Important Definitions & Formulas

Define Measurement. What is a Unit? List the essential characteristics of a standard unit.

Differentiate between Fundamental (Base) Quantities and Derived Quantities. Give the SI Unit and Dimensional Formula for two examples of each.

What is a System of Units? List the 7 Fundamental Units and 2 Supplementary Units in the SI system with their symbols.

Define the following Practical Units of Length and write their values in meters:
a) Astronomical Unit (AU)
b) Light Year (ly)
c) Parallactic Second (Parsec)

Define the following Units of Time:
a) Solar Day & Solar Year
b) Lunar Month
c) Shake (Write its value in seconds)

Distinguish between Accuracy and Precision in measurement with a suitable example.

Define Error in Measurement. Explain the causes and methods to minimize the following types of errors:
a) Systematic Error
b) Gross Error
c) Least Count Error

Define Rest and Motion. Explain the concept of Frame of Reference.

Define Path Length (Distance) and Displacement. Write their SI Units and Dimensional Formulas. Distinguish between them.

Define Uniform Motion and Non-Uniform Motion. Give one example of each.

Define Average Velocity and Average Speed. Write their mathematical formulas, SI Units, and Dimensional Formulas.

Define Instantaneous Velocity. Write its mathematical formula using limits.

Define Acceleration. Write its formula, SI Unit, and Dimensional Formula. Distinguish between Average Acceleration and Instantaneous Acceleration.

Write the three Kinematic Equations for uniformly accelerated motion. Under what condition are these equations valid?

What is Free Fall? Write the equations of motion for a freely falling body under gravity (assuming \( u=0 \)).

Define Scalar Quantity and Vector Quantity. Give two examples of each along with their SI units.

Define Position Vector and Displacement Vector. Write their mathematical expressions.

Define the following types of vectors:
a) Equal Vector, Negative Vector
b) Parallel Vectors, Anti-Parallel Vectors
c) Collinear Vector, Co-initial Vector
d) Coplanar Vector, Orthogonal Vector
e) Zero (Null) Vector

Define Unit Vector. Write its formula, notation, and significance. What is the unit vector of \( \vec{A} \)?

State the Triangle Law, Parallelogram Law, and Polygon Law of vector addition.

What is meant by the Resolution of a Vector? Write the expressions for rectangular components (\(A_x, A_y\)) of a vector in a plane.

Define Scalar Product (Dot Product). Write its formula. Is the result a scalar or vector?

Define Vector Product (Cross Product). Write its formula. How is the direction of the resultant vector determined?

Define Projectile Motion. Write the equation of the Trajectory of a Projectile.

Write the formulas for the following in Projectile Motion:
a) Time of Flight (T)
b) Horizontal Range (R)
c) Maximum Height (H)

Define Uniform Circular Motion. Is it an accelerated motion?

Define the following Angular Quantities. Write their SI Units and Dimensional Formulas:
a) Angular Displacement (\( \theta \))
b) Angular Velocity (\( \omega \))
c) Angular Acceleration (\( \alpha \))

Define Centripetal Acceleration. Write its formula in terms of linear velocity (\(v\)) and angular velocity (\( \omega \)). Write its SI unit and dimensional formula.

Distinguish between Centripetal Force and Centrifugal Force. Write the formula for Centripetal Force.

Define Inertia. Explain the following with examples:
a) Inertia of Rest
b) Inertia of Motion
c) Inertia of Direction

State Newton's First Law of Motion (Galileo's Law of Inertia).

Define Linear Momentum. Write its formula, SI Unit, and Dimensional Formula. Is it a scalar or vector quantity?

State Newton's Second Law of Motion. Write the mathematical relation between Force, Mass, and Acceleration.

Define Impulse. Write its formula, SI Unit, and Dimensional Formula. State the Impulse-Momentum Theorem.

State the Law of Conservation of Linear Momentum. Write the mathematical condition for it.

State Newton's Third Law of Motion. What are the essential conditions for forces to form an Action-Reaction pair?

Distinguish between Inertial Frames and Non-Inertial Frames of Reference with examples.

What is Normal Reaction (Normal Force)? Why is it always perpendicular to the contact surface?

Define Friction. Explain the following types with their definitions:
a) Static Friction
b) Limiting Friction
c) Kinetic Friction
d) Rolling Friction

Define Angle of Friction and Angle of Repose. Write the relation between them.

What is meant by Banking of Roads? Why is it necessary? Write the formula for the maximum safe velocity on a banked road.

What is a Pseudo Force? Under what condition does it act?

Define Work Done. Write its dot product formula, SI Unit, and Dimensional Formula. Is it a scalar or vector quantity?

Explain the conditions under which Work Done is:
a) Positive
b) Negative
c) Zero (Give examples for each)

Define Energy. Explain Kinetic Energy and Potential Energy. Write their formulas, SI Units, and Dimensional Formulas.

State the Work-Energy Theorem. Write its mathematical equation.

Distinguish between Conservative Forces and Non-Conservative Forces. Give two examples of each.

State the Law of Conservation of Mechanical Energy. Write the mathematical condition for it.

State the general Law of Conservation of Energy.

Define Power. Write its formula, SI Unit, and Dimensional Formula. Define 1 Horse Power (HP) and its relation to Watt.

Define Collision. Explain the following types based on direction:
a) Head-on Collision (1D)
b) Oblique Collision (2D)

Distinguish between the following types of collision based on Kinetic Energy:
a) Perfectly Elastic Collision
b) Inelastic Collision
c) Perfectly Inelastic Collision

State Newton's Law of Collision. Define Coefficient of Restitution (e). Write its values for Elastic, Inelastic, and Perfectly Inelastic collisions.

Define Rigid Body. What is the condition for a body to be rigid?

Explain the following types of motion for a rigid body:
a) Rectilinear Motion
b) Translational Motion
c) Circular Motion
d) Rotational Motion
e) Oscillatory Motion
f) Vibrational Motion

Define Centre of Mass. List the important properties or characteristics of Centre of Mass.

Define Centre of Gravity. How does it differ from Centre of Mass?

Define Torque (Moment of Force). Write its formula, SI Unit, and Dimensional Formula. Is it a vector?

Define Angular Momentum. Write its formula in terms of linear momentum, SI Unit, and Dimensional Formula. Write the relation between Torque and Angular Momentum.

State the Principle of Conservation of Angular Momentum. Give one example.

Define Moment of Inertia. Write its mathematical formula, SI Unit, and Dimensional Formula.

Define Radius of Gyration. Write its formula and SI Unit.

State the Theorem of Perpendicular Axes and the Theorem of Parallel Axes for Moment of Inertia.

Define Rolling Motion. Explain it as a combination of translation and rotation.

State Kepler's Laws of Planetary Motion:
a) Law of Orbits
b) Law of Areas
c) Law of Periods (Write the mathematical relation)

State Newton's Law of Universal Gravitation. Write its mathematical formula and vector form. List the important Characteristics of Gravitational Force.

Define Acceleration due to Gravity (\(g\)). Write its formula on the surface of the Earth. What is its SI Unit and Dimensional Formula?

Define Inertial Mass and Gravitational Mass. Write their formulas. How are they related?

Discuss the Variation of Acceleration due to Gravity (\(g\)) with:
a) Altitude (Height)
b) Depth
c) Shape of Earth
d) Rotation of Earth

Define Gravitational Field and Gravitational Field Intensity. Write the formula, SI Unit, and Dimensional Formula.

Define Gravitational Potential and Gravitational Potential Energy. Write their formulas. Are they scalar or vector quantities?

Define Escape Speed. Write its formula for Earth. What is its approximate value on Earth's surface?

Define Satellite. Write the formulas for:
a) Orbital Velocity of a satellite.
b) Time Period of Revolution of a satellite.

Write the formulas for the following energies of a satellite in orbit:
a) Kinetic Energy
b) Potential Energy
c) Total Energy (Mechanical Energy)

Define Geostationary Satellite and Polar Satellite. Write their essential conditions and uses.

What is Weightlessness in a satellite? Explain the condition under which an astronaut feels weightless.

Define Plasticity. Distinguish between the following types of solids:
a) Perfectly Elastic Solids
b) Inelastic (Plastic) Solids
c) Partially Elastic Solids

Define Stress. Write its formula, SI Unit, and Dimensional Formula.

Explain the following types of Stress:
a) Longitudinal Stress (Tensile & Compressive)
b) Volumetric (Hydraulic) Stress
c) Shearing (Tangential) Stress

Define Strain. Why is it a dimensionless quantity? Explain its types:
a) Longitudinal Strain
b) Volumetric Strain
c) Shearing Strain

State Hooke's Law. Define Modulus of Elasticity.

Draw the Stress-Strain Curve for a metallic wire. Define the terms:
a) Proportional Limit
b) Elastic Limit (Yield Point)
c) Permanent Set
d) Fracture Point

What are Elastomers? Give two examples. How does their stress-strain curve differ from metals?

Define Young's Modulus of Elasticity (Y). Write its formula, SI Unit, and Dimensional Formula.

Define Bulk Modulus of Elasticity (B). Write its formula and SI Unit. What is Compressibility?

Define Shear Modulus (Modulus of Rigidity, G). Write its formula and SI Unit.

Write the formula for Elastic Potential Energy stored in a stretched wire. Express it in terms of stress and strain.

Define Thrust and Pressure. Write their formulas, SI Units, and Dimensional Formulas.

Distinguish between the following types of pressure:
a) Atmospheric Pressure
b) Gauge Pressure
c) Absolute Pressure

State Pascal's Law of transmission of fluid pressure.

Define Density. Write its formula, SI Unit, and Dimensional Formula.

Distinguish between Streamline Flow and Turbulent Flow.

State Bernoulli's Principle. Write its mathematical equation.

Explain the following applications of Bernoulli's Principle:
a) Dynamic Lift of an Aeroplane
b) Magnus Effect (Spinning Ball)
c) Venturimeter

State Torricelli's Theorem. Write the formula for the Velocity of Efflux.

Define Viscosity. Define Coefficient of Viscosity and Velocity Gradient. Write their units.

State Stokes' Law. Write the formula for viscous drag force. What is its importance?

Define Terminal Velocity. Write its formula. Define Critical Velocity.

Define Surface Tension. Write its formula, SI Unit, and Dimensional Formula. Give one example.

Define Surface Energy. Define Angle of Contact.

What is Capillarity (Capillary Action)? Write the formula for capillary rise. How does Detergent affect Surface Tension?

Define Heat and Temperature. Distinguish between them. Write their SI Units and Dimensional Formulas.

State the principle of a Thermometer. Write the conversion formulas between Celsius, Fahrenheit, and Kelvin scales.

State the following Gas Laws:
a) Boyle's Law
b) Charles's Law
c) Gay Lussac's Law
d) Avogadro's Law

Write the Ideal Gas Equation. Define the Universal Gas Constant (R). Write its SI Unit and Dimensional Formula.

Define Absolute Temperature (Absolute Zero). What are the values of temperature and pressure at NTP and STP?

Define Thermal Expansion. Explain the following types with their formulas:
a) Linear Expansion (\(\alpha\))
b) Superficial Expansion (\(\beta\))
c) Cubical Expansion (\(\gamma\))

What is the Anomalous Behaviour of Water? Write the relation between the coefficients \(\alpha\), \(\beta\), and \(\gamma\).

What is Thermal Stress? Write its formula.

Define Specific Heat Capacity and Molar Specific Heat Capacity. Write their formulas, SI Units, and Dimensional Formulas.

Define Latent Heat (Hidden Heat). Write its formula, SI Unit, and Dimensional Formula.

Define the following terms related to Change of State:
a) Melting Point & Freezing Point
b) Boiling Point & Condensation
c) Sublimation & Evaporation
d) Triple Point

Explain the three modes of Heat Transfer: Conduction, Convection, and Radiation.

Define Thermal Conductivity. Write its formula, SI Unit, and Dimensional Formula.

Define the properties of Thermal Radiation:
a) Reflectance (Reflective Power)
b) Absorptance (Absorptive Power)
c) Transmittance (Transmittive Power)

Define Emissive Power and Emissivity. What is a Black Body?

State Kirchhoff's Law of thermal radiation.

State Stefan's Law (Stefan-Boltzmann Law). Write its mathematical formula. Write the SI Unit of Stefan's Constant (\(\sigma\)).

State Wien's Displacement Law. Write its formula. Write the SI Unit of Wien's Constant (\(b\)).

State Newton's Law of Cooling. Write its mathematical expression.

Define Thermodynamics. What is meant by Thermal Equilibrium? State the Zeroth Law of Thermodynamics.

Define Internal Energy. Write the formula for Work Done in thermodynamics. Is work a state function or a path function?

State the First Law of Thermodynamics. Write its mathematical expression (\( \Delta Q = \Delta U + \Delta W \)). List its limitations.

Define the following Thermodynamic Processes:
a) Isothermal Process
b) Isobaric Process
c) Isochoric Process
d) Adiabatic Process
e) Polytropic Process

Write the relations between \(P, V,\) and \(T\) for an Adiabatic Process involving an ideal gas (e.g., \(PV^\gamma = \text{constant}\)).

What is a Cyclic Process? What is the change in Internal Energy in a cyclic process? How is the Work Done calculated from a P-V diagram?

State the Second Law of Thermodynamics according to:
a) Kelvin-Planck Statement
b) Clausius Statement

Distinguish between Reversible and Irreversible Processes. Give two examples of each.

Write the Ideal Gas Equation (Perfect Gas Equation). State Dalton's Law of Partial Pressures.

Write the main Assumptions of the Kinetic Theory of Gases.

Define Degrees of Freedom. How many degrees of freedom does a monoatomic, diatomic, and triatomic gas molecule have?

State the Law of Equipartition of Energy. What is the energy associated with each degree of freedom per molecule?

Define Molar Specific Heat Capacity at:
a) Constant Volume (\(C_v\))
b) Constant Pressure (\(C_p\))
Write the relation between them (Mayer's Formula).

Define Mean Free Path. Write its formula. On what factors does it depend?

Define Oscillatory (Vibratory) Motion and Periodic Motion. Give one example of each. Is every oscillatory motion periodic?

Define Time Period and Frequency. Write their mathematical relation, SI Units, and Dimensional Formulas.

Define Simple Harmonic Motion (SHM). Explain how SHM is related to Uniform Circular Motion.

Define Restoring Force. Write its formula for a spring-mass system. Write its SI Unit and Dimensional Formula.

Distinguish between Damped Oscillations and Undamped Oscillations.

What are Forced Oscillations? Define Resonance (Resonant Vibration). What is the condition for resonance to occur?

Write the expression for the Time Period of a Simple Pendulum. On what factors does it depend?

Write the formula for the Potential Energy, Kinetic Energy, and Total Energy of a particle executing SHM.

What is the Phase of a vibrating particle? What is the phase difference between velocity and displacement in SHM?

Define Spring Constant (Force Constant). Write its formula, SI unit, and dimensional formula.

Define a Wave. Classify waves on the basis of vibration of particles into Transverse and Longitudinal waves. Give one example of each.

Classify waves on the basis of medium:
a) Mechanical Waves (Elastic Waves)
b) Non-Mechanical Waves (Electromagnetic Waves)
Give two examples of each.

Classify waves on the basis of dimensions (1D, 2D, and 3D). Give an example for each type.

Define the following components of a wave. Write their SI Units and Dimensional Formulas:
a) Amplitude (A)
b) Time Period (T)
c) Frequency (\(\nu\))

Define the following terms. Write their formulas, SI Units, and Dimensional Formulas:
a) Wavelength (\(\lambda\))
b) Wave Number (\(\bar{\nu}\))
c) Angular Wave Number (Propagation Constant, \(k\))

Define Wave Velocity (Phase Velocity) and Angular Frequency (\(\omega\)). Write the relation between Wave Velocity, Frequency, and Wavelength.

Write the general equation of a Plane Progressive Wave traveling in the positive x-direction. Explain each term in the equation.

Distinguish between Progressive Waves and Stationary (Standing) Waves.

Define Beats. What is Beat Frequency? Write the formula for beat frequency in terms of individual frequencies.

What are Nodes and Antinodes in a stationary wave? What is the distance between two consecutive nodes?