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IGNOU MPH-02 Classical Mechanics-I - IGNOU Solved Assignment (Latest)

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IGNOU - MPH-02 (Jan 25 - Dec 25, Jan 24 - Dec 24) Solved Assignment

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IGNOU MPH-02 (January 2025 – December 2025) Assignment Questions

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 Veff (r).
(ii) Determine the nature of the force associated with the potential.
(iii) Obtain rmin 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 displacement. 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.

IGNOU MPH-02 (January 2024 – December 2024) Assignment Questions

MPH-02 Assignments Details

University	:	IGNOU (Indira Gandhi National Open University)
Title	:	Classical Mechanics-I
Language(s)	:	English
Code	:	MPH-02
Degree	:	MSCPH
Subject	:	Physics
Course	:	Core Courses (CC)
Author	:	Gullybaba.com Panel
Publisher	:	Gullybaba Publishing House Pvt. Ltd.