Units and Measurements Class 11Th JEE

Physical Quantities

Physical quantities are properties of matter and energy that can be measured. Examples of physical quantities include mass, length, time, temperature, and electric current. These quantities are fundamental to the study of physics and are used to describe the behavior and interactions of matter and energy. Physical quantities can be classified as scalars, which have only magnitude, or vectors, which have both magnitude and direction.

Scalar quantities include quantities such as mass and temperature, while vector quantities include quantities such as velocity and force. Physical quantities are often represented by symbols and are accompanied by units of measurement, which are used to express the magnitude of the quantity in terms of a standard unit of measurement.

Fundamental and Derived Quantities

In the study of physics, physical quantities are properties of matter and energy that can be measured. These quantities are classified as either fundamental or derived.

Fundamental physical quantities are basic, independent quantities that cannot be expressed in terms of other quantities. Examples of fundamental physical quantities include mass, length, time, and temperature. These quantities are the building blocks upon which all other physical quantities are based.

Derived physical quantities are quantities that are derived from combinations of fundamental quantities. For example, velocity is a derived quantity that is defined as the displacement of an object per unit of time. It is expressed in terms of the fundamental quantities of length and time. Other examples of derived physical quantities include acceleration, force, and energy.

The International System of Units (SI) is a standardized unit system used to measure physical quantities. The SI system is based on the meter, kilogram, and second as the units for length, mass, and time, respectively.

It's important to note that the distinction between fundamental and derived physical quantities is not always clear-cut. For example, electric charge is sometimes considered a fundamental quantity, while at other times it is considered a derived quantity. The classification of a physical quantity as fundamental or derived may depend on the context in which it is being studied.

In conclusion, fundamental physical quantities are basic, independent quantities that form the foundation of all other physical quantities. Derived physical quantities are quantities that are derived from combinations of fundamental quantities. The International System of Units (SI) is a standardized unit system used to measure physical quantities. The distinction between fundamental and derived physical quantities is not always clear and may depend on the context in which the quantity is being studied.

Supplementary Quantities

Supplementary physical quantities are physical quantities that are derived from two or more base quantities, but which do not have their own unit of measurement in the International System of Units (SI). Instead, they are expressed in terms of the units of the base quantities from which they are derived.

An example of a supplementary physical quantity is the plane angle, which is derived from the base quantities of length and angle. A plane angle is a measure of the amount of rotation between two lines that intersect at a point, and it is expressed in terms of the units of length and angle. For example, a plane angle of 1 radian is defined as the angle formed by two lines that intersect at a point, with one line being the length of 1 meter and the other line being the radius of a circle.

Another example of a supplementary physical quantity is the solid angle, which is derived from the base quantities of length, angle, and area. Solid angle is a measure of the amount of three-dimensional space that is covered by an object, and it is expressed in terms of the units of length, angle, and area.

In conclusion, supplementary physical quantities are physical quantities derived from two or more base quantities but do not have their own unit of measurement in the International System of Units (SI). Examples of supplementary physical quantities include plane angle and solid angle. These quantities are expressed in terms of the units of the base quantities from which they are derived.

Units

Units of physical quantities are standard measures of the magnitude of a physical quantity. They are used to express the size or amount of a physical quantity in terms of a standardized unit of measurement.

There are many different units of physical quantities, and they are used to measure a wide range of physical quantities, including length, mass, time, temperature, and electric current.

One of the most widely used systems of units for measuring physical quantities is the International System of Units (SI), which is based on the meter, kilogram, and second as the units for length, mass, and time, respectively. Other units of physical quantities in the SI system include the kelvin for temperature, the ampere for electric current, and the mole for the amount of substance.

In addition to the SI system, other systems of units are used to measure physical quantities. For example, the imperial system of units, which is used in the United States, includes units such as the foot for length, the pound for mass, and the mile per hour for speed.

It's important to note that the choice of unit for a physical quantity depends on the context in which it is being measured. For example, the meter is the standard unit of length in the SI system, but in some contexts, it may be more convenient to use other units of length, such as the inch or the mile.

In conclusion, units of physical quantities are standard measures of the magnitude of a physical quantity, and they are used to express the size or amount of a physical quantity in terms of a standardized unit of measurement. The International System of Units (SI) is one of the most widely used systems of units for measuring physical quantities, and other systems of units are used in different contexts. The choice of unit for a physical quantity depends on the context in which it is being measured.

Conversion of Units

Converting between units of measurement involves expressing a physical quantity in one unit of measurement in terms of another unit of measurement. There are several methods for converting between units of measurement, including using conversion factors and using conversion charts or tables. It's important to pay attention to the dimensions of the physical quantities being converted to ensure that the conversion is valid.

Principle of Homogeneity

The principle of homogeneity states that the dimensions of a physical quantity are independent of the units used to measure it. This principle is important because it allows us to compare physical quantities regardless of the units used to measure them.

For example, the dimension of length is always L, regardless of whether it is measured in meters, kilometers, or inches. Similarly, the dimension of mass is always M, regardless of whether it is measured in kilograms, grams, or pounds.

The principle of homogeneity is useful because it allows us to convert between different units of measurement for a physical quantity. For example, if we know that the dimension of a physical quantity is L, we can convert between different units of length (such as meters and inches) by using conversion factors.

In conclusion, the principle of homogeneity states that the dimensions of a physical quantity are independent of the units used to measure it. This principle is important because it allows us to compare physical quantities and convert between different units of measurement.

Dimensions and Dimensional Formula

In the study of physics, dimensions are a way of classifying physical quantities based on the type of physical quantity being measured. For example, the dimension of length is represented by the letter L, while the dimension of mass is represented by the letter M.

A dimensional formula is an expression that shows the dimensions of a physical quantity in terms of the dimensions of other physical quantities. Dimensional formulas are used to relate physical quantities that have different dimensions, such as length and time.

For example, the dimensional formula for velocity is given by [L]/[T], where [L] represents the dimension of length and [T] represents the dimension of time. This dimensional formula tells us that velocity is a quantity that is derived from the base quantities of length and time.

Other examples of dimensional formulas include:

• Acceleration: [L]/[T]^2
• Force: [M]*[L]/[T]^2
• Energy: [M]*[L]^2/[T]^2

It's important to note that dimensional formulas are not used to calculate the actual value of a physical quantity. They are used to determine the dimensions of a physical quantity and to ensure that equations involving physical quantities are dimensionally consistent.

In conclusion, dimensions are a way of classifying physical quantities based on the type of physical quantity being measured. A dimensional formula is an expression that shows the dimensions of a physical quantity in terms of the dimensions of other physical quantities. Dimensional formulas are used to relate physical quantities that have different dimensions and to ensure that equations involving physical quantities are dimensionally consistent.

Here are the dimensional formulas for some important physical quantities:

• Length: [L]
• Mass: [M]
• Time: [T]
• Temperature: [K]
• Electric current: [I]
• Amount of substance: [mol]
• Luminous intensity: [Cd]
• Velocity: [L]/[T]
• Acceleration: [L]/[T]^2
• Force: [M]*[L]/[T]^2
• Energy: [M]*[L]^2/[T]^2
• Pressure: [M]*[L]/[T]^2
• Power: [M]*[L]^2/[T]^3
• Work: [M]*[L]^2/[T]^2
• Heat: [M]*[L]^2/[T]^2
• Frequency: 1/[T]
• Wave number: 1/[L]