LU B.Sc Sem 1 Physics Mechanics and Wave Motion Important Questions 2026 | PYQ Pattern

Q1. (a) Write the fundamental postulates of the special theory of relativity and, using the Lorentz transformation, obtain the expressions for length contraction and time dilation.
(b) Show that the relativistic energy of a particle is given by E² = m₀²c⁴ + p²c². [15 Marks]

Q2. (a) What is a conservative force? Show that the work done by a conservative force along any closed path is zero, and that curl F = 0 for a central force.
(b) A 10 kg shell initially at rest suddenly bursts into two fragments. The 2 kg fragment moves eastward at 6 m/sec. Determine the velocity of the remaining fragment. [15 Marks]

Q3. Give the parallel axes theorem of moment of inertia. Using it, obtain the moment of inertia of a solid cylinder (mass M, length L, radius R) about an axis through its centre of mass and perpendicular to its axis of symmetry. Also define radius of gyration. [20 Marks]

Q4. Write down the differential equation of a damped harmonic oscillator and solve it. Discuss in detail the over-damped, critically damped and under-damped cases, with suitable graphs showing how the amplitude changes with time. [20 Marks]

Q5. State Kepler’s laws of planetary motion. Using Newton’s law of gravitation, obtain Kepler’s third law. A planet of mass m moves round the Sun (mass M) in an orbit of semi-major and semi-minor axes α and β; show that its total energy is E = –GMm/(α + β). [20 Marks]

Q6. (a) For a linear elastic medium, establish that Y = 3K(1 – 2σ) and 9/Y = 1/K + 3/η (usual symbols).
(b) Discuss the theoretical limiting values of Poisson’s ratio (σ). [20 Marks]

Q7. What is an elastic collision? Obtain the velocities of the bodies after a one-dimensional elastic collision, and show that in a head-on elastic collision maximum energy is transferred when the two masses are equal. [20 Marks]

Q8. (a) What is a forced harmonic oscillator? Show that the amplitude of forced oscillations is A = f₀ / √[(ω₀² – p²)² + 4γ²p²].
(b) Explain the sharpness of resonance. [20 Marks]

Q9. (a) Define a cantilever and obtain the expression for the depression at its free end.
(b) Show that the total mechanical energy of a simple harmonic oscillator stays constant and varies as the square of its amplitude. [20 Marks]

Q10. Write short notes on: (a) Coriolis force (b) Geostationary satellite (c) Galilean invariance of acceleration (d) Energy in a progressive wave [20 Marks]