11th Physics - F.Sc. 1st Year Comprehensive MCQ Study Notes

Measurements

• Branches of Physics:     - Particle Physics: The branch dealing with the ultimate particles of which matter is composed.     - Nuclear Physics: The branch specifically dealing with atomic nuclei.

• Materials:     - Silicon: Abundantly obtained from sand.

• System of Units (SI):     - There are exactly seven base units in the SI system.     - Base Quantities and Units: Examples include Mass ($kilogram$), Length ($meter$), Time ($second$), Temperature ($Kelvin$), Luminous Intensity ($candela$), Electric Current ($ampere$), and Amount of Substance ($mole$).     - Derived Quantities and Units: Quantities that are derived from base units. Examples include Force ($Newton$), Pressure ($Pascal$), Work/Energy ($Joule$), and Power ($Watt$).     - Unit of Force: The standard unit is the newton, and its symbol is $\text{N}$. (Note: the name is lowercase, but the symbol is uppercase).     - Unit of Luminous Intensity: The SI unit is the candela ($\text{cd}$).     - Unit of Charge: A derived unit is the Coulomb ($\text{C}$).

• Measurements of Angles:     - Plane Angle: The SI unit is the radian ($rad$), typically used in two dimensions.     - Solid Angle: The SI unit is the steradian ($sr$), which lies in three dimensions.     - Definition of Steradian: The solid angle subtended at the center of a sphere by an area of its surface equal to the square of the radius of the sphere.

• Unit Relationships:     - An alternate unit to $kg\,m/s$ is the newton-second ($Ns$).     - Dimensions and Units of Pressure:         - Symbol: $P$         - Unit: $Newton/meter^2$ or $newton/meter^2$         - SI base units: $kg\,m^{-1}\,s^{-2}$

• Multiples and Scaling:     - Prefixes:         - Pico: equivalent to $10^{-12}$         - Femto: equivalent to $10^{-15}$         - Nano: equivalent to $10^{-9}$         - Atto: The least multiple represented in this context, equivalent to $10^{-18}$         - Giga: The highest power multiple among common high prefixes, equivalent to $10^{9}$

• Scientific Notation and Error:     - Conversion Examples:         - $0.0023 = 2.3 \times 10^{-3}$         - $1024 = 1.024 \times 10^{3}$     - Types of Error:         - Personal Error: Caused by negligence or inexperience of a person.         - Systematic Error: Occurs due to factors like faulty apparatus or inappropriate methods.

• Significant Figures:     - Definition: All accurately known digits and the first doubtful digit.     - Rules:         - Zeros to the right of non-zero digits are significant.         - Zeros to the left of a significant digit are not significant (e.g., in $0.0173$, there are 3 significant figures; in $0.000846$, there are 3 significant figures).         - Zeros between two digits are significant.         - Significant figures in $8.70 \times 10^3$ is 3.     - Operations:         - Addition/Subtraction: The result should be rounded to the same number of decimal places as the quantity with the fewest decimal places. (e.g., $72.1 + 3.32 + 0.003 = 75.4$).         - Rounding Examples: $75.560$ rounds to $75.6$; $73.650$ rounded to one decimal is $73.6$.

• Precision and Uncertainty:     - Precision: Relates to the absolute uncertainty. Smaller least count leads to higher precision.     - Accuracy: Relates to fractional or percentage uncertainty.     - Addition of Uncertainty: Absolute uncertainties are added during addition and subtraction operations.     - Calculation Example: If $L_1 = 10.5 \pm 0.1$ and $L_2 = 26.8 \pm 0.1$, then $L = L_2 - L_1 = 16.3 \pm 0.2$.

• Dimensions:     - Fundamental vs. Derived: Weight is not a fundamental quantity (it is a force).     - Force: $[MLT^{-2}]$     - Torque: $[ML^2T^{-2}]$     - Acceleration due to gravity ($g$): $[LT^{-2}]$     - Coefficient of Viscosity ($\eta$): $[ML^{-1}T^{-1}]$ (derived from $F = 6\pi\eta rv$).     - Frequency: $[T^{-1}]$ or $[M^0L^0T^{-1}]$.     - Strain: Dimensionless, represented as $[M^0L^0T^0]$.     - Light Year: A unit of distance representing the distance light travels in one year. Its dimension is $[L]$.     - Time Conversion: There are approximately $3.1 \times 10^{-8}$ years in one second.

Vectors and Equilibrium

• Scalars vs. Vectors:     - Scalars: Quantities with magnitude only (e.g., speed, volume, power, density, charge, work).     - Vectors: Quantities with magnitude and direction (e.g., velocity, acceleration, displacement, torque, moment of force).

• Coordinate Systems:     - Rectangular/Cartesian Coordinate System: Also known as the Cartesian coordinate system.     - Direction in Space: Specified by three angles (typically denoted as $\alpha, \beta, \gamma$).

• Vector Resultants and Quadrants:     - Quadrant Logic:         - First Quadrant: $x$-component (+), $y$-component (+).         - Second Quadrant: $x$-component (-), $y$-component (+).         - Third Quadrant: Both components are negative ($-x, -y$). Direction is calculated as $180^{\circ} + \theta$.         - Fourth Quadrant: $x$-component (+), $y$-component (-).

• Vector Addition:     - Properties: Addition is commutative ($\mathbf{A} + \mathbf{B} = \mathbf{B} + \mathbf{A}$) and associative.     - Resultant Vector: A single vector that has the same effect as all the original vectors combined.     - Anti-parallel Vectors: The angle between them is $180^{\circ}$.     - Pythagorean Resultants:         - Forces of $30\text{N}$ and $40\text{N}$ at $90^{\circ}$ yield a resultant of $\sqrt{30^2 + 40^2} = 50\text{N}$.         - Forces of $6\text{N}$ and $8\text{N}$ at $90^{\circ}$ yield a resultant of $10\text{N}$.

• Unit Vectors:     - Definition: A vector with a magnitude of one used to specify direction.     - Mathematical form: $\mathbf{\hat{A}} = \frac{\mathbf{A}}{|\mathbf{A}|}$.     - Standard Unit Vectors: $\hat{i}$ (x-axis), $\hat{j}$ (y-axis), $\hat{k}$ (z-axis).     - Magnitude of Vector $\mathbf{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$ is $\sqrt{A_x^2 + A_y^2 + A_z^2}$.     - Example: The unit vector in the direction of $\mathbf{A} = 2\hat{i} - 2\hat{j} + \hat{k}$ is $\frac{2\hat{i} - 2\hat{j} + \hat{k}}{3}$.

• Vector Components:     - If a vector is entirely along the y-axis, its x-component is zero.     - If $x$ and $y$ components are equal ($A_x = A_y$), the angle with the x-axis is $45^{\circ}$.

• Vector Products:     - Scalar (Dot) Product: $\mathbf{A} \cdot \mathbf{B} = AB \cos(\theta)$.         - Maximum when vectors are parallel ($0^{\circ}$).         - Zero when vectors are perpendicular ($90^{\circ}$).         - Dot product of $\hat{i} \cdot \hat{i} = 1$, while $\hat{i} \cdot \hat{j} = 0$.     - Vector (Cross) Product: $|\mathbf{A} \times \mathbf{B}| = AB \sin(\theta)$.         - Minimum when angle is $0^{\circ}$ or $180^{\circ}$.         - Direction found by the Right Hand Rule.         - The cross product of the same vector $\mathbf{A} \times \mathbf{A} = 0$.         - $\hat{i} \times \hat{j} = \hat{k}$.

• Torque (Moment of Force):     - Definition: The turning effect of a force. Mathematically: $\mathbf{\tau} = \mathbf{r} \times \mathbf{F}$.     - Formula: $\tau = rF \sin(\theta)$.     - Conditions:         - Zero if $\mathbf{r}$ and $\mathbf{F}$ are in the same direction ($0^{\circ}$) or if the line of action passes through the axis of rotation.         - Maximum if the angle is $90^{\circ}$.     - Direction: Perpendicular to the plane containing $\mathbf{r}$ and $\mathbf{F}$.     - SI Unit: $N\cdot m$.

• Equilibrium:     - Static Equilibrium: The body is at rest.     - Dynamic Equilibrium: The body moves with uniform velocity.     - Conditions for Complete Equilibrium:         - First Condition: $\sum \mathbf{F} = 0$ (translational equilibrium).         - Second Condition: $\sum \mathbf{\tau} = 0$ (rotational equilibrium).

• Special Geometric Cases:     - Two vectors of equal magnitude produce a resultant of the same magnitude when oriented at $120^{\circ}$.     - The minimum number of unequal forces that can produce a zero resultant is three.

Motion and Force

• Velocity and Acceleration:     - Uniform Velocity: Covering equal displacement in equal intervals of time.     - Acceleration: Slope of a velocity-time ($v-t$) graph.         - Positive Acceleration: Slope is increasing.         - Negative Acceleration (Deceleration): Slope is decreasing.         - Zero Acceleration: Graph is a straight line parallel to the time axis.     - Distance: Represented by the area between the $v-t$ graph and the time axis.

• Inertia and Newton's Laws:     - Inertia: The property of matter to oppose changes in its state of rest or motion. It is quantitatively measured by mass.     - Newton's First Law: Also known as the Law of Inertia.

• Momentum and Impulse:     - Momentum ($\mathbf{p}$): Predicted by the product of mass and velocity ($mv$).     - Impulse ($\mathbf{I}$): Defined as the change in momentum ($\mathbf{I} = \Delta \mathbf{p} = \mathbf{F} \Delta t$).     - Force: Defined as the time rate of change of momentum ($\mathbf{F} = \frac{\Delta \mathbf{p}}{\Delta t}$).     - Units: Momentum unit is $kg\,m\,s^{-1}$, which is alternate to the Newton-second ($Ns$).

• Gravity:     - An object moving toward Earth has a value of "$g$" taken as positive ($g \approx 9.8\,m/s^2$).

• Collisions:     - In an elastic collision between two snooker balls of the same mass where one is at rest ($v_2 = 0$) and the other is moving with velocity $v$, the first ball comes to rest and the second moves with velocity $v$.

• Rocket Propulsion: Explained by the Law of Conservation of Momentum.

• Projectile Motion:     - Dimensionality: It is a two-dimensional motion.     - Path/Trajectory: The path is a parabola.     - Components of Velocity:         - Horizontal component ($v_x$): Remains constant throughout the motion ($v_x = v_i \cos(\theta)$).         - Vertical component ($v_y$): Changes due to gravity. At maximum height, $v_y = 0$.     - Velocity at Peak: Only the horizontal component exists: $v = v_i \cos(\theta)$.     - Maximum Range: Achieved at an angle of projection of $45^{\circ}$.         - Formula: $R_{max} = \frac{v_i^2}{g}$.     - Symmetric Ranges: The range is identical for pairs of angles that add to $90^{\circ}$ (e.g., $30^{\circ}$ and $60^{\circ}$, $20^{\circ}$ and $80^{\circ}$).     - Total Time of Flight: $T = \frac{2v_i \sin(\theta)}{g}$.

Work and Energy

• Work ($W$):     - Definition: Product of force and displacement ($W = \mathbf{F} \cdot \mathbf{d} = Fd \cos(\theta)$).     - Graph: Work is the area under the force-displacement graph.     - Conditions:         - Maximum Work: Angle between $F$ and $d$ is $0^{\circ}$.         - Zero Work: Angle is $90^{\circ}$ (e.g., work done by centripetal force is zero).         - Negative Work: Angle is $180^{\circ}$ (anti-parallel, like friction).     - Dimensions: Work has the same dimensions as torque ($[ML^2T^{-2}]$).

• Conservative Fields:     - Definition: A field where work done in a closed path is zero and work done is independent of the path.     - Conservative Forces: Electric force, Gravitational force, Magnetic force.     - Non-conservative Forces: Frictional force.

• Power ($P$):     - Definition: The rate of doing work ($P = W/t$). It is the dot product of force and velocity ($\mathbf{F} \cdot \mathbf{v}$).     - Instantaneous vs. Average: They are equal if work is done at a uniform rate.     - Units:         - SI unit: Watt ($W$).         - Horsepower: $1\,hp = 746\,watts$.         - Kilowatt-hour: $1\,kWh = 3.6\,MJ$.         - Megawatt-hour: $1\,MWh = 3.6 \times 10^9\,J$.

• Kinetic and Potential Energy:     - Kinetic Energy ($K.E.$): $K.E. = \frac{1}{2}mv^2$. If mass is doubled at constant velocity, $K.E.$ becomes 2 times. If velocity is doubled, $K.E.$ becomes 4 times.     - Work-Energy Theorem: Work done on a body equals the change in its kinetic energy: $Fd = K.E._f - K.E._i$.     - Escape Velocity: The minimum velocity to leave Earth's gravitational field is approximately $11\,km/s$.

• Energy Consumption and Sources:     - Example: A $60\,W$ bulb in $2\,s$ consumes $120\,J$ ($P \times t$).     - Tidal Energy: Source is the Moon. Tides raise sea water roughly twice a day.     - Geothermal Energy: Result of radioactive decay, compression of materials, and residual heat in the Earth.

Circular Motion

• Angular Displacement ($\theta$):     - Units: Revolution, Radian, Degree.     - Conversion: $1\,rev = 360^{\circ} = 2\pi\,radians$.     - $1\,radian ≈ 57.3^{\circ}$.

• Angular Velocity ($\omega$):     - Rate of change of angular displacement.     - Units: $rad/s$, $rev/min$.     - Earth's rotation: $\omega ≈ 7.3 \times 10^{-5}\,rad/s$.

• Angular Acceleration ($\alpha$):     - Rate of change of angular velocity.     - Formula: $\mathbf{a} = \mathbf{\alpha} \times \mathbf{r}$.     - Direction: Along the axis of rotation.     - Produced by Torque.

• Centripetal Force ($F_c$):     - Formula: $F_c = \frac{mv^2}{r}$ or $F_c = mr\omega^2$.     - Work: Centripetal force does no work because it is always perpendicular to displacement.     - Direction: Directed along the radius toward the center.

• Moment of Inertia ($I$):     - Quantity: $I = mr^2$.     - Unit: $kg\,m^2$.

• Angular Momentum ($L$):     - Definition: $L = \mathbf{r} \times \mathbf{p}$.     - SI Unit: $J\cdot s$ or $kg\,m^2\,s^{-1}$.     - Conservation: If external torque is zero, angular momentum is constant.

• Rotational Kinetic Energy:     - General: $K.E.<em>{rot} = \frac{1}{2}I\omega^2$.     - For an empty hoop: $K.E.</em>{rot} = \frac{1}{2}mr^2\omega^2$.

• Satellites:     - Minimum orbital velocity: Approximately $7.9\,km/s$ (also called critical speed).     - Geostationary Satellites: Complete one rotation in 24 hours.     - Communication: Use microwaves; a minimum of 3 satellites can cover the whole Earth.

• Weight and Lift Dynamics:     - Apparent Weight:         - Ascending with acceleration $a$: Increases ($mg + ma$).         - Descending with acceleration $a$: Decreases ($mg - ma$).         - Free fall ($a = g$): Zero (weightlessness).     - Pull of Earth: On a $20\,kg$ mass, $W = 20 \times 9.8 = 196\text{N}$.

Fluid Dynamics

• Viscosity ($\eta$):     - Resistance of a fluid to flow.     - Dimensions: $[ML^{-1}T^{-1}]$.     - Unit: $kg\,m^{-1}\,s^{-1}$.

• Drag Force:     - Retarding force on objects in fluid.     - Stokes' Law: $F = 6\pi\eta rv$ (specifically for spherical bodies moving slowly).     - Increases as the speed of the object increases.

• Terminal Velocity ($v_t$):     - The maximum constant speed of an object falling vertically when drag force equals weight.     - Acceleration becomes zero.     - Formula: $v_t = \frac{2gr^2ρ}{9❃}$.     - Relationship: If radius is halved, terminal velocity becomes one fourth (Proportional to $r^2$).

• Fluid Flow Types:     - Streamline (Laminar): Steady, regular flow where paths don't cross.     - Turbulent: Unsteady, irregular flow.     - Ideal Fluid: Non-viscous, incompressible, and has steady flow.

• Principles of Fluid Motion:     - Equation of Continuity: $A_1v_1 = A_2v_2 = constant$. The constant represents the flow rate ($Volume/sec$). Based on Conservation of Mass.     - Bernoulli's Equation: Based on Conservation of Energy. States that where speed is high, pressure is low.     - Torricelli's Theorem: Used to find the speed of efflux ($v = \sqrt{2gh}$).

• Blood Flow:     - Blood pressure is always measured relative to atmospheric pressure (usually higher).     - Density of blood is roughly equal to water.     - Device: Sphygmomanometer.     - Units: $1\,Torr = 133.3\,N/m^2$.

Oscillations

• Restoring Force: The force that opposes applied displacement in a spring ($F = -kx$).

• Spring Constant ($k$):     - Unit: $N/m$ or $Nm^{-1}$.     - Example: If $F = 0.08\text{N}$ and $x = 4\,cm$, then $k = \frac{0.08}{0.04} = 2\,N/m$.

• Simple Harmonic Motion (SHM):     - A type of vibratory motion.     - Condition: $a ∝ -x$ (Acceleration is proportional to negative displacement).     - Frequency ($f$): Number of vibrations per second. SI unit is Hertz ($Hz$).     - Time Period ($T$): Time for one vibration. $T \times f = 1$.     - Angular Frequency ($\omega$): $\omega = 2\pi f$. For mass on a spring, $\omega = \sqrt{k/m}$.

• Energy in SHM:     - Total energy remains constant.     - At Mean Position: $P.E.$ is minimum (zero), $K.E.$ is maximum.     - At Extreme Position: $K.E.$ is zero, $P.E.$ is maximum.

• The Simple Pendulum:     - Motion is SHM only if amplitude is small ($\sin(\theta) ≈ θ$).     - Time Period: $T = 2\pi\sqrt{L/g}$. Depends on length, not mass.

• Second Pendulum:     - Time period: $2\,seconds$.     - Frequency: $0.5\,Hz$.     - Length: Approximately $99.2\,cm$.

• Damping and Resonance:     - Damping: Energy dissipation in an oscillating system resulting in decreased amplitude.     - Resonance: When the frequency of the external force matches the natural frequency. Sharpness is inversely proportional to damping force.     - Examples of Resonance: Radio tuning (electrical resonance), Microwave ovens ($2450\,MHz$).

Waves

• Propagation:     - Waves transmit energy without transporting matter.     - Mechanical Waves: Require a material medium (e.g., water, air, sound).     - Sound Waves: Cannot travel in a vacuum; velocity in vacuum is $0\,m/s$.

• Speed of Sound:     - Speed at $0^{\circ}C$: $332\,m/s$.     - Rise with temperature: $0.61\,m/s$ per degree Celsius.     - Laplace Correction: Sound travels in air under adiabatic conditions ($v = \sqrt{γP/ρ}$).     - Speed is greater in solids than gases due to higher elasticity.

• Wave Characteristics:     - Formula: $v = f\lambda$ or $v = \lambda/T$.     - Wavelength ($\lambda$): Distance between consecutive crests or troughs.     - Distance between crest and trough: $\lambda/2$.

• Interference and Beats:     - Constructive Interference: Path difference is an integral multiple of wavelength ($n\lambda$).     - Beats: Periodic variation in loudness when two notes of slightly different frequencies are played. Beat frequency = $|f_1 - f_2|$.     - Max beats heard by human ear: approximately 10 per second.

• Reflection:     - Rarer to Denser: Reflected wave undergoes a $180^{\circ}$ phase shift ($\lambda/2$ path difference).     - Denser to Rarer: No change in phase.

• Stationary (Standing) Waves:     - Created by two waves of equal frequency/amplitude traveling in opposite directions.     - Nodes: Points of zero displacement. Fixed ends of a string are always nodes.     - Antinodes: Points of maximum displacement.     - Distance between two nodes: $\lambda/2$.     - Distance between a node and adjacent antinode: $\lambda/4$.     - Fundamental frequency of a string ($l$): $f_1 = v/2l$.

• Doppler Effect:     - Apparent change in frequency due to relative motion between source and observer.     - Blue Shift: Observed when stars/sources move toward Earth (increase in frequency).     - Red Shift: Observed when sources move away.

Physical Optics

• Wavefronts: Surface connecting points have the same phase of vibration.     - Distance between two consecutive wavefronts is one wavelength.

• Interference:     - Coherent Sources: Emit light of same wavelength with constant phase difference.     - Constructive Condition: Path difference $= m\lambda$.     - Destructive Condition: Path difference $= (m + 1/2)\lambda$.     - Young's Double Slit: Fringe spacing $\Delta y = \lambda L / d$.

• Newton's Rings:     - Formed by interference in a thin air film.     - Central spot is dark in reflected light due to destructive interference/phase change.

• Diffraction:     - The bending of light around edges and obstacles.     - Bragg's Law: $2d \sin(\theta) = m\lambda$ (for x-ray diffraction in crystals).

• Michelson's Interferometer:     - Used for precise distance measurements. Mirror movement $L = m\lambda/2$.

Optical Instruments

• Vision and Lenses:     - Least distance of distinct vision: $25\,cm$.     - Power of Lens: Measured in diopters.     - Convex Lens: Converging. Real enlarged image if object outside focus; virtual enlarged image if inside focus.

• Magnifying Power:     - Simple Microscope: $M = 1 + d/f$.     - Telescope: $M = f_o/f_e$. Length of telescope in normal adjustment: $f_o + f_e$.

• Refraction and Total Internal Reflection:     - Refractive Index: $n = c/v$.     - Total Internal Reflection: Occurs when light travels from denser to rarer medium and the angle of incidence exceeds the critical angle.     - Critical angle for glass-air: $41.8^{\circ}$.

• Fiber Optics:     - Propagation happens through total internal reflection or continuous refraction.     - Step-index fiber: Constant refractive index in core.     - Graded-index fiber: Density decreases towards the periphery; reduces dispersion error.

Thermodynamics

• Definitions:     - Heat: A form of energy.     - Pressure: Depends on molecular speed, mass, and number of molecules in a unit volume.

• Laws of Thermodynamics:     - First Law: Statement of Conservation of Energy.     - Isothermal Process: Temperature remains constant ($PV = const$). Obeys Boyle's Law. In this process, $Q = W$ ($\Delta U = 0$).     - Adiabatic Process: No heat exchange ($Q = 0$). Formula: $PV^{\gamma} = constant$. Entropy remains constant. Cloud formation is an example.

• Internal Energy: Sum of all microscopic energies. In an ideal gas, it is proportional to translational kinetic energy.

• Specific Heats:     - C_p > C_v (Heat at constant pressure vs constant volume).     - $\gamma = C_p/C_v$.     - Joule-Kelvin effect: $\Delta T$ when gas expands.

• Constants:     - Boltzmann's Constant ($k$): $1.38 \times 10^{-23}\,J/K$.     - Triple point of water: $273.16\,K$.     - Normal human body temp: $98.6^{\circ}F = 37^{\circ}C$.

• Heat Engines:     - Carnot Engine: Reversible cycle. Efficiency increases if sink temperature is lowered.     - Efficiency of Petrol Engine: $25\%$–$30\%$.     - Efficiency of Diesel Engine: $35\%$–$40\%$.

• Entropy ($S$):     - Measure of disorder ($\Delta S = \Delta Q/T$).     - Heat addition to a system increases entropy (positive).