Revision: Physical World and Measurement Physics (Theory) ISC (Science) ISC Class 11 CISCE

Derived quantities are physical quantities that depend on and can be calculated using fundamental quantities.

The measured value of a physical quantity denoting the number of digits in which we have confidence — where a larger number indicates greater accuracy of measurement — is called significant figures.

The powers to which the fundamental quantities are raised to express the derived unit of a physical quantity is called dimensions.

The study of the relationship between physical quantities with the help of dimensions and units of measurement is called dimensional analysis.

A physical quantity having a fixed value with certain dimensions (e.g., velocity of light in vacuum, gravitational constant) is called a dimensional constant.

A quantity that is variable but has no dimensions (e.g., angle, specific gravity, strain, efficiency of a machine) is called a dimensionless variable.

A constant quantity having no dimensions (e.g., numbers 1, 2, 3, π) is called a dimensionless constant.

Three main applications are:

1. Checking the correctness of the given physical relation
2. To derive the relationship between various physical quantities
3. Conversion of one system of units into the other

Limitations of Dimensional Analysis:

• No information about dimensionless variables and constants.
• Applicable only for quantities of mass (M), length (L), and time (T).
• Cannot establish relations containing addition or subtraction like Y = A + B − C.
• Not applicable for trigonometric, exponential, and logarithmic functions.

• Gravitational force — Force of attraction between any two masses; infinite range; weakest force (strength 10⁻³⁹); acts on all objects in the universe.
• Electromagnetic force — Attractive or repulsive force between charged particles; infinite range; strength 10⁻²; acts only among charged particles.
• Strong nuclear force — Binds protons and neutrons together in the nucleus; short range (10⁻¹⁵ m); strongest of all four forces (strength = 1).
• Weak nuclear force — Responsible for radioactive decay of atoms; very short sub-nuclear range (10⁻¹⁶ m); strength 10⁻¹³; acts among electrons, neutrinos, and subatomic particles.