IGNOU MPH 2 SOLVED ASSIGNMENT

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MPH 2 2025 - English

Tutor Marked Assignment

CLASSICAL MECHANICS I

Course Code: MPH-002

Assignment Code: MPH-002/TMA/2025

Max. Marks: 50

Note: Attempt all questions. The marks for each question are indicated against it.

1. a) (i) What are holonomic and non- holonomic constraints ? Write down the equations for the constraints for three point masses connected by rigid rods of length L.

(ii) A bead of mass m slides on a smooth rod which is rotating about one fixed end in a vertical plane with uniform angular velocity ω .

Write the Lagrangian for the system and obtain the equation of motion.

b) (i) Derive the Euler-Lagrange equation of motion for a bead of mass m sliding due to gravity on a circular wire.

(ii) Consider a spring mass pendulum, where m is the mass of the pendulum. The motion of the pendulum is constrained as given in the figure:

The motion is assume to take place only in the vertical plane. The equilibrium length of the spring is l , while its angle with the vertical is θ(t) . Obtain the equations of motion for x and θ.

2. a) Consider a potential V (r) = kr² , k > 0.

(i) Obtain the expression for effective potential V_eff (r) .

(ii) Determine the nature of the force associated with the potential.

(iii) Obtain r_min  and for a two-body system.

(iv) Show that the Laplace-Runge-Lenz vector is not conserved for the given potential.

b) Consider a system as given in the figure, where the masses M are fixed and m is the dynamical system:

(i) Write the change in potential for a small displacement.

(ii) Write the change in potential for a small perpendicular displacemen.

Explain whether the displacement is stable or unstable for the two cases. 

c) A mass on the end of a spring, has a natural frequency 2ω , The system is immersed in a fluid that causes the motion to be overdamped,  Γ =  -bq  . Obtain the times at which the speed of the mass becomes maximum

MPH 002 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment

CLASSICAL MECHANICS I

Course Code: MPH-002

Assignment Code: MPH-002/TMA/2026

Max. Marks: 50

Note: Attempt all questions. The marks for each question are indicated against it.

1. a) Two frictionless blocks of equal masses m are connected by a massless rigid rod of length L. The system is constrained to move in the vertical plane under the action of an applied force as shown in the figure. Obtain the equation of motion of the system and calculate the condition for static equilibrium. 

b) Two equal of mass m attached by a thread of length b are oriented vertically as shown in the figure. The acceleration decrease according to height as , where g₀ and a are constants. Calculate the vertical acceleration of the system as measured from the centre of the thread.

c) A pendulum of mass m is pivoted to a support of mass M sliding without friction along x-axis as shown in the figure. Obtain the Lagrange equation of motion for the given system.

d) Consider a simple pendulum of mass m whose length changes with time as . Obtain the Lagrange equation of motion, the generalised momentum and the energy function for the system.

2. a) A central potential is given as V(r):

(i) Obtain the criterion for a stable circular orbit.

(ii) If the central potential is given as . For what values of n are the circular orbits stable.

b) The orbit of a particle in a central force field is given by , obtain the force law.

c) Two objects of equal mass are connected by a three spring with spring constants as shown in figure. Obtain the normal mode frequencies.

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Course Name	Master of Science (Physics)
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