Consolidated Question Bank - Classical and Statistical Mechanics - 23BPH5C3

UNIT - I
PART A - 2 MARK QUESTIONS

1.Differentiate between external and internal forces.
2.Define the center of mass of a system of particles.
3.State the law of conservation of linear momentum.
4.Define angular momentum.
5.State the law of conservation of angular momentum.
6.State the law of conservation of energy.
7.State the work-energy theorem.
8.Define conservative forces and give an example.
9.Define degrees of freedom in a physical system.
10.Define generalized momentum.


PART B - 5 MARK QUESTIONS

1. Define the center of mass and explain its importance in mechanics.
2.State and explain the law of conservation of linear momentum with an example.
3.What is the work-energy theorem? Derive its expression for a particle moving under a constant force.
4.Differentiate between conservative and non-conservative forces, providing one example of each.
5.Define degrees of freedom and explain how they are affected by constraints in a mechanical system.

PART C - 10 MARK QUESTIONS

1.Explain the work-energy theorem in detail. Derive its expression and discuss its significance in mechanics with a practical example.
2. Discuss the types of constraints in mechanics.

UNIT - II
PART A - 2 MARK QUESTIONS

1.State the principle of virtual work.
2.What is D'Alembert’s principle?
3.Define generalized coordinates.
4.Write the Lagrange equation of motion for a conservative system.
5.State Hamilton's principle.

PART B - 5 MARK QUESTIONS

1.State and explain D'Alembert’s principle.
2.Describe the principle of virtual work.
3.Write down the Lagrange equation of motion for a conservative system and briefly explain each term.
4.Derive the Lagrange equation of motion for a simple pendulum.
5.Explain how to apply the Lagrangian method to the Atwood machine. Derive the equation of motion for the system.

PART C - 10 MARK QUESTIONS

1.Derive the Lagrange equation of motion for a conservative system.
2.State Hamilton’s principle and  derive the Lagrange's equations from it.

UNIT - III
PART A - 2 MARK QUESTIONS

1.Define phase space.
2.What is the Hamiltonian function  in mechanics?
3.State Hamilton's canonical equations of motion.
4.What is the physical significance of the Hamiltonian function HH in a mechanical system?
5.What is a variational principle in Hamiltonian mechanics?

PART B - 5 MARK QUESTIONS

1.Explain the concept of phase space and its significance in Hamiltonian mechanics.
2.Define the Hamiltonian function H and describe its role in representing the total energy of a system.
3.State and explain Hamilton’s canonical equations of motion for a simple system.
4.What is the physical significance of the Hamiltonian in classical mechanics? Discuss briefly.

PART C - 10 MARK QUESTIONS

1.Derive Hamilton's canonical equations from the variational principle.
2.Discuss the application of Hamilton's equations of motion to a compound pendulum. Derive and solve the equation of motion for the system.

UNIT - IV
PART A - 2 MARK QUESTIONS

1.Define microstate and macrostate in statistical mechanics.
2.What is the difference between Mu space and Gamma space?
3.State the fundamental postulate of statistical mechanics.
4.What is thermodynamical probability?
5.Write down Boltzmann's theorem relating entropy and probability.

PART B - 5 MARK QUESTIONS

1.Explain the difference between microstates and macrostates in statistical mechanics, with an example.
2.Define Mu space and Gamma space. Discuss their significance in representing systems in statistical mechanics.
3.State and explain the fundamental postulate of statistical mechanics.
4.Derive the Maxwell-Boltzmann velocity distribution law.

PART C - 10 MARK QUESTIONS

1.Define the different types of ensembles (microcanonical, canonical, and grand canonical) used in statistical mechanics, and explain their importance in describing systems under various conditions.
2.State and derive the Maxwell-Boltzmann energy distribution law.

UNIT - V
PART A - 2 MARK QUESTIONS

1.What is the main difference between Bose-Einstein and Fermi-Dirac statistics?
2.Define Fermi gas.
3.State one key difference between classical and quantum statistics.
4.Name the quantum statistics that apply to free electrons in a metal.
5.What is the Pauli exclusion principle, and how does it relate to Fermi-Dirac statistics?
6.Write the Planck radiation formula.

PART B - 5 MARK QUESTIONS

1.Explain the basic principles of Bose-Einstein statistics and its application in quantum mechanics.
2.State and explain the key assumptions of Fermi-Dirac statistics.
3.Describe the main differences between classical statistics and quantum statistics.
4.Explain the concept of a Fermi gas and its significance in describing free electrons in metals.
5.What is the Fermi energy, and why is it important in understanding the behavior of electrons in a metal?

PART C - 10 MARK QUESTIONS

1.Discuss the differences between Bose-Einstein and Fermi-Dirac statistics.
2.Derive the Planck radiation formula using Bose-Einstein statistics, and discuss its significance in blackbody radiation.
3.Discuss the key differences between classical statistics (Maxwell-Boltzmann) and quantum statistics (Bose-Einstein and Fermi-Dirac),

Question Bank - Classical and Statistical Mechanics - 22BPH5C3 - UNIT V

    

UNIT - V
PART A - 2 MARK QUESTIONS

1.What is the main difference between Bose-Einstein and Fermi-Dirac statistics?
2.Define Fermi gas.
3.State one key difference between classical and quantum statistics.
4.Name the quantum statistics that apply to free electrons in a metal.
5.What is the Pauli exclusion principle, and how does it relate to Fermi-Dirac statistics?
6.Write the Planck radiation formula.

PART B - 5 MARK QUESTIONS

1.Explain the basic principles of Bose-Einstein statistics and its application in quantum mechanics.
2.State and explain the key assumptions of Fermi-Dirac statistics.
3.Describe the main differences between classical statistics and quantum statistics.
4.Explain the concept of a Fermi gas and its significance in describing free electrons in metals.
5.What is the Fermi energy, and why is it important in understanding the behavior of electrons in a metal?

PART C - 10 MARK QUESTIONS

1.Discuss the differences between Bose-Einstein and Fermi-Dirac statistics.
2.Derive the Planck radiation formula using Bose-Einstein statistics, and discuss its significance in blackbody radiation.
3.Discuss the key differences between classical statistics (Maxwell-Boltzmann) and quantum statistics (Bose-Einstein and Fermi-Dirac),

Question Bank - Classical and Statistical Mechanics - 22BPH5C3 - UNIT IV

   

UNIT - IV
PART A - 2 MARK QUESTIONS

1.Define microstate and macrostate in statistical mechanics.
2.What is the difference between Mu space and Gamma space?
3.State the fundamental postulate of statistical mechanics.
4.What is thermodynamical probability?
5.Write down Boltzmann's theorem relating entropy and probability.

PART B - 5 MARK QUESTIONS

1.Explain the difference between microstates and macrostates in statistical mechanics, with an example.
2.Define Mu space and Gamma space. Discuss their significance in representing systems in statistical mechanics.
3.State and explain the fundamental postulate of statistical mechanics.
4.Derive the Maxwell-Boltzmann velocity distribution law.

PART C - 10 MARK QUESTIONS

1.Define the different types of ensembles (microcanonical, canonical, and grand canonical) used in statistical mechanics, and explain their importance in describing systems under various conditions.
2.State and derive the Maxwell-Boltzmann energy distribution law.

Question Bank - Classical and Statistical Mechanics - 22BPH5C3 - UNIT III

  

UNIT - III
PART A - 2 MARK QUESTIONS

1.Define phase space.
2.What is the Hamiltonian function  in mechanics?
3.State Hamilton's canonical equations of motion.
4.What is the physical significance of the Hamiltonian function HH in a mechanical system?
5.What is a variational principle in Hamiltonian mechanics?

PART B - 5 MARK QUESTIONS

1.Explain the concept of phase space and its significance in Hamiltonian mechanics.
2.Define the Hamiltonian function H and describe its role in representing the total energy of a system.
3.State and explain Hamilton’s canonical equations of motion for a simple system.
4.What is the physical significance of the Hamiltonian in classical mechanics? Discuss briefly.

PART C - 10 MARK QUESTIONS

1.Derive Hamilton's canonical equations from the variational principle.
2.Discuss the application of Hamilton's equations of motion to a compound pendulum. Derive and solve the equation of motion for the system.

Question Bank - Classical and Statistical Mechanics - 22BPH5C3 - UNIT II

 

UNIT - II
PART A - 2 MARK QUESTIONS

1.State the principle of virtual work.
2.What is D'Alembert’s principle?
3.Define generalized coordinates.
4.Write the Lagrange equation of motion for a conservative system.
5.State Hamilton's principle.

PART B - 5 MARK QUESTIONS

1.State and explain D'Alembert’s principle.
2.Describe the principle of virtual work.
3.Write down the Lagrange equation of motion for a conservative system and briefly explain each term.
4.Derive the Lagrange equation of motion for a simple pendulum.
5.Explain how to apply the Lagrangian method to the Atwood machine. Derive the equation of motion for the system.

PART C - 10 MARK QUESTIONS

1.Derive the Lagrange equation of motion for a conservative system.
2.State Hamilton’s principle and  derive the Lagrange's equations from it.

Newton's Laws of Motion - Significance and Examples :

Newton's Laws :
First Law (Law of Inertia): An object will stay at rest or keep moving at a constant velocity unless acted upon by an external force.
Second Law (F = ma): The force acting on an object is proportional to the rate of change of its momentum  mv. In the case of constant mass and with the choice of suitable units F = ma .
Third Law (Action-Reaction Law): For every action, there is an equal and opposite reaction.

Significance : Newton's Laws are important because they give us a clear way to describe and predict how objects move when forces act on them. These laws are the foundation of classical mechanics and are essential in fields like engineering, astronomy, and everyday situations involving force and motion.

Examples
First Law : If we are in a moving car that suddenly stops, our body tends to keep moving forward even though the car has stopped, which is why seat belts are essential—they provide the external force needed to stop your body safely. This tendency to keep moving in the same direction until an outside force acts is an illustration of inertia.
Second Law : When we hit cricket ball with a bat, the more force we apply to the ball the more momentum the ball gains. 
Third Law : The flapping of a bird's wings is a good example of Newton's Third Law. When a bird pushes its wings downward, it exerts a force on the air. According to Newton's Third Law, the air pushes back with an equal and opposite force, propelling the bird upward and forward. This action-reaction pair allows the bird to stay in the air and control its direction while flying.


Question Bank - Classical and Statistical Mechanics - 22BPH5C3 - UNIT I

UNIT - I
PART A - 2 MARK QUESTIONS

1.Differentiate between external and internal forces.
2.Define the center of mass of a system of particles.
3.State the law of conservation of linear momentum.
4.Define angular momentum.
5.State the law of conservation of angular momentum.
6.State the law of conservation of energy.
7.State the work-energy theorem.
8.Define conservative forces and give an example.
9.Define degrees of freedom in a physical system.
10.Define generalized momentum.


PART B - 5 MARK QUESTIONS

1. Define the center of mass and explain its importance in mechanics.
2.State and explain the law of conservation of linear momentum with an example.
3.What is the work-energy theorem? Derive its expression for a particle moving under a constant force.
4.Differentiate between conservative and non-conservative forces, providing one example of each.
5.Define degrees of freedom and explain how they are affected by constraints in a mechanical system.

PART C - 10 MARK QUESTIONS

1.Explain the work-energy theorem in detail. Derive its expression and discuss its significance in mechanics with a practical example.
2. Discuss the types of constraints in mechanics.


Degrees of Freedom - Definition and Examples

Definition : Degrees of freedom of a system the minimum number of independent coordinates needed to uniquely define the position or configuration of the system

Examples : 

Single Particle in 3D Space : A single particle in three-dimensional space has 3 degrees of freedom. It can move independently in the x, y and z directions.

Rigid body in  3D Space : A rigid body  has 6 degrees of freedom. Since it has 3 translational (movement along x, y and z axes) degrees of freedom and can rotate freely about three perpendicular axes, hence has 3 rotational degrees of freedom in addition.

Simple Pendulum : The bob of a simple pendulum has only one degree of freedom  as it can only swing around a fixed point in a plane with fixed orientation in space. This degree of freedom is indicated by the angle θ of the deflection of the pendulum string from the normal from the support point.

Double Pendulum :  A double pendulum consisting of two pendula connected in sequence, has 2 degrees of freedom. One degree of freedom corresponds to the angle of the first pendulum, and the second corresponds to the angle of the second pendulum relative to the first.




Diatomic Molecule : A diatomic molecule (like O₂) in a three-dimensional space has 5 degrees of freedom at room temperature: 3 translational (motion along x, y, and z axes) and 2 rotational (rotation about two perpendicular axes). The third rotation axis along the bond length is negligible for most diatomic gases due to quantum constraints.




Classical and Statistical Mechanics - Internal and Model Exam Questions - For the Semester Nov 2024


Consolidated Question Bank - Mechanics - 23BPH3C1

 

 UNIT - I
PART A - 2 MARK QUESTIONS

1. State Newton's First Law of Motion.
2. What is frictional force?
3. Define gravitational potential.
4. State Newton's Law of Gravitation.
4. What is the escape velocity from the Earth's surface?
5. State Kepler's First Law and its significance in planetary motion.
6. State Kepler's Second Law.
8. State Kepler's Third Law.
9. What is the Principle of Equivalence?
10. Explain gravitational redshift.

PART B - 5 MARK QUESTIONS

1.Discuss the types of everyday forces in physics with examples.
2. Derive the equations of motion for a particle moving under a uniform gravitational field.
3. Derive the equations of motion for a particle moving under a uniform gravitational field.
4.Describe the concept of escape velocity and derive the formula for escape velocity from the Earth.
5.State and explain Kepler’s three laws of planetary motion.
6.Explain the Earth-Moon system and discuss its influence on tides and orbital motion.
7.Describe the gravitational potential energy of a satellite in orbit.
8. Describe Einstein’s Theory of Gravitation
9.Explain the phenomenon of the perihelion shift of Mercury.

PART C - 10  MARK QUESTIONS

1. Explain Newton's laws of motion in detail. Discuss their significance and provide examples to illustrate each law.
2. Derive and explain the equation for the gravitational potential.
3.Explain the determination of the universal gravitational constant (G) using Boys' method.
4. Discuss Kepler’s laws of planetary motion in detail. Derive Kepler’s Third Law.
5. Explain Einstein’s Theory of Gravitation with reference to the Principle of Equivalence. Discuss the experimental tests supporting the theory, including gravitational redshift and light bending.


 UNIT - II
PART A - 2 MARK QUESTIONS

1.State the law of conservation of linear momentum.
2.What is the center of mass of a system?
3.Define torque.
4.What is an elastic collision? Give one example.
5.State the principle of conservation of angular momentum.
6.Explain what is meant by "system with variable mass" with an example.
7.What happens to the angular momentum in a proton scattering event with a heavy nucleus?


PART B - 5 MARK QUESTIONS

1.Describe the concept of a center of mass and explain its importance in the motion of a  system of particles.
2.Explain the law of conservation of linear momentum with an example involving internal and external forces.
3.What is angular momentum? Derive the expression for the angular momentum of a rigid body about its center of mass.
4.Write Note on Torque Due to Gravity.


PART C - 10 MARK QUESTIONS

1.Derive the Expressions for Velocities of Two Particles Elastically Colliding with Each Other Along Their Line of Sight, After Impact.
2.Describe the mechanics of proton scattering by a heavy nucleus. Explain how conservation laws apply to the process and discuss the implications for angular momentum and energy transfer.


 

 UNIT - III
PART A - 2 MARK QUESTIONS

1.What is the significance of conservation laws in physics?
2.Define work and provide its SI unit
3.What are conservative forces? Give one example.
4.State the law of conservation of energy.
5.What is potential energy in a gravitational field?
6.Differentiate between conservative and non-conservative forces.
7.Explain the concept of power and provide its SI unit.


PART B - 5 MARK QUESTIONS

1.Explain the law of conservation of energy with an example in a gravitational field.
2.Describe the relationship between work, power, and energy.
3.Explain the concept of potential energy in an electric field and how it relates to conservative forces.
4.Discuss the difference between conservative and non-conservative forces.
5.Explain the concept of work done by a force and derive the formula for work done in moving an object over a distance.


PART C - 10 MARK QUESTIONS

1.Explain the law of conservation of energy in detail. Derive the general law of conservation of energy, including the concepts of work done by conservative and non-conservative forces.
2.Discuss the concepts of work, power, and energy in physics. Derive the formulas for work done by a constant force, power, and kinetic energy.
3.Explain the concept of mechanical energy and its conservation in a closed system. Derive the principle of conservation of mechanical energy, including the roles of kinetic and potential energy.
4.Describe the relationship between work and energy using the work-energy theorem. Derive the theorem and discuss its implications for kinetic energy.



  

 UNIT - IV
PART A - 2 MARK QUESTIONS

1.Define angular momentum and state its SI unit.
2.What is moment of inertia? State its significance in rotational motion.
3.State the parallel axis theorem for the moment of inertia.
4.State the perpendicular axis theorem for the moment of inertia.
5.What is kinetic energy of rotation? Write its formula.
6.What is gyroscopic precession?
7.Differentiate between translational and rotational motion.
8.Write expression for the acceleration of of a body rolling down an inclined plane.
9.What is gyrostatic effect? Provide one example of its application.


PART B - 5 MARK QUESTIONS

1.Derive the formula for rotational kinetic energy in terms of moment of inertia and angular velocity.
2.State and prove the parallel axis theorem. 
3.State and prove the perpendicular axis theorem. 
4.Derive the expression for the moment of inertia of a solid cylinder about its central axis.
5.Describe gyroscopic precession and derive an expression for the precession speed. 
6.Explain the motion of a body rolling down an inclined plane. Derive an expression for its acceleration in terms of its moment of inertia and radius.


PART C - 10 MARK QUESTIONS

1.Explain the dynamics of a rigid body rotating about a fixed axis. Derive the equations of rotational motion and discuss the relationship between torque, angular momentum, and angular acceleration.
2.Discuss the concept of a body rolling without slipping along a plane surface. Derive the expression for the total kinetic energy of the rolling body in terms of its translational and rotational kinetic energy.
3.Explain gyroscopic precession in detail. Derive the precession rate for a gyroscope,
4.Describe the general theorems of moment of inertia (parallel axis and perpendicular axis theorems) and provide proofs for each.


   

 UNIT - V
PART A - 2 MARK QUESTIONS

1.What are generalized coordinates? Provide one example.
2.Define degrees of freedom in a mechanical system.
3.What is a constraint in mechanics? Give an example of a constraint in a physical system.
4.What is the principle of virtual work?
5.State D’Alembert’s Principle in mechanics.
6.Write down Lagrange’s equation of motion and briefly explain its significance.


PART B - 5 MARK QUESTIONS

1.Describe degrees of freedom in a mechanical system and explain how constraints affect the degrees of freedom.
2.Explain the concept of generalized coordinates and illustrate their use with an example involving a pendulum.
3.State and explain D'Alembert's Principle. 
4.Apply Lagrange’s equation to derive the equation of motion for a simple pendulum.
5.Explain the working of Atwood’s Machine and derive its equation of motion using Lagrange’s method.

PART C - 10 MARK QUESTIONS

1.Derive Lagrange’s equation of motion from D’Alembert’s 






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