Revision: Measurements and Experimentation Physics (English Medium) ICSE Class 9 CISCE

One year is defined as the time in which earth completes one complete revolution around the sun.

“A second is defined as 1/86400 the part of a mean solar day.”
OR
Second may also be defined “as to be equal to the duration of9,192,631,770 vibrations corresponding to the transition between two hyperfine levels of cesium – 133 atoms in the ground state.”

The time taken by the earth to complete one rotation about its own axis is called solar day.

The physical quantities like mass, length and time which do not depend on each other are known as fundamental quantities.

A standard metreis equal to 1650763.73 wavelengths in vacuum, of the radiation from krypton isotope of mass 86.

Measurement is the process of comparison of the given physical quantity with the known standard quantity of the same nature.

The standard metre is defined in terms of the speed of light, according to which one metre is the distance travelled by light in `1/(299,792,458)` of a second in the air (or vacuum).

The quantity of matter contained in a body is known as its mass.

Mass is the measure of the amount of matter in an object.

It is defined as 1/24 the part of the mean solar day.

The average of the varying solar days, when the earth completes one revolution around the sun, is called mean solar day.

It is defined as the 1/1440 part of the mean solar day.

A set of particular physical quantities from which different other units can be obtained, which are neither derived from one another nor resolved into any other units is called fundamental units.

Mass is the amount of matter contained in a body. Its unit is a kilogram (kg).

The density of a substance is defined as the mass of a unit volume of that substance.

`"Density" = "Mass"/"Volume"`

One metre is defined as the distance travelled by light in the air in  `1/(299,792,458)` of a second.

The S. I. unit of length is meter.

Multiple of metre = Kilometre (km).

Submultiple of metre = Centimetre (cm)

A value, quantity, or magnitude in terms of which other values, quantities, or magnitudes are expressed is called a unit.

The smallest value up to which an instrument can measure is called the least count.

Units that are neither fundamental nor derived but are accepted in the SI system (e.g., radian for plane angle, steradian for solid angle) is called supplementary units.

Units that are derived from fundamental units — such as force, which is mass × acceleration — and are expressed algebraically using base units is called derived units.

The basic physical quantities that cannot be derived from other quantities and serve as the foundation for all measurements is called fundamental quantities.

The quantities that are derived from fundamental quantities through mathematical relationships is called derived quantities.

A quantity that can be measured by an instrument and through which we describe the laws of the physical world is called a physical quantity.

Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature.

The smallest value that can be measured by the measuring instrument is called its least count.

One metre is defined as 1,650,763.73 times the wavelength of a specified orange-red spectral line in emission spectrum of Krypton = 86.
OR
One metre is defined as 1,553,164.1 times the wavelength of the red line in the emission spectrum of cadmium.

One metre is defined as the one ten-millionth part of distance from the pole to the equator.

Least count of a vernier callipers is the difference between one main scale division (M.S.D.) and one vernier scale division (V.S.D.)

“The pitch of a screw is the distance moved by the screw in one complete rotation of its head.”
OR
Pitch may also be defined as “the distance between two consecutive threads of screw measured along the axis of the screw.”

Pitch = `"Distance moved by thimble on M.S."/"Number of rotations of thimble"`

A heavy but small sized metallic bob suspended by a light, inextensible and flexible string, which performs oscillatory motion, is called a simple pendulum.

A simple pendulum whose period is two seconds is called a second's pendulum.

An ideal simple pendulum consists a point mass suspended from a perfectly rigid support by weightless, inextensible and perfectly flexible fibre.

An ideal simple pendulum is a heavy particle suspended by a massless, inextensible, flexible string from a rigid support.

A simple pendulum whose period of oscillation is exactly two seconds is called a second’s pendulum.

The frequency with which a body oscillates freely is called natural frequency.

Least count = \[\frac {\text {Smallest reading on main scale}}{\text {No. of divisions on main scale}}\]

Instrument Least Count = \[\frac {\text {Main scale least count}}{\text {Divisions on secondary scale}}\]

\[\text{Actual Reading}=MSR+VSR\times LC\]

\[LC=\frac{\text{Smallest division on main scale}}{\text{Number of divisions on Vernier scale}}\]

\[\text{Actual Reading}=MSR+CSR\times LC\]

\[LC=\frac{\text{Pitch of screw}}{\text{Number of divisions on circular scale}}\]

n = \[\frac {1}{2π}\]\[\sqrt {\frac {g}{l}}\]

T = 2π\[\sqrt{\frac {L_s}{g}}\] = 2 seconds

\[g=\frac{4\pi^2L}{T^2}\]

\[E=PE+KE\]

\[PE=mgh\]

where,

m is mass

g is gravity

h is height

\[KE=\frac{1}{2}mv^2\]

T = 2π\[\sqrt {\frac {l}{g}}\]

• Fundamental (base) units — independent units for fundamental quantities (length, mass, time, etc.)
• Derived units — combinations of base units (e.g., m/s for speed, kg/m³ for density, Pa = kg m⁻¹ s⁻² for pressure)

The SI system has 7 base units:

Temperature Conversions:

K = ^°C + 273.15

\[°F=\frac{9}{5}°C+32\]

• A simple pendulum is a mass on a string swinging under gravity
• Used to determine acceleration due to gravity (g)
• Energy dissipation can be analysed by plotting the square of amplitude vs. time
• At any point: total mechanical energy = PE + KE
• PE depends on height; KE depends on velocity