance travelled by light in one year in vacuum.

1 light year = 9.46 × 1015 m

❖❖ Parsec (Parallactic Second): The distance at which an arc of length equals

to one astronomical unit subtends an angle of one second at a point.

Units of Length or Distance

1 Nautical Mile 1.825 km

1 Mile 1.609 km

1 km 1000 m

1 cm 10–2 m

1 mm 10–3 m

1 mm 10–6 m

1 Nano metre 10–9 m

1 Å 10–10 m

1 pico metre 10–12 m

1 Fermi metre 10–15 m

❖❖ Area is related with square of length; some units of area are:

●● 1 acre = 4047 m2

●● 1 hectare = 104 m2

❖❖ Volume is related with cube of length; some units of volume are:

●● 1 cubic centimetre (cm3) = 1 millilitre (mL)

●● 1 Gallon = 3.7 Litre

●● 1 barrel = 159 Litre

Unit of Mass

❖❖ The SI unit of mass is kilogram. One kilogram is defined as the mass of

5.0188 × 1025 atoms of carbon-12.

Other Units of Mass

❖❖ 1 gram = 10–3 kg

❖❖ 1 ounce-oz = 28.35 gram

❖❖ 1 milligram = 10–6 kg

❖❖ 1 atomic mass unit (amu) = 1.66 × 10–27 kg

❖❖ 1 quintal = 100 kg

❖❖ 1 tonne or metric ton = 1000 kg

❖❖ 1 Chandra Sekhar Limit (CSL) = 1.4 times the mass of sun = 2.8 × 1030 kg

Unit of Time

❖❖ The SI unit of time is second. One second is defined as 1/86400 part of a mean solar day.

Other Units of Time

❖❖ 1 picosecond =10–12 s

❖❖ 1 nanosecond = 10–9 s

❖❖ 1 microsecond = 10–6 s

❖❖ 1 hour = 60 minute = 3600 seconds

❖❖ 1 day = 24 hours = 1440 minute = 86400 seconds

❖❖ 1 solar month = 30 or 31 days

❖❖ 1 lunar month = 29.5 days or 4 weeks

❖❖ 1 year = 13 lunar months and 1 day = 12 solar months = 365.25 days

❖❖ 1 leap year = 366 days

Indian Measurement System

1. System in the Ancient Period: 8 Parmanus = 1 Rajahkan (dust particle

from the wheel of a chariot)

8 Rajahkans = 1 Liksha (egg of lice)

8 Likshas = 1 Yookamadhya

8 Yookamadhyas = 1 Yavamadhya

8 Yavamadhyas = 1 Angul

8 Anguls = 1 Dhanurmushti

2. System in the Medieval Period: Gaz was divided into 24 equal parts, and

each part was called Tassuj.

Motion, Force, and Laws of Motion

❖❖ The change of position or the movement of any object from one position to another position with respect to the observer is called Motion. It can be described in terms of the distance moved or displacement.

❖❖ Motion of any body is defined by its position with respect to its observer.

❖❖ Distance is the actual path travelled by the object from its initial point to

final point, and it is a scalar quantity.

❖❖ Displacement is the shortest straight line path between initial and final positions. If the initial and final positions are the same, then the displacement is zero.

❖❖ Distance depends upon path but displacement does not.

❖❖ Distance is greater than or equal to displacement; they are equal only

when in straight line motion, without taking a U-turn.

❖❖ The SI Unit of both distance and displacement is Metre (m).

Uniform and Non-uniform Motions

❖❖ Uniform motion is the motion in which equal distance is covered in equal

time intervals.

❖❖ Non-uniform motion on the other hand is one in which an unequal distance is covered in equal intervals of time.

Speed and Velocity

❖❖ Speed is the distance travelled by an object per unit of time.

Speed = Distance travelled/Time taken

❖❖ Average speed, the ratio of total distance travelled to the total time taken by the body to cover it, is known as the average speed.

Average speed = Total distance travelled/Total time taken

❖❖ Instantaneous Speed is the speed of the object at a particular moment in time.

❖❖ Velocity is the displacement of the body per unit time.

Velocity = Displacement of object/Time taken

❖❖ Average Velocity: the ratio of the total displacement to the total time taken by the body is the average velocity.

Average Velocity = Total Displacement/Total time taken

❖❖ Instantaneous Velocity is the velocity of an object in motion at a particular point in time.

❖❖ Speed is a scalar quantity, and its SI unit is metre/ sec, while on the other hand, velocity is a vector

quantity, and its SI unit is metre/sec.

Acceleration

❖❖ Acceleration is the measure of change of velocity with respect to time. It is also called the rate of change of velocity.

Acceleration = (Final velocity – Initial velocity)/Total time taken

❖❖ SI unit of acceleration is metre/sec2. It is a vector quantity.

❖❖ Acceleration has the same direction as velocity if the velocity increases.

Whereas it has opposite direction as velocity if velocity decreases, and in this case, the acceleration is negative. Negative acceleration is also known as Retardation or De-acceleration.

Uniform and Non-uniform Acceleration

❖❖ When the velocity of a body changes by equal amounts in equal time intervals, the acceleration is said to be uniform.

❖❖ When the velocity of a body changes by unequal amounts in equal time intervals, the acceleration is said to be non-uniform.

❖❖ Velocity has both magnitude and direction while speed has only magnitude and no direction.

Velocity has the same direction as displacement.

❖❖ Average speed is always greater than the average velocity except in the case of straight line motion without a U-turn, where both are equal.

❖❖ When a body returns to its initial position, the average velocity will be zero but the average speed will not be zero.

❖❖ When the direction of motion changes, the velocity also changes.