Physics 12 Complete Book with Water Mark Low Quality-1

Gravitation

• Gravity is essential in shaping the universe, influencing the movements of stars in galaxies.
• Newton's law of gravitation is: Every object attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• Gravitational force formula: $F = G \frac{m<em>1 \times m</em>2}{r^2}$, where $G = 6.67 \times 10^{-11} N m^2 kg^{-2}$.
• Gravitational force is always attractive and doesn't depend on the medium.
• Gravitational force decreases by a factor of 4 when the distance increases by a factor of 2.
• Forces acting on two objects due to gravitational force demonstrate action and reaction.

Gravitational Field Strength

• Gravitational field is the area around a massive object where its gravitational force acts.
• Gravitational field is represented by field lines.
• Gravitational field strength is a vector with magnitude 'g' pointing in the direction of the gravitational force.
• Gravitational field strength and acceleration due to gravity are equivalent.
• Outside a uniform sphere, the field acts as if all mass is concentrated at the center.

Value of 'g' on Surface of the Earth

• The gravitational force: $F = W = m_0 g$.
• Formula: $g = G \frac{M<em>E}{R</em>E^2}$, where $M<em>E$ is the mass of the Earth and $R</em>E$ is the radius of the Earth.

Variation of 'g' with Altitude

• As we go further away from the center or surface of the Earth, the value of 'g' decreases.
• Formula: $g<em>h = \frac{gR^2}{(R</em>E + h)^2}$.

Satellites and Orbits

• A satellite is any object that orbits a planet due to gravity.

Orbital Velocity

• In circular orbit, a satellite has a constant tangential velocity called orbital velocity.
• Formula: $v<em>o = \sqrt{\frac{G M</em>E}{r}}$.

Geostationary Satellites

• Geostationary satellites remain stationary above some point on Earth.
• Orbital radius formula: $r = \sqrt[3]{\frac{G M_E T^2}{4 \pi^2}}$.

Gravitational Potential

• Gravitational potential energy formula: $U = - \frac{G M<em>E m}{R</em>E}$.
• Gravitational potential formula: $V = \frac{U}{m}$. $V = - \frac{G M<em>E}{R</em>E}$.

Statistical Mechanics and Thermodynamics

• Statistical mechanics provides a foundation for understanding thermodynamic properties.

Pressure Exerted by Gas Molecules

• Pressure is the force exerted by gas molecules per unit area.
• Expressing pressure of ideal gas : $P = \frac{mN \langle v^2 \rangle}{3V}$, where mN is the total mass of N gas molecules.
• The pressure exerted by the gas molecules on the walls of the container is directly proportional to the average translational kinetic energy of the gas molecules.
• The absolute temperature of an ideal gas is directly proportional to the average translational kinetic energy of the gas molecules.

Root Mean Square Speed of an Ideal Gas

• Root mean square speed formula : $v<em>{r.m.s} = \sqrt{\frac{v</em>1^2 + v<em>2^2 + v</em>3^2 + \dots + v_N^2}{N}}$.
• The root mean square speed of the given gas molecule is directly proportional to the square root of the absolute temperature of the gas molecules.

Modification of The Ideal Gas Model to Discuss Behaviour of Non-Ideal Gases

• Wan der Waals equation: $\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT$. This equation is designed to describe the behavior of real gases, but it can still be used for ideal gases as well.

Behaviour of Matter Under Extreme Physical Conditions

• Pauli Exclusion Principle: Two electrons cannot occupy the same quantum state.
• Gravitational pressure happens when gravity squeezes atoms so tightly under extremely high pressure in a star that they change from their normal state.

Bose-Einstein Condensation

• Bose-Einstein Condensation (BEC) is a state of matter that forms at extremely low temperatures, such as close to absolute zero, causing particles kinetic energies to decrease significantly.
• Superfluidity is observed when certain fluids are cooled to extremely low temperatures, close to absolute zero.
• In certain conditions, Bose-Einstein condensation leads to superconductivity, where electrical resistance drops to zero, allowing current to flow without resistance.
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