Essential Astronomy Facts and Celestial Mechanics
Earth and Celestial Coordinates
What is the meridian?
The great circle passing through the poles of Earth is called the meridian.
Calculating zenith distance
The zenith distance (Z) is given by the formula: Z = 90° – A, where A is the altitude.
Earth’s spin axis
The spin axis of Earth intersects the celestial sphere at the North Celestial Pole and the South Celestial Pole.
Solar time measurements
- Mean solar day: 24 hours.
- Sidereal day: Approximately 23 hours, 56 minutes, and 4 seconds.
Astronomy and Telescopes
Ecliptic
Read MoreFluid Mechanics: Laplacian Operator and Laminar Flow Analysis
What is the Laplacian Operator?
The 3D balance equation in ψ terms is:
∂ψ/∂t + (v·∇)ψ = ψ̇a + (∇·δ∇ψ) − ψ(∇·v)
If diffusivity δ is constant, then:
(∇·δ∇ψ) = δ(∇·∇ψ)
Substituting this, we get:
∂ψ/∂t + (v·∇ψ) = ψ̇a + δ(∇·∇ψ) − ψ(∇·v)
The term (∇·∇ψ) is defined as:
∇[ i(∂ψ/∂x) + j(∂ψ/∂y) + k(∂ψ/∂z) ] = ∂²ψ/∂x² + ∂²ψ/∂y² + ∂²ψ/∂z²
The dot product (∇·∇) operating on a scalar is given the special symbol
Read MoreCore Principles of Thermodynamics: Laws and Processes
1. The First Law of Thermodynamics
The First Law of Thermodynamics is a specific application of the Law of Conservation of Energy. It establishes that energy cannot be created or destroyed, only converted from one form to another. In a thermodynamic system, it describes the relationship between heat, work, and internal energy.
Statement of the Law
The change in the internal energy of a closed system is equal to the heat supplied to the system minus the work done by the system on its surroundings.
Mathematical
Read MorePhysics Short Questions and Answers for Exam Preparation
SECTION B: SHORT QUESTIONS
Q1. Define the Following with Examples
- Frequency (f): The number of complete waves passing a point per second. Unit: Hertz (Hz). Formula: f = 1/T. Example: 50 cycles per second = 50 Hz.
- Wavelength (λ): The distance between two consecutive crests or troughs. Unit: Metre (m). Formula: v = fλ. Example: Visible light is 400–700 nm.
- Time Period (T): The time taken to complete one full vibration. Unit: Second (s). Formula: T = 1/f. Example: A pendulum swing taking 2 seconds.
Essential Physics Concepts: Circuits, Waves, and Mechanics
1. Ohm’s Law, Series, and Parallel Circuits
Q: State Ohm’s Law and derive formulas for series and parallel combinations of resistors.
Answer:
Ohm’s Law:
Ohm’s Law states that the current through a conductor is directly proportional to the potential difference across its ends, provided the temperature remains constant.
Formula: V = IR
Series Combination
In a series circuit, resistors are connected end-to-end.
- The same current flows through all resistors.
- Total voltage is the sum of individual voltages:
Dielectric Polarization, Semiconductors, and Superconductivity
Explain the concept of polarisation in dielectrics. Illustrate and discuss the different types with
diagrams and formulas.The Concept of Polarisation
In a dielectric material, polarization is defined as the process of creating or inducing electric dipoles using an external electric field.
When an external electric field is applied, it interacts with the dielectric in two primary ways:
1 Distortion
The field distorts the internal charge distribution, producing an induced dipole moment in each molecule.