COMEDK UGET Physics - Mechanics and Thermal Physics Syllabus

Give the formulas for kinetic energy and gravitational potential energy.

Kinetic energy KE = (1/2)mv^2. Gravitational potential energy (near Earth) PE = mgh, where h is height above the reference level.

Distinguish conservative and non-conservative forces with an example of each.

For a conservative force, work done is path-independent and round-trip work is zero (e.g. gravity, spring force). For a non-conservative force, work depends on the path and energy is dissipated (e.g. friction, air resistance).

Compare perfectly elastic and perfectly inelastic collisions.

In a perfectly elastic collision both momentum and kinetic energy are conserved. In a perfectly inelastic collision momentum is conserved but kinetic energy is not, and the bodies stick together moving with a common velocity.

Define power and give its formula in terms of force and velocity.

Power is the rate of doing work: P = W/t. In terms of force and velocity, P = F·v (dot product). SI unit: watt (W) = J/s.

Define the centre of mass of a system of particles.

The centre of mass is the point that moves as though all the system's mass were concentrated there and all external forces acted there. For particles, X(cm) = Σ m_i x_i / Σ m_i (and similarly for y, z).

State the relation between torque and angular momentum.

Torque equals the rate of change of angular momentum: τ = dL/dt. If net external torque is zero, angular momentum L is conserved.

Define moment of inertia and write the rotational analogue of Newton's second law.

Moment of inertia I = Σ m_i r_i^2 measures resistance to angular acceleration about an axis. The rotational analogue of F=ma is τ = Iα, where α is angular acceleration.

Give the moment of inertia of (a) a solid sphere about a diameter and (b) a thin ring about its central axis.

(a) Solid sphere: I = (2/5)MR^2. (b) Thin ring/hoop about central axis: I = MR^2, where M is mass and R radius.

State the parallel axis theorem.

I = I(cm) + Md^2: the moment of inertia about any axis equals the moment of inertia about a parallel axis through the centre of mass plus M times the square of the distance d between the axes.

Write the rotational kinetic energy and the rotational analogue of linear momentum.

Rotational KE = (1/2)Iω^2. Angular momentum L = Iω is the rotational analogue of linear momentum p = mv.

State Newton's law of universal gravitation.

Every two point masses attract each other with a force F = G m1 m2 / r^2, directed along the line joining them, where G ≈ 6.67×10^-11 N·m^2/kg^2 is the universal gravitational constant.

How does acceleration due to gravity g vary with height h above Earth's surface (h small)?

g' = g (1 − 2h/R) approximately, so g decreases with height; R is Earth's radius. (Exact: g' = g R^2 / (R+h)^2.)

Give the formulas for orbital velocity and escape velocity near Earth's surface.

Orbital velocity v(o) = √(GM/r) = √(gR) for a low orbit. Escape velocity v(e) = √(2GM/R) = √(2gR) ≈ 11.2 km/s for Earth.

State Kepler's three laws of planetary motion.

1) Each planet moves in an ellipse with the Sun at one focus. 2) The line joining planet and Sun sweeps equal areas in equal times (constant areal velocity). 3) The square of the orbital period is proportional to the cube of the semi-major axis: T^2 ∝ a^3.

Define stress and strain.

Stress = restoring force per unit area (F/A), unit N/m^2 or pascal. Strain = ratio of change in dimension to original dimension (dimensionless), e.g. ΔL/L.

State Hooke's law and define Young's modulus.

Hooke's law: within the elastic limit, stress is proportional to strain. Young's modulus Y = longitudinal stress / longitudinal strain = (F/A)/(ΔL/L).

What are the elastic limit and the yield point on a stress-strain curve?

The elastic limit is the maximum stress up to which the body returns to its original shape on removing the load. The yield point is the stress beyond which strain increases rapidly with little extra stress (permanent/plastic deformation begins).

State Pascal's law and give one application.

Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and the walls of the container. Application: hydraulic lift/brakes, where a small force produces a large force.

State Archimedes' principle.

A body wholly or partly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the body.

State the equation of continuity for fluid flow and what it expresses.

A1 v1 = A2 v2 (Av = constant). It expresses conservation of mass for an incompressible fluid: the volume flow rate is constant, so fluid moves faster where the pipe is narrower.

State Bernoulli's principle (equation) for streamline flow.

P + (1/2)ρv^2 + ρgh = constant along a streamline. It expresses conservation of energy per unit volume: where speed is high, pressure is low.

Define surface tension and viscosity.

Surface tension is the force per unit length acting along the surface of a liquid (or surface energy per unit area), due to cohesive forces. Viscosity is the internal friction opposing relative motion between fluid layers.

What is the difference between heat and temperature?

Heat is energy transferred between bodies due to a temperature difference (measured in joules). Temperature is a measure of the average kinetic energy of the molecules / the degree of hotness (measured in K, °C).

Give the conversion between Celsius, Fahrenheit, and Kelvin scales.

K = °C + 273.15; °F = (9/5)°C + 32; and °C = (5/9)(°F − 32).

Distinguish conduction, convection, and radiation.

Conduction: heat transfer through a medium by molecular collisions without bulk movement (solids). Convection: transfer by actual movement of heated fluid. Radiation: transfer by electromagnetic waves, requiring no medium.

State the formula for heat absorbed and define specific heat capacity and latent heat.

Q = mcΔT for temperature change, where c is specific heat (heat to raise 1 kg by 1 K). During a phase change, Q = mL, where L is latent heat (heat per unit mass to change state at constant temperature).

State the first law of thermodynamics.

ΔU = Q − W: the change in internal energy of a system equals the heat added to it minus the work done by the system. It is the law of conservation of energy applied to heat.

Compare isothermal and adiabatic processes.

Isothermal: temperature constant (ΔU=0, so Q=W), obeys PV = constant. Adiabatic: no heat exchange (Q=0, so ΔU = −W), obeys PV^γ = constant, where γ = Cp/Cv.

State the postulates and key result of the kinetic theory of gases for pressure.

Gas molecules are tiny, in constant random motion, collide elastically, and intermolecular forces are negligible. Pressure P = (1/3)(m N / V) v(rms)^2 = (1/3)ρ v(rms)^2; average translational KE per molecule = (3/2)kT.

Define simple harmonic motion and give its defining equation.

SHM is oscillatory motion in which the restoring force (or acceleration) is directly proportional to displacement and directed toward the mean position: a = −ω^2 x. Time period T = 2π/ω.

Give the time period of a simple pendulum and of a mass-spring system.

Simple pendulum: T = 2π√(L/g). Mass-spring: T = 2π√(m/k), where L is length, g gravity, m mass, k spring constant.

Write the relation between wave speed, frequency, and wavelength, and the condition for resonance/beats.

Wave speed v = f λ (frequency × wavelength). Beats occur when two waves of slightly different frequencies superpose; beat frequency = |f1 − f2|. Resonance occurs when driving frequency equals the natural frequency, giving maximum amplitude.