CSS Physics Paper-I 2021 Solved

CSS Physics Paper-I 2021 Solved Question 2 belongs mainly to nuclear physics. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 2. Describe Einstein postulates of special theory of Relativi ty. Express the difference between the special and the general theories of Relativity.

Einstein’s two postulates are: laws of physics are identical in all inertial frames, and light speed in vacuum is constant for all inertial observers. Special relativity handles uniform motion; general relativity handles gravity as curved spacetime.

Einstein’s special theory of relativity is based on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in vacuum is the same for every inertial observer. These postulates replace the older idea of absolute time and absolute space.

Special relativity deals with uniform relative motion and gives time dilation, length contraction, relativity of simultaneity and mass-energy equivalence. General relativity extends the idea to accelerated frames and gravitation, treating gravity as curvature of space-time rather than as an ordinary Newtonian force.

Answer to Part (b)

Part being solved: Establish the energy-mass relationship and give its significance. (10) (10) (20)

The relativistic energy-momentum relation is E squared = p squared c squared + m squared c to the fourth. For a particle at rest, p = 0 and the equation becomes E = mc squared. This is the mass-energy relation.

Its significance is that mass can appear as energy and energy can appear as mass. Nuclear binding energy, annihilation of electron-positron pairs and pair production are direct applications of this relation.

Working Block 1

1. Line 1: Relativistic energy-momentum relation: This statement sets the physical condition used by the next line.
2. Line 2: E² = p²c² + m0²c^4. This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: For p = 0, E0 = m0c². This is the substitution stage, where the general relation is converted into the present problem.

Calculation and Derivation Written Line by Line

Working Block 1

1. Relativistic energy-momentum relation:
2. E² = p²c² + m0²c^4.
3. For p = 0, E0 = m0c².

CSS Physics Paper-I 2021 Solved Question 3 belongs mainly to nuclear physics. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 3. Differentiate between Fermi-Dirac, Bose-Einstein and Maxwell Statistics. Give application of each.

Maxwell-Boltzmann statistics apply to classical distinguishable particles. Bose-Einstein applies to integer-spin bosons that can occupy the same state. Fermi-Dirac applies to half-integer-spin fermions obeying Pauli exclusion.

Einstein’s special theory of relativity is based on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in vacuum is the same for every inertial observer. These postulates replace the older idea of absolute time and absolute space.

Special relativity deals with uniform relative motion and gives time dilation, length contraction, relativity of simultaneity and mass-energy equivalence. General relativity extends the idea to accelerated frames and gravitation, treating gravity as curvature of space-time rather than as an ordinary Newtonian force.

Answer to Part (b)

Part being solved: Draw a labelled diagram of a nuclear reactor and give significance of each part. (10) (10) (20)

A nuclear reactor contains fuel rods, moderator, control rods, coolant, shielding and a heat exchanger. Moderator slows neutrons; control rods absorb neutrons; coolant removes heat; shielding absorbs radiation.

A nuclear reactor is a device in which a controlled chain reaction is maintained. Fuel such as uranium-235 undergoes fission, releasing energy and neutrons.

The moderator slows neutrons, control rods absorb excess neutrons, coolant removes heat, shielding protects workers from radiation, and the heat is used to produce steam for electricity generation.

CSS Physics Paper-I 2021 Solved Question 4 belongs mainly to orbital mechanics. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 4. Distinguish between the linear and angular momentum. E xpress Newton ’s second law in terms of the linear and angular motion.

Linear momentum is p = mv and Newton’s second law is F = dp/dt. Angular momentum is L = r × p and torque is τ = dL/dt.

Angular momentum is L = r cross p. It remains conserved when the net external torque about the chosen origin is zero. This is why a planet speeds up near perihelion and why a skater spins faster after pulling the arms inward.

In a CSS answer, always mention the condition for conservation. Angular momentum is not automatically conserved in every problem; it is conserved only when external torque vanishes.

Answer to Part (b)

Part being solved: Discuss the acceptor and rejecter electronic circuits. (10) (10) (20)

Acceptor and rejector circuits are resonant circuits. A series RLC circuit has minimum impedance at resonance and accepts a narrow band. A parallel resonant circuit has high impedance at resonance and rejects that frequency band.

CSS Physics Paper-I 2021 Solved Question 5 belongs mainly to solid state physics. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 5. Describe and explain the Miller indices. Recognize the sy mbols <111>, [010], (111).

Miller indices (hkl) describe crystal planes by taking reciprocals of intercepts with crystallographic axes. [010] is a direction, (111) is a plane, and <111> is a family of equivalent directions.

Miller indices describe the orientation of crystal planes. To find them, take the intercepts of the plane on the crystallographic axes, take reciprocals, and reduce to the smallest integers.

Round brackets such as (111) denote a plane, square brackets such as [010] denote a direction, and angle brackets such as <111> denote a family of equivalent directions.

Answer to Part (b)

Part being solved: Discuss the closest packed crystal structures. (10) (10) (20)

Close packing includes HCP with ABAB stacking and FCC/CCP with ABCABC stacking. Both have coordination number 12 and packing fraction about 0.74.

A lattice is a periodic arrangement of points in space. A unit cell is the smallest repeating volume that can generate the full crystal by translation.

In a base-centered cell, atoms or lattice points are at the corners and at the centers of two opposite faces. In a face-centered cubic cell, points are at the corners and at the centers of all six faces.

CSS Physics Paper-I 2021 Solved Question 6 belongs mainly to oscillations and waves. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 6. Can you imagine a three dimensional diffraction grating? Describe in detail.

A crystal acts as a three-dimensional diffraction grating because atoms are arranged periodically in all three dimensions. Bragg’s condition is 2d sinθ = nλ.

Diffraction is the spreading of waves when they pass through an aperture or around an obstacle. It becomes prominent when the aperture size is comparable with the wavelength.

For X-rays in crystals, atomic planes behave like reflecting layers. Bragg’s law 2d sin theta = n lambda gives the condition for strong reflection and allows the spacing between crystal planes to be measured.

Answer to Part (b)

Part being solved: Justify the dual nature of light with elaborative examples. (10) (10) (20)

Light has wave nature shown by interference, diffraction and polarization; it has particle nature shown by photoelectric effect and Compton scattering.

De Broglie proposed that every moving particle has an associated wavelength lambda = h/p. This connects particle momentum with wave behavior.

The dual nature of matter and radiation means electrons can show particle properties such as charge and tracks, but also wave properties such as diffraction. Light shows wave properties in interference and particle properties in the photoelectric effect.

CSS Physics Paper-I 2021 Solved Question 7 belongs mainly to thermodynamics. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 7. State and explain the three laws of Thermodynamics.

The first law of thermodynamics is conservation of energy: Delta U = Q – W when W is work done by the system. It says heat supplied to a system either increases internal energy or appears as work.

The second law states that heat does not spontaneously flow from a colder body to a hotter body and that entropy of an isolated system never decreases. The third law states that the entropy of a perfect crystal approaches zero as temperature approaches absolute zero.

Answer to Part (b)

Part being solved: What is a heat engine? Determine the efficiency of the engine if it takes 10,000 J of heat and delivers 2000 J of work per cycle. (10) (10) (20)

Zeroth law defines temperature. First law states ΔU = Q – W. Second law gives the direction of heat flow and limits engine efficiency. Third law says entropy approaches a constant minimum near absolute zero.

A heat engine is a cyclic device that absorbs heat Qh from a hot reservoir, converts part of it into work W, and rejects remaining heat Qc to a cold reservoir. Its efficiency is eta = W/Qh = 1 – Qc/Qh.

If the engine absorbs 10000 J and delivers 2000 J of work, eta = 2000/10000 = 0.20, or 20 percent. The rejected heat is 8000 J per cycle.

Working Block 1

1. Line 1: Efficiency η = W/Qh = 2000/10000 = 0.20 = 20%. This line is kept visible because it is the algebraic bridge to the final result.

Calculation and Derivation Written Line by Line

Working Block 1

1. Efficiency η = W/Qh = 2000/10000 = 0.20 = 20%.

CSS Physics Paper-I 2021 Solved Question 8 belongs mainly to orbital mechanics. This solved response answers every printed part directly, including definitions, explanations, derivations, calculations and final results where required.

Answer to Part (a)

Part being solved: Q. 8. Write notes on any TWO of the following: (10 each) Mickelson-Morley experiment and its latest usage in a recent Nobel award.

Michelson-Morley failed to detect ether drift and supported invariant light speed. Modern precision interferometry is central in gravitational wave detection.

Answer to Part (b)

Part being solved: Unification of forces and Abdus Salam contribution.

Force unification seeks one framework for fundamental interactions. Abdus Salam contributed to electroweak unification with Glashow and Weinberg.

Answer to Part (c)

Part being solved: An essay on Large Hadron Partical Accelerator. (20)

The Large Hadron Collider accelerates protons to high energies to test particle physics, including the Higgs mechanism and standard-model predictions.

Particle accelerators increase the kinetic energy of charged particles using electric fields. Magnetic fields are used to bend and guide the particles along controlled paths.

A cyclotron uses a perpendicular magnetic field and alternating electric field between dees. A synchrotron varies the magnetic field and accelerating frequency so particles remain on a fixed orbit as their energy increases.