Physics is a quantitative science. Every physical quantity is measured in terms of a standard unit. A complete measurement consists of a numerical value and a unit.
These are independent units. There are seven fundamental units in the SI system:
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric Current | ampere | A |
| Temperature | kelvin | K |
| Amount of Substance | mole | mol |
| Luminous Intensity | candela | cd |
Units obtained by combining fundamental units.
Every physical quantity can be expressed in terms of fundamental dimensions: [M], [L], [T], [A], [K], [mol], [cd].
Q1. The dimensional formula of torque is the same as that of:
Q2. Number of significant figures in 0.0003400 is:
Q3. The number of significant figures in 2.50 × 10³ is:
Q4. In the number 0.0700, how many significant figures are there?
Q5. The result of 12.34 + 2.5 should be reported as:
Q6. Dimensional formula of Planck’s constant is:
Q7. Which of the following has same dimensions as impulse?
Q8. If unit of mass is doubled and unit of time is halved, the unit of power becomes:
Q9. The unit of magnetic permeability μ₀ is:
Q10. Which of the following quantities is dimensionless?
Q11. Dimensional formula of ε₀ (permittivity of free space) is:
Q12. If F, V and T are taken as fundamental units, then dimensional formula of mass is:
Q13. If mass is doubled and velocity is halved, kinetic energy becomes:
Q14. Which of the following pairs have the same dimensions?
Q15. In error analysis, for Z = A ²B, the relative error is:
Q16. Which has dimensional formula [M⁰L⁰T⁻¹]?
Q17. The quantity which has same dimensions as that of √(P/ρ) is:
Q18. Which of the following is a dimensionless quantity?
Q19. The dimensional formula of angular momentum is:
Q20. The unit of gravitational constant G is:
Kinematics is the branch of physics that describes the motion of objects without considering the forces causing the motion.
Distance: Total path length (scalar)
Displacement: Shortest straight line distance from initial to final position (vector, can be zero)
Speed = Distance/Time (scalar)
Velocity = Displacement/Time (vector)
Acceleration = Change in velocity / Time
a = (v – u)/t
v = u + at
s = ut + ½at²
v² = u² + 2as
For downward motion: a = +g = +9.8 m/s²
For upward motion: a = –g
Horizontal velocity remains constant (aₓ = 0)
Time of flight: T = (2u sinθ)/g
Maximum height: H = (u² sin²θ)/(2g)
Horizontal range: R = (u² sin2θ)/g (Maximum at θ = 45°)
Velocity of A w.r.t. B = v_A – v_B
Q1. A particle moves with uniform velocity. Its acceleration is:
Q2. The slope of velocity-time graph gives:
Q3. A body is thrown vertically upward with velocity u. The maximum height reached is:
Q4. Time of flight for a projectile projected with velocity u at angle θ is:
Q5. The horizontal range of a projectile is maximum when angle of projection is:
Q6. A stone is dropped from a height h. It takes time t to reach ground. If it is dropped from height 4h, time taken will be:
Q7. The area under velocity-time graph represents:
Q8. A car moving with uniform acceleration covers 100 m in 5 s. If initial velocity is 10 m/s, acceleration is:
Q9. For a projectile, the ratio of maximum height to range is:
Q10. A particle is moving with constant speed in a circle. Its acceleration is:
Q11. The slope of displacement-time graph gives:
Q12. A ball is thrown upward with velocity 20 m/s. Time to reach highest point is (g=10 m/s²):
Q13. In projectile motion, the horizontal component of velocity:
Q14. The equation of motion v = u + at is applicable for:
Q15. A body covers 200 m in 10 s with uniform acceleration. Initial velocity is 5 m/s. Final velocity is:
Q16. The path of a projectile is:
Q17. If a body is projected vertically upward, its velocity at highest point is:
Q18. The unit of acceleration is:
Q19. A train moving with uniform acceleration has velocity 10 m/s at one point and 20 m/s after 5 s. Distance covered in 5 s is:
Q20. The area under acceleration-time graph gives:
Laws of Motion, given by Sir Isaac Newton, form the foundation of classical mechanics. They explain the relationship between force, mass, and motion.
An object at rest stays at rest and an object in motion continues in uniform motion in a straight line unless acted upon by an external unbalanced force.
The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
F = ma
Unit of force: Newton (N) = kg m s⁻²
Momentum (p) = mv
Impulse = F × Δt = Change in momentum
For every action, there is an equal and opposite reaction. Action and reaction act on different bodies.
In an isolated system (no external force), total momentum remains constant.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Static friction (fₛ) ≤ μₛ N
Kinetic friction (fₖ) = μₖ N
Centripetal Force: F = mv² / r
Banking of Roads (without friction):
tan θ = v² / (r g)
Q1. Newton’s first law is also known as:
Q2. A body of mass 5 kg is moving with velocity 10 m/s. Force required to stop it in 2 s is:
Q3. Action and reaction forces act on:
Q4. The law of conservation of momentum is a consequence of:
Q5. A 10 kg body is acted upon by a force of 20 N. Acceleration produced is:
Q6. The unit of impulse is:
Q7. A body of mass m is moving with velocity v. Its momentum is:
Q8. When a force is applied on a body, it can change:
Q9. A rocket works on the principle of:
Q10. The frictional force is maximum when the body is:
Q11. Coefficient of friction is:
Q12. A 5 kg block is on a horizontal surface. If μ = 0.4, limiting friction is (g=10 m/s²):
Q13. Inertia is a measure of:
Q14. A body of mass 2 kg is acted upon by two forces of 4 N and 6 N in opposite directions. Acceleration is:
Q15. The force required to keep a body moving with constant velocity on a horizontal surface is equal to:
Q16. A gun of mass 10 kg fires a bullet of mass 0.01 kg with velocity 400 m/s. Recoil velocity of gun is:
Q17. The unit of force in SI system is:
Q18. A 100 kg man stands on a weighing scale in a lift accelerating upward at 2 m/s². Reading of scale is (g=10 m/s²):
Q19. Which of the following is a self-adjusting force?
Q20. A ball of mass 0.5 kg is moving with velocity 10 m/s. Force required to stop it in 0.1 s is:
Work, Energy and Power are interrelated concepts. Work is done when a force produces displacement. Energy is the capacity to do work. Power is the rate of doing work.
Work done by a constant force:
W = F · s = F s cosθ (Scalar quantity, unit: Joule)
Work done by variable force = Area under F-s graph.
Kinetic Energy (K): K = ½ m v²
Potential Energy (U):
Mechanical Energy = KE + PE
Wnet = ΔK = ½ m v² – ½ m u²
K₁ + U₁ = K₂ + U₂ (in absence of non-conservative forces)
P = F · v = Work/Time, Unit: Watt (J/s)
Elastic: Momentum & KE conserved
Inelastic: Momentum conserved, KE not conserved
Q1. Work done by a force is maximum when angle between force and displacement is:
Q2. The unit of work is:
Q3. Kinetic energy of a body depends on:
Q4. A body of mass 2 kg is moving with velocity 10 m/s. Its kinetic energy is:
Q5. Work done in lifting a 10 kg mass to a height of 5 m is (g=10 m/s²):
Q6. The work done by gravity on a body moving horizontally is:
Q7. Potential energy of a body is maximum when:
Q8. The work-energy theorem states that work done by net force equals:
Q9. Power is measured in:
Q10. A machine does 1000 J of work in 10 s. Its power is:
Q11. The elastic potential energy stored in a spring is:
Q12. A 2 kg body falls from 10 m height. Its kinetic energy just before hitting ground is (g=10 m/s²):
Q13. The work done in stretching a spring by 10 cm is 2 J. Spring constant k is:
Q14. A body is moving with constant velocity. The work done by net force is:
Q15. The SI unit of power is:
Q16. For a freely falling body, total mechanical energy:
Q17. The work done in moving a charge in an electric field is maximum when angle between force and displacement is:
Q18. A pump lifts 100 kg of water to a height of 10 m in 20 s. Its power is (g=10 m/s²):
Q19. The slope of potential energy vs displacement graph gives:
Q20. A spring is stretched by 5 cm. If its spring constant is 200 N/m, potential energy stored is:
This chapter deals with extended bodies, centre of mass, and rotational motion.
For a system of particles:
Xcm = (m₁x₁ + m₂x₂ + ...)/M
Ycm = (m₁y₁ + m₂y₂ + ...)/M
COM of uniform rod is at mid-point, uniform disc/ring at centre.
Total linear momentum = M × Vcm
If no external force, total momentum is conserved.
I = Σmr² (about axis)
For ring (about central axis): MR²
For disc (about central axis): ½MR
²
For rod (about centre, perpendicular): ML²/12
τ = r × F = r F sinθ
τ = Iα (analogous to F = ma)
L = Iω
τ = dL/dt
In absence of external torque, angular momentum is conserved.
KE = ½ Iω²
v = rω
Total KE = ½mv² + ½Iω²
Q1. Centre of mass of a uniform rod of length L lies at:
Q2. Moment of inertia of a thin ring about its central axis is:
Q3. Torque is analogous to which linear quantity?
Q4. Angular momentum of a system is conserved when:
Q5. Moment of inertia of a solid disc about its diameter is:
Q6. For a system of particles, if no external force acts, then velocity of centre of mass:
Q7. Rotational kinetic energy of a body is given by:
Q8. The physical quantity analogous to mass in rotational motion is:
Q9. For pure rolling without slipping, the relation is:
Q10. SI unit of angular momentum is:
Q11. If net external torque on a system is zero, then:
Q12. Moment of inertia of a hollow sphere about its diameter is:
Q13. A body is rotating with constant angular velocity. Its angular acceleration is:
Q14. The relation between linear velocity and angular velocity is:
Q15. If a body is rotating about an axis, the torque required to stop it in time t is proportional to:
Q16. For a system in equilibrium, the net torque about any point is:
Q17. The moment of inertia is maximum for:
Q18. A wheel is rotating with angular velocity ω. If its moment of inertia is doubled and angular velocity is halved, angular momentum becomes:
Q19. The unit of torque is:
Q20. A solid sphere and a hollow sphere of same mass and radius are rolling down an inclined plane. Which one reaches the bottom first?
Gravitation is the universal force of attraction between any two bodies in the universe. It is the weakest fundamental force but has the longest range.
Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
F = G m₁m₂ / r²
G = 6.67 × 10⁻¹¹ N m² kg⁻² (Universal Gravitational Constant)
g = G M / R²
Value on Earth ≈ 9.8 m/s²
g decreases with height and depth. Value at poles > equator.
U = – G M m / r
Gravitational potential = – G M / r
vₑ = √(2GM/R) = √(2gR) ≈ 11.2 km/s (for Earth)
Escape velocity is independent of the mass of the body.
1. Law of Orbits: Planets move in elliptical orbits with the Sun at one focus.
2. Law of Areas: Areal velocity is constant.
3. Law of Periods: T² ∝ a³ (square of time period is proportional to cube of semi-major axis)
Orbital velocity = √(GM/r)
Time period T = 2π √(r³/GM)
Geostationary satellites have T = 24 hours.
Q1. The value of universal gravitational constant G is:
Q2. Acceleration due to gravity is maximum at:
Q3. Escape velocity from the surface of Earth is approximately:
Q4. Gravitational force is:
Q5. Kepler’s second law is based on conservation of:
Q6. The time period of a geostationary satellite is:
Q7. Gravitational potential energy of a body is:
Q8. The orbital velocity of a satellite close to Earth is:
Q9. g is maximum at:
Q10. The value of g at the centre of Earth is:
Q11. Kepler’s third law states that:
Q12. The escape velocity is independent of:
Q13. The gravitational force between two bodies is F. If the distance between them is doubled, the force becomes:
Q14. The value of g decreases with:
Q15. A satellite is revolving close to Earth. Its orbital velocity is nearly:
Q16. The gravitational potential at a point is:
Q17. The force of attraction between two bodies is F. If the mass of one body is doubled and distance is halved, the new force is:
Q18. The time period of a satellite orbiting close to Earth is:
Q19. The dimensional formula of G is:
Q20. A solid sphere and a hollow sphere of same mass and radius roll down an inclined plane. Which one reaches the bottom first?
This chapter deals with the behaviour of matter in bulk (solids, liquids, gases) under various conditions such as pressure, temperature, and force. It includes elasticity, surface tension, viscosity, and fluid mechanics.
Property of a material to regain its original shape and size after removal of deforming force.
Stress = Force / Area (unit: N/m²)
Strain = Change in dimension / Original dimension (dimensionless)
Hooke’s Law: Within elastic limit, stress ∝ strain
Modulus of Elasticity = Stress / Strain
Poisson’s Ratio (σ) = Lateral strain / Longitudinal strain (0.2 to 0.4)
Elastic Potential Energy = ½ × Stress × Strain × Volume
Pressure in a fluid = ρ g h
Pascal’s Law: Pressure applied to an enclosed fluid is transmitted undiminished.
Surface Tension (S) = Force / Length = Energy / Area
Capillary rise: h = 2 S cosθ / (ρ g r)
Excess pressure in liquid drop: 2S / r
Excess pressure in soap bubble: 4S / r
Stokes’ law: F = 6πη r v
Bernoulli’s principle: P + ρgh + ½ρv
² = constant
Q1. The SI unit of Young’s modulus is:
Q2. The property of a material to regain its original shape after removal of deforming force is called:
Q3. The ratio of lateral strain to longitudinal strain is called:
Q4. The excess pressure inside a soap bubble is:
Q5. The terminal velocity of a spherical body is proportional to:
Q6. The SI unit of surface tension is:
Q7. Bernoulli’s principle is based on:
Q8. The viscous force on a spherical body is given by:
Q9. The capillary rise is maximum in a tube of:
Q10. The bulk modulus of elasticity is defined as:
Q11. The angle of contact for water and glass is:
Q12. The velocity of efflux from an orifice at depth h below the free surface is:
Q13. The coefficient of viscosity has unit:
Q14. A liquid rises in a capillary tube. The height of rise is maximum when the angle of contact is:
Q15. The excess pressure inside a liquid drop of radius r is:
Q16. The Reynold’s number for streamline flow is:
Q17. The potential energy stored in a stretched wire is:
Q18. The viscosity of liquids:
Q19. The height of capillary rise is inversely proportional to:
Q20. In Bernoulli’s equation, the term ρgh represents:
Thermodynamics deals with the study of heat, work, and energy transformation in systems. It is governed by four fundamental laws.
If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This defines temperature.
Energy is conserved. Heat supplied to a system is used to increase its internal energy and to do work.
ΔU = Q – W (First law is the law of conservation of energy)
Specific heat capacity (c): Q = m c ΔT
Molar specific heat: Cₚ = Cᵥ + R (ideal gas)
Latent Heat: Heat required to change state without temperature change.
Entropy of the universe always increases (ΔS ≥ 0).
Carnot efficiency: η = 1 – (T₂ / T₁)
Q1. The first law of thermodynamics is a statement of:
Q2. In an isothermal process, the change in internal energy is:
Q3. The efficiency of a Carnot engine depends on:
Q4. The second law of thermodynamics implies that:
Q5. For an adiabatic process, PVγ = constant, where γ is:
Q6. The work done in an isochoric process is:
Q7. The entropy of the universe:
Q8. For an ideal gas, the internal energy depends only on:
Q9. The coefficient of performance of a refrigerator is:
Q10. In an adiabatic expansion, the temperature of the gas:
Q11. The process in which no heat is exchanged is called:
Q12. The slope of adiabatic curve is:
Q13. The efficiency of Carnot engine is 50%. If temperature of sink is 300 K, temperature of source is:
Q14. The change in internal energy in a cyclic process is:
Q15. The first law of thermodynamics is applicable to:
Q16. For an ideal gas, Cᵥ = (3/2) R. The gas is:
Q17. The area under P-V diagram represents:
Q18. The second law of thermodynamics gives the concept of:
Q19. In free expansion of an ideal gas, the work done is:
Q20. The relation between Cₚ and Cᵥ for an ideal gas is:
Kinetic Theory explains the behaviour of gases based on the motion of their molecules. It assumes gases consist of a large number of tiny particles in random motion.
P = (1/3) ρ v_rms²
Average KE per molecule = (3/2) kT
v_rms = √(3RT/M)
Each degree of freedom contributes (1/2) kT energy per molecule.
γ = 1 + 2/f
λ = 1 / (√2 π d² n)
(P + a/V²)(V – b) = RT
Q1. According to kinetic theory of gases, the pressure exerted by gas is due to:
Q2. The root mean square speed of gas molecules is:
Q3. The average kinetic energy per molecule of a gas is:
Q4. For a diatomic gas, the value of γ (Cₚ/Cᵥ) is:
Q5. The mean free path of gas molecules is inversely proportional to:
Q6. The real gas equation is:
Q7. At high temperature and low pressure, real gases behave like:
Q8. The law of equipartition of energy states that each degree of freedom contributes:
Q9. For monatomic gas, the molar specific heat at constant volume Cᵥ is:
Q10. The root mean square speed is related to most probable speed as:
Q11. The pressure of an ideal gas is given by:
Q12. The average speed of gas molecules is:
Q13. In kinetic theory, the collision between molecules is:
Q14. The temperature at which real gas behaves ideally is called:
Q15. The van der Waals constant ‘a’ is a measure of:
Q16. For hydrogen gas, the value of γ is:
Q17. The mean free path is independent of:
Q18. The internal energy of an ideal gas depends only on:
Q19. The ratio of specific heats γ is minimum for:
Q20. At absolute zero temperature, the rms speed of gas molecules is:
Oscillations are periodic to-and-fro motions about a mean position. Simple Harmonic Motion (SHM) is the simplest form of oscillatory motion.
Period (T), Frequency (f = 1/T), Angular frequency (ω = 2πf).
a = –ω²x
x = A sin(ωt + φ)
v = Aω cos(ωt + φ) (max = Aω)
a = –Aω
² sin(ωt + φ) (max = Aω²)
KE = ½ m ω² (A² – x²)
PE = ½ m ω² x²
Total Energy = ½ m ω² A² (constant)
T = 2π √(L/g)
T = 2π √(m/k)
Resonance occurs when driving frequency = natural frequency.
Q1. In simple harmonic motion, the acceleration is:
Q2. The time period of a simple pendulum is independent of:
Q3. The total energy in simple harmonic motion is:
Q4. The velocity of a particle in SHM is maximum at:
Q5. The time period of a spring-mass system is:
Q6. In SHM, the phase difference between velocity and displacement is:
Q7. The restoring force in SHM is:
Q8. A simple pendulum has time period 2 s on Earth. On a planet where g is 4 times, time period will be:
Q9. The amplitude of SHM is:
Q10. For a particle in SHM, the potential energy is minimum at:
Q11. The frequency of oscillation of a simple pendulum is independent of:
Q12. In damped oscillation, the amplitude:
Q13. The condition for resonance in forced oscillation is:
Q14. The total energy in undamped SHM is:
Q15. A particle executes SHM with amplitude A. The distance from mean position where KE = PE is:
Q16. The time period of a simple pendulum on the Moon (g_moon = g/6) is:
Q17. In SHM, the acceleration is zero at:
Q18. The physical quantity that remains constant in undamped SHM is:
Q19. The equation of SHM is x = A sin(ωt). The velocity is:
Q20. For a spring-mass system, if mass is doubled and spring constant is halved, the time period becomes:
Waves are disturbances that transfer energy from one point to another without the transfer of matter. They are of two main types: mechanical and electromagnetic.
y = A sin(kx – ωt) or y = A sin(ωt – kx)
where k = 2π/λ (wave number), ω = 2πf (angular frequency)
Speed of sound increases with temperature and decreases with density.
When two or more waves meet, the resultant displacement is the algebraic sum of individual displacements.
Interference:
Constructive: Path difference = nλ → Maximum intensity
Destructive: Path difference = (2n+1)λ/2 → Minimum intensity
Formed by superposition of two waves of same frequency and amplitude travelling in opposite directions.
For string fixed at both ends:
λ = 2L / n (n = 1,2,3...)
Fundamental frequency = v / (2L)
Beat frequency = |f₁ – f₂|
f' = f (v ± v_o) / (v ± v_s)
Q1. The speed of a wave on a string is given by:
Q2. The distance between two consecutive crests is called:
Q3. The frequency of a wave is 50 Hz. Its time period is:
Q4. In a longitudinal wave, the particles vibrate:
Q5. The speed of sound in air is approximately:
Q6. When two waves of same frequency and amplitude interfere constructively, the resultant amplitude is:
Q7. The phenomenon of beats is due to:
Q8. The Doppler effect is observed when:
Q9. For a standing wave on a string fixed at both ends, the distance between two consecutive nodes is:
Q10. The fundamental frequency of a string of length L is:
Q11. Sound waves cannot travel in:
Q12. The speed of sound is maximum in:
Q13. In an open organ pipe, the fundamental frequency has:
Q14. The beat frequency is equal to:
Q15. The wavelength of a sound wave is 1 m. Its frequency in air (v=340 m/s) is:
Q16. In a closed organ pipe, the fundamental frequency has:
Q17. The speed of sound in air is independent of:
Q18. When a wave travels from rarer to denser medium, its speed:
Q19. The phenomenon of superposition of two waves is called:
Q20. The minimum distance between a node and an antinode in a standing wave is:
Electrostatics is the study of electric charges at rest. Charges are of two types: positive and negative. Like charges repel, unlike charges attract.
The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
F = k |q₁ q₂| / r²
(k = 1/(4πε₀) = 9 × 10⁹ N m² C⁻²)
Force experienced by a unit positive test charge.
E = F / q₀ = k Q / r² (directed away from positive charge)
Electric field lines start from positive charge and end on negative charge, never intersect.
Φ = E · A = E A cosθ
Gauss’s Law: Total electric flux through a closed surface = Q_enclosed / ε₀
Work done per unit positive test charge from infinity.
V = k Q / r (scalar, unit: Volt)
Surfaces where potential is same. No work is done in moving a charge on an equipotential surface.
C = Q / V
Parallel plate capacitor: C = ε₀ A / d
With dielectric: C = K ε₀ A / d
Energy stored: U = ½ C V² = Q² / (2C)
Q1. The dimensional formula of electric field is:
Q2. Two charges +q and +4q are placed 6 cm apart. The point where electric field is zero is:
Q3. The SI unit of electric flux is:
Q4. According to Gauss’s law, electric flux through a closed surface depends upon:
Q5. Electric potential is a:
Q6. The capacitance of a parallel plate capacitor increases when:
Q7. Energy stored in a charged capacitor is given by:
Q8. In series combination of capacitors, the equivalent capacitance is:
Q9. The electric field inside a charged conductor is always:
Q10. Electric potential at the midpoint between two charges +q and –q separated by 2a is:
Q11. When a dielectric is inserted in a charged capacitor (battery disconnected), its potential difference:
Q12. Work done in moving a charge along an equipotential surface is:
Q13. Electric field due to an infinite plane sheet of charge is:
Q14. Three capacitors 2 μF, 4 μF and 6 μF are connected in parallel. Equivalent capacitance is:
Q15. Torque on an electric dipole in uniform electric field is maximum when angle between p and E is:
Q16. If a dielectric is introduced between the plates of a charged isolated capacitor, its energy:
Q17. Electric potential due to a point charge at distance r is 30 V. If distance is doubled, potential becomes:
Q18. A 10 μF capacitor is charged to 100 V. Energy stored in it is:
Q19. Force between two charges is F. If both charges are doubled and distance is halved, new force is:
Q20. Electric field at equatorial point due to a dipole is:
Current electricity deals with the flow of electric charges in conductors. It is the study of steady (direct) current in electrical circuits.
Rate of flow of charge through a cross-section.
I = Q / t (SI unit: Ampere, A)
Current is a scalar quantity. Conventional current flows from positive to negative terminal.
For ohmic conductors at constant temperature, potential difference is directly proportional to current.
V = I R
R = Resistance (unit: Ohm, Ω)
R = ρ L / A
ρ = Resistivity (material property, unit: Ω m)
- Resistance of metals increases with temperature.
- Resistance of semiconductors decreases with temperature.
Balanced when P/Q = R/S → No current through galvanometer.
Meter Bridge is a practical form used to measure unknown resistance.
A device to measure potential difference accurately.
Principle: Potential gradient along uniform wire is constant.
Applications: Comparison of emfs, measurement of internal resistance.
EMF (E): Work done by cell per unit charge.
Terminal voltage V = E – Ir (when current flows)
- Series: Total EMF = nE, Total r = nr
- Parallel: Total EMF = E, Total r = r/n
H = I² R t
Power P = I² R = V I = V² / R
Q1. The SI unit of electric current is:
Q2. According to Ohm’s law, if temperature is constant:
Q3. Resistance of a wire is doubled when its length is doubled and area of cross-section is:
Q4. Three resistors of 2 Ω, 3 Ω and 6 Ω are connected in parallel. Equivalent resistance is:
Q5. Kirchhoff’s Current Law is based on the conservation of:
Q6. In series combination of resistors, the equivalent resistance is:
Q7. The condition for balance in a Wheatstone bridge is:
Q8. A potentiometer is used to:
Q9. Terminal voltage of a cell is less than its emf when:
Q10. According to Joule’s law of heating, heat produced is:
Q11. Resistivity of a material depends on:
Q12. In a series circuit, the current is:
Q13. The internal resistance of a cell is:
Q14. Meter bridge is based on the principle of:
Q15. Power dissipated in a resistor is maximum when:
Q16. Three cells of emf 2 V each and internal resistance 1 Ω each are connected in series. Total emf and total internal resistance are:
Q17. The colour code for a 1 kΩ resistor is:
Q18. In a potentiometer, the null point is obtained at 40 cm for a cell of emf 1.2 V. For another cell, null point is at 60 cm. Its emf is:
Q19. The heating element of an electric heater should have:
Q20. A 100 W bulb is connected to 200 V supply. Current drawn by the bulb is:
This chapter deals with the magnetic field produced by electric current and the properties of magnets.
Magnetic field due to a small current element:
dB = (μ₀ / 4π) (I dl sinθ / r²)
(μ₀ = 4π × 10⁻⁷ T m A⁻¹)
∮ B · dl = μ₀ I_enclosed
F = q (v × B)
F = q v B sinθ
Radius of path: r = m v / (q B)
Time period: T = 2π m / (q B)
F = I (L × B)
F = I L B sinθ
τ = N I A B sinθ
Moving coil galvanometer works on this principle.
B = μ₀ (H + M)
χ = M / H, μ_r = 1 + χ
Curie’s Law: χ ∝ 1/T (for paramagnetic materials)
Q1. The SI unit of magnetic field B is:
Q2. Magnetic field due to a straight current-carrying wire at distance r is:
Q3. Magnetic field at the centre of a circular loop of radius R carrying current I is:
Q4. Inside a long solenoid, magnetic field is:
Q5. Ampere’s circuital law is:
Q6. Force on a moving charge in magnetic field is given by:
Q7. A charged particle moves in a magnetic field. The work done by magnetic force is:
Q8. Force on a current-carrying conductor in magnetic field is:
Q9. Torque on a current loop in uniform magnetic field is maximum when angle between area vector and B is:
Q10. The magnetic field inside a toroid is:
Q11. A charged particle enters perpendicular to magnetic field. Its path is:
Q12. The working principle of moving coil galvanometer is:
Q13. Diamagnetic materials have:
Q14. Curie’s law is applicable for:
Q15. Hysteresis curve is shown by:
Q16. The magnetic field inside a solenoid does not depend on:
Q17. A proton and an α-particle enter a magnetic field with same velocity. The ratio of radii of their paths is:
Q18. The direction of magnetic field due to a current-carrying wire is given by:
Q19. The magnetic susceptibility of diamagnetic material is:
Q20. Area of hysteresis loop represents:
Electromagnetic Induction is the phenomenon of inducing an emf (and hence current) in a conductor due to change in magnetic flux linked with it.
Φ = B · A = B A cosθ
(SI unit: Weber, Wb)
The direction of induced emf is such that it opposes the change in magnetic flux that produces it (conservation of energy).
e = B l v (rod moving perpendicular to B)
For rotating rod: e = ½ B ω L²
Induced currents in bulk conductors. They cause energy loss (heating) but are useful in induction furnaces, electromagnetic damping, speedometers, etc.
Induced emf due to change in current in the same coil.
e = – L di/dt
L = Self-inductance (unit: Henry)
For solenoid: L = μ₀ N² A / l
Induced emf in one coil due to change in current in neighbouring coil.
e₂ = – M di₁/dt
M = Mutual inductance
Works on electromagnetic induction.
Induced emf = N B A ω sin(ωt)
Q1. The phenomenon of electromagnetic induction is based on the law of conservation of:
Q2. Induced emf in a coil is given by Faraday’s law as:
Q3. Lenz’s law is a consequence of the law of conservation of:
Q4. Motional emf induced in a rod of length l moving with velocity v perpendicular to magnetic field B is:
Q5. The self-inductance of a coil is measured in:
Q6. Eddy currents are used in:
Q7. The energy stored in an inductor carrying current I is:
Q8. In mutual induction, the induced emf in secondary coil is:
Q9. The peak value of emf induced in AC generator is:
Q10. The direction of induced current is given by:
Q11. Self-inductance of a coil depends on:
Q12. When a magnet is moved towards a coil, the induced current opposes the motion. This is due to:
Q13. The unit of mutual inductance is:
Q14. In an AC generator, the induced emf is maximum when the coil is:
Q15. Eddy currents can be minimised by:
Q16. The inductance of a solenoid is increased by:
Q17. A conducting rod of length l moves with velocity v perpendicular to magnetic field B. Induced emf is maximum when angle between v and B is:
Q18. The energy stored in a magnetic field of inductor is:
Q19. When a magnet is dropped into a metallic tube, its acceleration is:
Q20. In an AC generator, the frequency of induced emf is:
Alternating Current (AC) periodically reverses its direction. It is easier to transmit over long distances and can be stepped up or down using transformers.
V = V₀ sin(ωt) or V = V₀ cos(ωt)
I = I₀ sin(ωt + φ)
Impedance Z = √[R² + (X_L – X_C)²]
Phase angle φ = tan⁻¹[(X_L – X_C)/R]
Average Power P_avg = V_rms I_rms cosφ
Power factor = cosφ (1 for resistor, 0 for pure L or C)
Energy oscillates between capacitor and inductor.
Resonant frequency f = 1 / (2π √(LC))
Step-up / Step-down AC voltage.
V_s / V_p = N_s / N_p
I_p / I_s = N_s / N_p (ideal)
Efficiency = (Output Power / Input Power) × 100%
Losses: Copper loss, Iron loss (hysteresis + eddy current), Flux leakage.
Q1. The RMS value of AC current is related to peak value I₀ as:
Q2. In a purely inductive circuit, the phase difference between voltage and current is:
Q3. The power factor of a purely capacitive circuit is:
Q4. In an LCR series circuit at resonance, the impedance is:
Q5. The average power dissipated in a pure inductor is:
Q6. For a transformer, the turns ratio N_s / N_p = 4. It is a:
Q7. The resonant frequency of an LC circuit is:
Q8. In a series LCR circuit, power factor is maximum when:
Q9. The inductive reactance X_L is:
Q10. In a transformer, if input power is 1000 W and efficiency is 90%, output power is:
Q11. The capacitive reactance X_C decreases with:
Q12. In a purely resistive AC circuit, the average power dissipated is:
Q13. The unit of inductive reactance is:
Q14. At resonance in LCR circuit, the current is:
Q15. The power factor of a series LCR circuit at resonance is:
Q16. In a transformer, core is laminated to reduce:
Q17. The frequency of AC supply in India is:
Q18. In a purely capacitive circuit, current:
Q19. The reactance of a capacitor at very high frequency becomes:
Q20. In an ideal transformer, the efficiency is:
Electromagnetic waves are transverse waves produced by accelerating charges. They do not require a medium and travel with the speed of light in vacuum (c = 3 × 10⁸ m/s).
Maxwell modified Ampere’s law by introducing displacement current.
I_d = ε₀ dΦ_E / dt
This makes the equations consistent and leads to the prediction of electromagnetic waves.
EM waves are classified by frequency/wavelength:
Poynting Vector S = (1/μ₀) E × B (direction of energy flow)
Average intensity I = (1/2) c ε₀ E₀² = (1/2) E₀ B₀ / μ₀
Momentum p = U / c (U = energy)
Radiation pressure = I / c (perfect absorber)
= 2I / c (perfect reflector)
Q1. Electromagnetic waves are:
Q2. The speed of electromagnetic waves in vacuum is given by:
Q3. Displacement current was introduced by:
Q4. Which of the following has the longest wavelength?
Q5. The Poynting vector represents:
Q6. Radiation pressure on a perfect absorber is:
Q7. EM waves are produced by:
Q8. Which EM wave is used in radar?
Q9. The frequency range of visible light is approximately:
Q10. The wave that carries maximum energy per photon is:
Q11. Displacement current exists only when:
Q12. The ratio of electric field to magnetic field in EM wave is:
Q13. Which EM wave is used for sterilisation?
Q14. The energy density of EM wave is:
Q15. Which of the following can be polarised?
Q16. The wavelength range of X-rays is approximately:
Q17. The source of gamma rays is:
Q18. Intensity of EM wave is proportional to:
Q19. Which wave has the highest penetrating power?
Q20. The relation c = 1/√(μ₀ ε₀) shows that speed of light depends on:
Ray Optics treats light as rays travelling in straight lines. It explains reflection, refraction, and image formation by mirrors and lenses.
Laws of Reflection: Angle of incidence = angle of reflection; incident ray, reflected ray and normal lie in the same plane.
Plane Mirror: Virtual, erect image of same size.
Spherical Mirrors:
Concave (converging), Convex (diverging)
Mirror Formula: 1/v + 1/u = 1/f
Magnification: m = –v/u = h'/h
Snell’s Law: μ = sin i / sin r
Refractive index μ = c / v
Refraction at Spherical Surface: μ₂/v – μ₁/u = (μ₂ – μ₁)/R
Thin Lens Formula: 1/v – 1/u = 1/f
Lens Maker’s Formula: 1/f = (μ – 1)(1/R₁ – 1/R₂)
Power of Lens: P = 1/f (metre) → unit: Dioptre (D)
Combination in contact: P = P₁ + P₂
Deviation δ = (μ – 1)A (small angle prism)
Dispersion: Splitting of white light into colours (VIBGYOR)
Rainbow: Natural dispersion by water droplets.
Q1. The focal length of a concave mirror is:
Q2. Image formed by a plane mirror is:
Q3. Mirror formula is:
Q4. For a convex mirror, focal length is:
Q5. Snell’s law is:
Q6. Power of a lens is measured in:
Q7. For a convex lens, when object is at 2F, image is:
Q8. Rainbow is formed due to:
Q9. The magnifying power of a simple microscope is:
Q10. Myopia is corrected by:
Q11. The focal length of a convex lens is 20 cm. Its power is:
Q12. For a concave mirror, object at infinity, image is formed at:
Q13. The angle of minimum deviation for a prism depends on:
Q14. Astronomical telescope in normal adjustment has magnification:
Q15. Hypermetropia is corrected by:
Q16. Critical angle is the angle of incidence for which angle of refraction is:
Q17. A convex lens forms real image when object is placed:
Q18. The splitting of white light into colours is called:
Q19. For compound microscope, magnification is:
Q20. Astigmatism is corrected by:
Wave Optics deals with the wave nature of light. It explains phenomena like interference, diffraction, and polarisation that cannot be explained by ray optics.
Every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the tangent to these secondary wavelets.
Superposition of two waves of same frequency and constant phase difference.
Young’s Double Slit Experiment:
Bright fringe: Path difference = nλ
Dark fringe: Path difference = (2n+1)λ/2
Fringe width β = λ D / d
Bending of light around obstacles or through apertures.
Single Slit Diffraction:
Central maximum width ≈ 2λD/a
Minima: a sinθ = nλ
Restriction of vibration of electric field vector in a particular plane.
Malus’ Law: I = I₀ cos²θ
Brewster’s Law: tan i_p = μ
Ability to distinguish two closely spaced objects.
Resolving power of microscope = 1.22λ / (2μ sinθ)
Resolving power of telescope = 1.22λ / D
Q1. Wave optics is based on the:
Q2. According to Huygens’ principle, the new wavefront is:
Q3. In Young’s double slit experiment, bright fringes occur when path difference is:
Q4. Fringe width in Young’s double slit experiment is given by:
Q5. Central fringe in Young’s double slit experiment is:
Q6. In single slit diffraction, the width of central maximum is:
Q7. Malus’ law is related to:
Q8. Brewster’s law gives the relation for:
Q9. Resolving power of a telescope is proportional to:
Q10. In interference pattern, if one slit is closed, the pattern becomes:
Q11. Coherent sources are required for:
Q12. The condition for constructive interference is:
Q13. Polarisation proves that light is:
Q14. In single slit diffraction, position of first minima is given by:
Q15. The resolving power of a microscope increases with:
Q16. Which of the following cannot be polarised?
Q17. In interference, the intensity at bright fringe is:
Q18. The angular width of central maximum in single slit diffraction is proportional to:
Q19. Polaroids are used in:
Q20. The phenomenon responsible for the blue colour of the sky is:
This chapter explains the dual nature of light and matter — both behave as waves as well as particles.
Phenomenon of emission of electrons from a metal surface when light of suitable frequency falls on it.
Experimental Observations:
Einstein’s Photoelectric Equation:
hf = φ₀ + ½ m v_max² (where φ₀ = hf₀ = work function)
Stopping potential V₀ = (hf – φ₀)/e
All moving particles have wave nature.
de Broglie wavelength: λ = h / p = h / (m v) = h / √(2mK)
Wavelength is significant for microscopic particles (electrons, protons etc.).
Confirmed wave nature of electrons by observing diffraction pattern from nickel crystal.
It is impossible to simultaneously determine both position and momentum of a particle with absolute accuracy.
Δx · Δp ≥ h / (4π) (or ≥ ħ/2)
Q1. The photoelectric effect proves the:
Q2. The threshold frequency for a metal is f₀. If the frequency of incident light is doubled, the maximum kinetic energy of photoelectrons becomes:
Q3. The slope of the graph between stopping potential (V₀) and frequency (f) of incident light is:
Q4. de Broglie wavelength of an electron accelerated through potential V is:
Q5. Which experiment confirmed the wave nature of electrons?
Q6. If the momentum of a particle is doubled, its de Broglie wavelength becomes:
Q7. The work function of a metal is 2 eV. Light of wavelength 2000 Å is incident on it. The maximum kinetic energy of photoelectrons is (hc = 12400 eV Å):
Q8. Heisenberg’s uncertainty principle is a consequence of:
Q9. The de Broglie wavelength associated with an electron of mass m moving with velocity v is:
Q10. In photoelectric effect, if intensity is doubled, the maximum kinetic energy of photoelectrons:
Q11. The minimum uncertainty in position of an electron (mass = 9.1 × 10⁻³¹ kg) moving with velocity 300 m/s is (h = 6.63 × 10⁻³⁴ J s):
Q12. Which of the following particles has the largest de Broglie wavelength when moving with same velocity?
Q13. In photoelectric effect, the graph of maximum kinetic energy vs frequency is:
Q14. The de Broglie wavelength of a particle at rest is:
Q15. If the frequency of incident light is increased by 20%, the stopping potential increases by 50%. The work function of the metal is (in eV, approx):
Q16. Which of the following has the smallest de Broglie wavelength?
Q17. The photoelectric current is directly proportional to:
Q18. Uncertainty in position of an electron is 0.01 Å. The uncertainty in its momentum is (approx):
Q19. The de Broglie wavelength of a 100 g ball moving with velocity 100 m/s is:
Q20. In photoelectric effect, the number of photoelectrons emitted is proportional to:
This chapter deals with the structure of atoms and the experimental evidence that led to the modern model of the atom.
Most alpha particles passed straight through the thin gold foil, a few were deflected by large angles, and very few bounced back.
Conclusions:
Distance of closest approach: d = (Z e²) / (4πε₀ K) where K is kinetic energy of α-particle.
Postulates:
Radius of nth orbit: rₙ = n² a₀ / Z (a₀ = 0.529 Å)
Velocity: vₙ = (2.18 × 10⁶ Z / n) m/s
Energy: Eₙ = –13.6 Z² / n² eV
Energy difference: ΔE = 13.6 Z ² (1/n₁² – 1/n₂ ²) eV
Rydberg Formula: 1/λ = R (1/n₁² – 1/n₂²) (R = 1.097 × 10⁷ m⁻¹)
Q1. In Rutherford’s α-particle scattering experiment, most particles passed undeflected because:
Q2. The radius of first Bohr orbit of hydrogen atom is 0.529 Å. The radius of second orbit is:
Q3. The energy required to excite electron in hydrogen atom from n=2 to n=3 is:
Q4. Which series of hydrogen spectrum lies in the visible region?
Q5. Bohr’s model could not explain:
Q6. The ratio of radii of first three Bohr orbits in hydrogen atom is:
Q7. Shortest wavelength in Lyman series of hydrogen is (R = 1.097 × 10⁷ m⁻¹):
Q8. Angular momentum of electron in 3rd Bohr orbit is:
Q9. Ionisation energy of hydrogen atom is 13.6 eV. Energy required to excite from n=1 to n=2 is:
Q10. Which of the following is a limitation of Bohr’s model?
Q11. The ratio of velocities of electron in first and second Bohr orbit is:
Q12. Rydberg formula is used to calculate:
Q13. Distance of closest approach in Rutherford experiment is directly proportional to:
Q14. The series limit of Balmer series corresponds to transition from:
Q15. If the energy of electron in n=1 orbit is –13.6 eV, energy in n=4 orbit is:
Q16. Which of the following transitions gives maximum energy in hydrogen spectrum?
Q17. The speed of electron in first Bohr orbit is:
Q18. The number of spectral lines when electron jumps from n=5 to n=1 in hydrogen atom is:
Q19. Rutherford’s experiment could not explain:
Q20. The ratio of wavelengths of first line of Lyman series to first line of Balmer series is:
The nucleus is the central core of the atom containing protons and neutrons (collectively called nucleons). It is extremely small (~10⁻¹⁵ m) but contains almost all the mass of the atom.
Isotopes: Same Z, different A
Isobars: Same A, different Z
Isotones: Same N, different Z
Radius R = R₀ A¹/³ (R₀ ≈ 1.2 × 10⁻¹⁵ m)
Density ≈ 10¹⁷ kg/m³ (almost constant for all nuclei)
Strong, short-range, charge-independent attractive force between nucleons. Much stronger than electromagnetic force inside the nucleus.
Mass Defect Δm = [Z m_p + (A–Z) m_n – M]
Binding Energy BE = Δm c²
Binding energy per nucleon is maximum near A = 56 (Fe-56).
Spontaneous disintegration of unstable nuclei.
Three types: α-decay, β-decay, γ-decay.
Law of Radioactive Decay: N = N₀ e^{-λt}
Half-life T_{1/2} = 0.693 / λ
Mean Life τ = 1/λ = 1.44 T_{1/2}
Nuclear Fission: Heavy nucleus splits into lighter nuclei + energy (used in nuclear reactors).
Nuclear Fusion: Light nuclei combine to form heavier nucleus + energy (source of energy in stars).
Q1. The radius of a nucleus is proportional to:
Q2. Nuclear density is approximately:
Q3. Binding energy per nucleon is maximum for:
Q4. Isotopes of an element have same:
Q5. Half-life of a radioactive substance is 4 days. After 16 days the fraction of substance left is:
Q6. The nuclear force is:
Q7. Mass defect is converted into:
Q8. In α-decay, the daughter nucleus has:
Q9. The mean life of a radioactive substance is 1.44 times its half-life. This relation is:
Q10. In nuclear fission:
Q11. The SI unit of decay constant (λ) is:
Q12. Which of the following is used as a moderator in nuclear reactors?
Q13. In β⁻ decay, the atomic number of daughter nucleus:
Q14. The source of energy in stars is:
Q15. Binding energy per nucleon curve shows that:
Q16. The relation between half-life and mean life is:
Q17. In γ-decay:
Q18. The process responsible for energy production in the Sun is:
Q19. Which of the following is a fissile material?
Q20. Energy is released in nuclear fusion because:
Semiconductors have conductivity between conductors and insulators. Their conductivity can be controlled by temperature, impurities, and electric field.
Intrinsic Semiconductor: Pure Si or Ge.
Extrinsic Semiconductor: Doped.
• n-type: Pentavalent impurity (e.g., P, As) → majority electrons.
• p-type: Trivalent impurity (e.g., B, In) → majority holes.
Formed by joining p-type and n-type semiconductors.
Depletion region forms with barrier potential (~0.7 V for Si, 0.3 V for Ge).
Forward Bias: Low resistance, current flows.
Reverse Bias: High resistance, very small reverse saturation current.
npn and pnp types.
Current gain β = I_C / I_B (Common Emitter).
Used as amplifier and switch.
AND, OR, NOT, NAND, NOR, XOR.
NAND and NOR are universal gates.
Q1. In an intrinsic semiconductor, the number of electrons and holes are:
Q2. In n-type semiconductor, the majority charge carriers are:
Q3. The barrier potential of a silicon p-n junction diode is approximately:
Q4. In forward bias of a p-n junction diode, the current is mainly due to:
Q5. Zener diode is primarily used as a:
Q6. In a transistor, the current gain β in common emitter configuration is:
Q7. Which of the following is a universal gate?
Q8. In reverse bias, the width of depletion layer:
Q9. LED emits light when the diode is:
Q10. In common emitter configuration, input is applied between:
Q11. The energy gap of a semiconductor is:
Q12. In a p-n junction diode, the reverse saturation current is due to:
Q13. Solar cell works on the principle of:
Q14. In a transistor, the emitter is doped:
Q15. The truth table of NAND gate is same as:
Q16. Photodiode is used in:
Q17. In logic gates, the output of OR gate is 1 when:
Q18. The majority charge carriers in p-type semiconductor are:
Q19. In a transistor, the base region is:
Q20. Which of the following is a universal gate?
Communication is the process of transmitting information from one place to another. Modern systems use electromagnetic waves as carrier waves.
Range of frequencies required for transmission.
Speech: ~ 2800 Hz, Music: ~ 20 kHz, TV: ~ 6 MHz.
Superimposing a low-frequency message signal on a high-frequency carrier wave.
Need for Modulation: Long distance transmission, avoid interference, reduce antenna size.
Types: Amplitude Modulation (AM), Frequency Modulation (FM), Phase Modulation (PM).
Modulation index m = Aₘ / A_c (for AM, m ≤ 1).
Process of recovering the original message signal from the modulated carrier.
Uses geostationary satellites (height ≈ 36,000 km). Uplink and downlink frequencies.
Optical fibre communication, Mobile telephony (cellular concept), Internet, Satellite communication.
Q1. The process of superimposing a low frequency message signal on a high frequency carrier wave is called:
Q2. Modulation is necessary because:
Q3. In amplitude modulation, the modulation index m is:
Q4. Sky wave propagation is suitable for frequencies in the range:
Q5. The height of a geostationary satellite above Earth’s surface is approximately:
Q6. In ground wave propagation, the wave follows:
Q7. Optical fibre communication works on the principle of:
Q8. Bandwidth of a TV signal is approximately:
Q9. In frequency modulation (FM), the frequency of carrier wave:
Q10. Demodulation is the process of:
Q11. Critical frequency is related to:
Q12. In satellite communication, the uplink frequency is:
Q13. Which propagation mode is used for TV transmission?
Q14. The main advantage of optical fibre communication is:
Q15. In AM, the sideband frequencies are:
Q16. The cellular concept is used in:
Q17. Maximum usable frequency (MUF) is related to:
Q18. In a communication system, the transducer converts:
Q19. Which of the following has the highest bandwidth?
Q20. The main advantage of frequency modulation over amplitude modulation is:
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