Dimensional Formulae of Physical Quantities

Study Notes

Physical Quantities and Their Dimensional Formulae

Area is the product of length and breadth, measured in square meters (L²) and has a dimensional formula of [M⁰ L² T⁰].
Volume is the product of length, breadth, and height, measured in cubic meters (L³) and has a dimensional formula of [M⁰ L³ T⁰].
Mass density is the ratio of mass to volume, measured in kilograms per cubic meter (ML⁻³) and has a dimensional formula of [ML⁻³ T⁰].
Frequency is the reciprocal of time period, measured in hertz (Hz) and has a dimensional formula of [M⁰ L⁰ T⁻¹].
Velocity and speed are measured as displacement per unit time, in meters per second (m/s) and have a dimensional formula of [M⁰ L¹ T⁻¹].
Acceleration is the rate of change of velocity, measured in meters per second squared (m/s²) and has a dimensional formula of [M⁰ L¹ T⁻²].
Force is the product of mass and acceleration, measured in newtons (N) and has a dimensional formula of [M¹ L¹ T⁻²].
Impulse is the product of force and time, measured in newton-seconds (Ns) and has a dimensional formula of [M¹ L¹ T⁻¹].
Work and energy are measured as the product of force and distance, in joules (J) and have a dimensional formula of [M¹ L² T⁻²].
Power is the rate of doing work, measured in watts (W) and has a dimensional formula of [M¹ L² T⁻³].
Momentum is the product of mass and velocity, measured in kilogram-meters per second (kgm/s) and has a dimensional formula of [M¹ L¹ T⁻¹].
Pressure and stress are measured as force per unit area, in pascals (Pa) and have a dimensional formula of [M¹ L⁻¹ T⁻²].
Strain is a dimensionless quantity, measured as the ratio of change in dimension to original dimension.
Modulus of elasticity is the ratio of stress to strain, measured in pascals (Pa) and has a dimensional formula of [M¹ L⁻¹ T⁻²].
Surface tension is measured as force per unit length, in newtons per meter (N/m) and has a dimensional formula of [M¹ L⁰ T⁻²].
Surface energy is the energy per unit area, measured in joules per square meter (J/m²) and has a dimensional formula of [M¹ L⁰ T⁻²].
Velocity gradient is the rate of change of velocity with distance, measured in meters per second per meter (m/s/m) and has a dimensional formula of [M⁰ L⁰ T⁻¹].
Pressure gradient is the rate of change of pressure with distance, measured in pascals per meter (Pa/m) and has a dimensional formula of [M¹ L⁻² T⁻²].
Pressure energy is the product of pressure and volume, measured in joules (J) and has a dimensional formula of [M¹ L² T⁻²].
Coefficient of viscosity is measured as the ratio of force per unit area to velocity gradient, in pascal-seconds (Pa·s) and has a dimensional formula of [M¹ L⁻¹ T⁻¹].
Angle and angular displacement are dimensionless quantities, measured as the ratio of arc length to radius.

Description

This quiz covers the dimensional formulae of various physical quantities such as area, volume, mass density, frequency, and velocity. It provides relationships between physical quantities and their dimensions.