Class 11 Physics Complete Derivations List (2M, 3M, 5M)

Curated by Er. VISHAL TAANK Updated for 2026 Exams • Based on CBSE/HP Board Syllabus

Exam Alert: Stop wasting time on unnecessary theory! Master this exact list to secure your 5-mark and 3-mark derivation questions directly in your Class 11 finals.

1. Units and Dimensions

1. Explain the three applications of dimensional analysis with examples (checking correctness, conversion of units, deriving formulas).
3M

2. Kinematics

1.State Parallelogram (or Triangle) Law of Vector addition and derive the magnitude and direction of the resultant vector.
3M
2.Derive the equations of motion (v=u+at, s=ut+½at², v²-u²=2as) using graphical method.
3M
3.Derive the equations of motion (v=u+at, s=ut+½at², v²-u²=2as) using calculus method.
3M
4.Projectile fired at an angle θ with horizontal: Derive expressions for Time of Flight, Maximum Height, Horizontal Range, and the Equation of Trajectory (ground to ground projectile). Also show the path is parabolic.
5M
5.Projectile fired from the top of a tower horizontally: Derive expressions for Time of Flight, Horizontal Range, and Equation of Trajectory. Also show the path is parabolic.
5M

3. Laws of Motion

1.State and Derive Newton's Second and Third laws of motion.
3M+3M
2.State and prove the Law of Conservation of Linear Momentum.
3M
3.Find the acceleration of a block sliding down a rough inclined plane with constant velocity.
3M
4.Find the acceleration of a block sliding up a rough inclined plane with constant velocity.
3M
5."It is easier to pull than to push a lawn roller." Explain with a diagram and resolution of vectors.
3M
6.Derive the expression for the maximum safe velocity of a car taking a turn on a level circular road (including friction).
3M
7.Explain the bending of a cyclist while taking a turn and derive the angle of bend.
3M
8.Derive the expression for the maximum velocity of a car on a banked road (without friction).
3M
9.Show that Newton's Second Law is the real law of motion.
5M
10.Derive the expression for the velocity of a car taking a turn on a banked road including friction.
5M

4. Work, Power & Energy

1.Find the work done in stretching a spring.
3M
2.Derive an expression for Kinetic Energy if due to external force particle start moving from rest.
3M
3.State and prove the Work-Energy Theorem.
3M
4.Derive the expression for the Elastic Potential Energy of a stretched spring.
3M
5.State and prove the Conservation of Mechanical Energy for a freely falling body.
4M
6.Show that in a 1D elastic collision, if the masses of bodies are the same, they interchange their velocities.
5M
7.Show that in a 1D elastic collision, the velocity of separation is equal to the velocity of approach.
5M

5. System of Particles & Rotational Motion

1.Define Radius of Gyration and derive its expression.
3M
2.Derive the relation between Torque (τ) and Angular Momentum (L).
3M
3.Derive the Moment of Inertia (MOI) of a ring about its axis perpendicular to the plane and passing through the center.
3M
4.Derive the Moment of Inertia (MOI) of a disc about its axis perpendicular to the plane and passing through the center.
3M

6. Gravitation

1.State Newton's Law of Gravitation.
2M
2.Derive the relation between acceleration due to gravity (g) and gravitational constant (G).
2M
3.State Kepler's laws of planetary motion. Deduce the second law.
2M
4.Derive the expression for the effect of height (altitude) on acceleration due to gravity.
3M
5.Derive the expression for the effect of depth on acceleration due to gravity.
3M
6.Discuss the effect of the rotation of the earth on acceleration due to gravity.
3M
7.Define Orbital Velocity and derive its expression.
3M
8.Define Escape Velocity and derive its expression.
3M
9.Derive the expression for the time period of a satellite revolving in an orbit around the Earth.
3M

7. Solids & Fluids

1.Derive the expression for the variation of pressure with depth.
2M
2.State and prove the Equation of Continuity.
2M
3.Prove Surface Energy is dimensionally equal to surface tension.
2M
4.Find the work done in stretching a rod/wire of length l.
3M
5.Derive the expression for excess pressure inside a liquid drop and a soap bubble.
3M
6.Derive the Ascent Formula (Capillary Rise).
3M
7.State and Prove Stokes' Law using the method of Dimensional Analysis.
3M
8.State and Prove Terminal Velocity.
3M
9.State Archimedes' Principle. Explain the force exerted by a liquid on an object submerged in it (Buoyant Force).
4M
10.State and prove Bernoulli's Theorem.
5M

8. Thermal Physics

1.Derive the relation between α (linear), β (areal), and γ (volume) expansion coefficients.
3M
2.State and Prove Stefan's Law of cooling.
3M
3.Calculate the work done in an Isothermal Process.
3M
4.Calculate the work done in an Adiabatic Process.
3M
5.Derive the relation between Cp and Cv (Mayer's Formula).
3M
6.Derive the expression for the pressure exerted by an ideal gas on the walls of a container.
5M

9. Oscillations (SHM)

1.Derive the expression for the displacement of a particle executing SHM.
2M
2.Derive the expression for the velocity of a particle executing SHM.
3M
3.Derive the expression for the acceleration of a particle executing SHM.
3M
4.Derive the expression for the Time Period of a particle of mass M (in spring mass system) executing SHM.
3M
5.Derive expressions for the Energies (KE, PE & TE) of SHM.
3M
6.Derive the expression for the Time Period of a Simple Pendulum.
3M

10. Waves

1.Derive the relation between particle velocity and wave velocity.
2M
2.Derive Newton’s formula for the velocity of sound in gases and discuss Laplace’s correction.
5M
3.Discuss the formation of standing waves in a string fixed at both ends (and one end) and find the different modes of vibration.
5M
4.Discuss the formation of standing waves in an organ pipe and find the different modes of vibration.
3M

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