Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Gravitational force → Universal gravitation ↓


Black holes and gravitational lensing


Black holes and gravitational lensing are two fascinating phenomena that arise from the universal law of gravity. These concepts are linked to the fundamentals of physics and provide a glimpse into the workings of our universe. To understand them, it is important to understand how gravity works on both small and cosmic scales.

Understanding gravity

Gravity is one of the four fundamental forces of nature. It is the force of attraction between two masses. The law of universal gravitation, formulated by Sir Isaac Newton, states that every point mass attracts every other point mass in the universe with a force along a straight line that connects them. This force is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it is expressed as:

F = g * (m1 * m2) / r^2

Here, F is the gravitational force between the two objects, m1 and m2 are their masses, r is the distance between the centers of the two masses, and G is the gravitational constant.

Black holes

Black holes are regions in space where the gravitational pull is so strong that nothing, not even light, can escape it. The boundary of this region is called the event horizon. Beyond this, we cannot directly observe any event. The main concept behind black holes is linked to the idea of escape velocity, which is the speed required to escape a gravitational field.

When the mass of an object is highly concentrated in a small area, such as in a black hole, the escape velocity is greater than the speed of light, meaning nothing can escape it. Black holes form when massive stars collapse due to their own gravity at the end of their lifecycles. There are three main types of black holes: stellar, supermassive, and intermediate.

event horizon

A simplified illustration of a black hole and its event horizon.

Stellar black holes

These are formed from the remains of massive stars. When a star with a mass of about 20 times that of our Sun runs out of nuclear fuel, it collapses due to its own gravity. If the remaining mass is more than about three times the Sun's mass, no known force can stop the collapse, resulting in a stellar black hole. These are the most common types of black holes.

Supermassive black hole

These are located at the centers of most galaxies, including our own Milky Way. They contain masses ranging from millions to billions of times greater than our Sun. The process by which they form is still a matter of research, but they grow by accreting mass from the surrounding gas and stars.

Intermediate black holes

These black holes have a mass between stellar black holes and supermassive black holes. Their formation is not well understood, and they are harder to observe than other types. They may form when stars in a group collide in a chain reaction.

Gravitational lensing

One of the fascinating effects of gravity in the universe is gravitational lensing. It occurs when a massive object, such as a black hole or galaxy, lies between a distant source, such as a star or another galaxy, and an observer. The gravitational field of the massive object bends the light coming from the source, just as a lens bends light. This effect was predicted by Albert Einstein and is an essential part of his general theory of relativity.

Gravitational lensing can create multiple images, magnify the source, and also create rings of light around the lens, known as Einstein rings. This effect makes distant galaxies and other cosmic phenomena visible to us and helps us understand the distribution of dark matter in the universe.

Lens Source supervisor

An illustration of gravitational lensing showing light bending around a massive object.

Applications of gravitational lensing

Gravitational lensing has a variety of applications in astronomy and cosmology. One of the most important uses is in the search for dark matter. Dark matter does not emit light, making it invisible to telescopes. However, its gravitational effects can be detected through lensing. By studying how light bends around galaxies containing dark matter, scientists can infer its properties and distribution.

Additionally, gravitational lensing is used to measure the mass of celestial objects. Since the amount of bending depends on the mass of the lens, scientists can analyze lensing events to calculate how massive an object, such as a galaxy or black hole, is.

Conclusion

Black holes and gravitational lensing are important in increasing our understanding of the role of gravity in the universe. Black holes serve as extreme examples of gravitational forces, while gravitational lensing provides a unique method to observe invisible parts of the universe and learn about the structure of the universe.

These phenomena are not just theoretical concepts, but have observable effects that astronomers study to gain insights into the nature of space, time, and matter. Their exploration is at the forefront of both theoretical research and observational astronomy.


Grade 11 → 2.1.9


U
username
0%
completed in Grade 11

← Prev (2.1.8)
Gravitational potential energy and energy in orbits
Next (3) →
Properties of matter

Comments 



Black holes and gravitational lensing

https://www.physicsflow.com/g11/2.1.9?pfal=en