CSS Physics Paper-I 2020 Solved

What the Examiner Is Asking

This question belongs mainly to vector calculus. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

For a vector-calculus question, begin by writing the operator in Cartesian form. Do not jump directly to the final derivative. Write grad, div or curl first, then identify which components depend on x, y and z. If the problem asks for physical significance, connect the mathematics with field flow: gradient gives the steepest increase of a scalar, divergence gives source strength per unit volume, and curl gives circulation density. When a theorem is required, state the theorem in words, write the integral form and then explain the meaning of each integral. This makes the answer look complete even before numerical substitution begins.

Answer to Part (a)

Question demand: Q. 2. What is the curl of a vector field? Explain its physical significance. (10)

The curl of a vector field measures local rotation. For a field F, curl F = ∇ × F. Physically, in fluid flow it gives twice the local angular velocity of a small paddle wheel; in electromagnetism it connects changing fields through Maxwell equations.

A scalar field has magnitude at every point, while a vector field has magnitude and direction at every point. The gradient acts on a scalar field and points in the direction of maximum increase. Divergence acts on a vector field and measures whether field lines behave like sources or sinks. Curl also acts on a vector field, but it measures local rotation or circulation.

For a complete answer, do not merely list the symbols. Write grad phi = nabla phi, div A = nabla dot A and curl A = nabla cross A. Then give one physical example: temperature gradient for gradient, outward electric field of positive charge for divergence, and rotating fluid or magnetic circulation for curl.

Working Block 1

1. Line 1: Vector triple product: This statement sets the physical condition used by the next line.
2. Line 2: A × (B × C) = B(A·C) – C(A·B) This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: This follows by expanding determinant components or using Levi-Civita notation. This statement sets the physical condition used by the next line.

Answer to Part (b)

Question demand: What is vector triple product? Show that (6) A B C AC B A B C (4) (20)

The vector triple product is A cross (B cross C). Its result is a vector lying in the plane of B and C, not generally perpendicular to both. The standard expansion is A cross (B cross C) = B(A dot C) – C(A dot B).

A good derivation expands the cross products using components or the Levi-Civita symbol. The important point is the order: changing the bracket changes the answer, so the expression must not be treated like ordinary multiplication.

Working Block 1

1. Line 1: If phi = 2x^3 y^2 z^4, then This line is kept visible because it is the algebraic bridge to the final result.
2. Line 2: ∇²phi = ∂²phi/∂x² + ∂²phi/∂y² + ∂²phi/∂z² This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: = 12x y^2 z^4 + 4x^3 z^4 + 24x^3 y^2 z^2. This line is kept visible because it is the algebraic bridge to the final result.

Answer to Part (c)

Question demand: If phi 2x y z3 2 4 then find the div grad phi.

This subpart belongs to vector calculus. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Identify the concept from vector calculus and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Calculation and Derivation Written Line by Line

Working Block 1

1. Vector triple product:
2. A × (B × C) = B(A·C) – C(A·B)
3. This follows by expanding determinant components or using Levi-Civita notation.

Working Block 2

1. If phi = 2x^3 y^2 z^4, then
2. ∇²phi = ∂²phi/∂x² + ∂²phi/∂y² + ∂²phi/∂z²
3. = 12x y^2 z^4 + 4x^3 z^4 + 24x^3 y^2 z^2.

Subpart-by-Subpart Breakdown

1. Part (a) – Definition and explanation: Q. 2. What is the curl of a vector field? Explain its physical significance. (10) Use: Vector triple product:.
2. Part (b) – Derivation: What is vector triple product? Show that (6) A B C AC B A B C (4) (20) Use: If phi = 2x^3 y^2 z^4, then.
3. Part (c) – Numerical calculation: If phi 2x y z3 2 4 then find the div grad phi. Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.

What the Examiner Is Asking

This question belongs mainly to orbital mechanics. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

In an orbital-mechanics question, first decide whether the force is central. If it is central, torque about the center is zero and angular momentum is conserved. For circular orbits, start from gravitational force equal to centripetal force. For elliptical orbits, use the vis-viva equation and then Kepler’s period relation. Always define r, a, T and v because CSS examiners award marks for physical clarity, not only for the numerical value. If comparison is asked, compare orders of magnitude instead of writing a vague statement.

Answer to Part (a)

Question demand: Q. 3. State and explain Kepler’s law of areas. (8)

Kepler’s second law states that the radius vector joining a planet and the Sun sweeps equal areas in equal times. It is a consequence of zero torque under a central gravitational force, so angular momentum is conserved.

Kepler’s laws describe planetary and satellite motion under a central inverse-square gravitational force. The area law follows from conservation of angular momentum because the torque about the attracting center is zero.

For the third law, start with gravitational attraction providing centripetal force. Then insert v = 2 pi r / T. This gives T squared proportional to r cubed for circular orbits and to the semimajor axis cubed for ellipses.

Working Block 1

1. Line 1: Initial circular speed: v0 = 2πr/T0. This line lists the data or converts the symbols into usable quantities.
2. Line 2: After burn: vp = 0.96v0. This line lists the data or converts the symbols into usable quantities.
3. Line 3: For an ellipse at perigee: This statement sets the physical condition used by the next line.
4. Line 4: vp² = GM(2/r – 1/a), while v0² = GM/r. This line lists the data or converts the symbols into usable quantities.
5. Line 5: So (0.96)² = 2 – r/a => a = r/(2 – 0.9216) = r/1.0784. This line is kept visible because it is the algebraic bridge to the final result.
6. Line 6: T/T0 = (a/r)^(3/2) = (1/1.0784)^(3/2) = 0.893. This line is kept visible because it is the algebraic bridge to the final result.

Answer to Part (b)

Question demand: A spaceship of mass m = 4.50 × 103 kg is in a circular Earth orbit of radius (6) r 8.00 1 0 6 m and period To = 118.6 min = 7.119 × 103 s when a thruster is fired in the forward direction to decrease the speed to 96.0% of the original speed. What is the period T of the resulting elliptical orbit? (6) (20)

This subpart belongs to orbital mechanics. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Begin with a one-sentence definition using correct physics terminology.
2. Write the standard mathematical relation if the concept has one.
3. Explain the symbols and physical meaning of the relation.
4. Add one example or application because CSS theory answers need illustration.

Answer to Part (c)

Question demand: Which has greater magnitude, the angular momentum of the Earth (relative to its center) associated with its rotation on its axis or the angular momentum of the Earth (relative to the center of its orbit) associated with its orbital motion around the Sun?

Earth’s orbital angular momentum is vastly greater than spin angular momentum because L_orb = Mvr uses the astronomical orbital radius, while spin uses Earth’s much smaller radius of gyration.

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.

1. Identify the concept from orbital mechanics and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Calculation and Derivation Written Line by Line

Working Block 1

1. Initial circular speed: v0 = 2πr/T0.
2. After burn: vp = 0.96v0.
3. For an ellipse at perigee:
4. vp² = GM(2/r – 1/a), while v0² = GM/r.
5. So (0.96)² = 2 – r/a => a = r/(2 – 0.9216) = r/1.0784.
6. T/T0 = (a/r)^(3/2) = (1/1.0784)^(3/2) = 0.893.

Subpart-by-Subpart Breakdown

1. Part (a) – Definition and explanation: Q. 3. State and explain Kepler’s law of areas. (8) Use: Initial circular speed: v0 = 2πr/T0..
2. Part (b) – Definition and explanation: A spaceship of mass m = 4.50 × 103 kg is in a circular Earth orbit of radius (6) r 8.00 1 0 6 m and period To = 118.6 min = 7.119 × 103 s when a thruster is fired in the forward direction to decrease the speed to 96.0% of the original speed. What is the period T of the resulting elliptical orbit? (6) (20) Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.
3. Part (c) – Direct answer: Which has greater magnitude, the angular momentum of the Earth (relative to its center) associated with its rotation on its axis or the angular momentum of the Earth (relative to the center of its orbit) associated with its orbital motion around the Sun? Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.

What the Examiner Is Asking

This question belongs mainly to nuclear physics. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

For nuclear physics, begin by identifying conservation laws: charge number, mass number, energy and momentum. For decay energy, subtract product masses from parent mass and multiply by 931.5 MeV per atomic mass unit. For reactors and detectors, answer in labelled components and functions. For conceptual parts such as magic numbers or quadrupole moment, define the term, give the physical reason and then add one consequence.

Answer to Part (a)

Question demand: Q. 4. Explain the equivalence of mass and energy. (6)

Mass and energy are equivalent because the relativistic total energy is E = γmc². At rest, γ = 1, so E0 = mc². This explains nuclear energy, pair production and binding-energy defects.

Mass-energy equivalence means mass is a concentrated form of energy. The rest energy of a body is E0 = mc squared. Nuclear reactions, binding energy, pair production and annihilation all become understandable through this relation.

The answer should explain that a small mass defect can release a large amount of energy because c squared is very large. This turns the formula into physics rather than a memorized slogan.

Working Block 1

1. Line 1: Given proper lifetime tau0 = 2.2000 micro s and observed lifetime tau = 16.000 micro s: This line lists the data or converts the symbols into usable quantities.
2. Line 2: gamma = tau/tau0 = 7.2727 This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: beta = sqrt(1 – 1/gamma²) = sqrt(1 – 1/52.8926) = 0.99050. This line is kept visible because it is the algebraic bridge to the final result.

Answer to Part (b)

Question demand: Explain two tests of time dilation i.e microscopic and macroscopic clocks. (8)

Microscopic clock tests use unstable particles such as muons. Macroscopic tests use transported atomic clocks or fast aircraft/satellite clocks.

Time dilation means a moving clock is observed to run slow compared with a clock at rest in the observer’s frame. The relation is Delta t = gamma Delta t0, where Delta t0 is proper time and gamma = 1 / sqrt(1 – beta squared).

Microscopic tests use unstable particles such as muons. Macroscopic tests use precise clocks in aircraft or satellites. Both confirm that time intervals depend on relative motion.

1. Identify the concept from nuclear physics and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Answer to Part (c)

Question demand: The mean lifetime of stationary muons is measured to be 2.2000 micro s. The mean (6) (20) lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000 μs. To five significant figures, what is the speed parameter b of these cosmic-rays’ muons relative to Earth?

This subpart belongs to nuclear physics. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Begin with a one-sentence definition using correct physics terminology.
2. Write the standard mathematical relation if the concept has one.
3. Explain the symbols and physical meaning of the relation.
4. Add one example or application because CSS theory answers need illustration.

Calculation and Derivation Written Line by Line

Working Block 1

1. Given proper lifetime tau0 = 2.2000 micro s and observed lifetime tau = 16.000 micro s:
2. gamma = tau/tau0 = 7.2727
3. beta = sqrt(1 – 1/gamma²) = sqrt(1 – 1/52.8926) = 0.99050.

Subpart-by-Subpart Breakdown

1. Part (a) – Conceptual explanation: Q. 4. Explain the equivalence of mass and energy. (6) Use: Given proper lifetime tau0 = 2.2000 micro s and observed lifetime tau = 16.000 micro s:.
2. Part (b) – Conceptual explanation: Explain two tests of time dilation i.e microscopic and macroscopic clocks. (8) Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.
3. Part (c) – Definition and explanation: The mean lifetime of stationary muons is measured to be 2.2000 micro s. The mean (6) (20) lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000 μs. To five significant figures, what is the speed parameter b of these cosmic-rays’ muons relative to Earth? Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.

What the Examiner Is Asking

This question belongs mainly to fluids. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

For fluids, mention the assumptions before applying a formula. Bernoulli’s theorem assumes steady, incompressible, non-viscous flow along a streamline. Poiseuille flow assumes laminar flow through a circular tube. For pressure and capillarity, draw a simple force balance in words: upward surface-tension component versus weight, or pressure force versus external load. For numerical work, convert centimetres to metres, density to kg per cubic metre and pressure to pascals before substitution.

Answer to Part (a)

Question demand: Q. 5. What is viscosity? Explain in detail. What is the effect of temperature on viscosity? (8)

Viscosity is internal friction between adjacent fluid layers. For liquids it usually decreases with temperature because molecular cohesion weakens; for gases it increases because molecular momentum transfer rises.

Viscosity is internal friction in a fluid. It resists relative motion between adjacent layers. In liquids it normally decreases with temperature because cohesive forces weaken; in gases it usually increases because faster molecules transfer momentum more effectively.

A complete answer should include Newton’s law of viscosity: shear stress is proportional to velocity gradient. The coefficient of proportionality is the dynamic viscosity eta.

Working Block 1

1. Line 1: Poiseuille law: Q = π r^4 ΔP / (8ηL) This line is kept visible because it is the algebraic bridge to the final result.
2. Line 2: Collected volume V = m/rho = 1.23/(0.96×10^3) = 1.281×10^-3 m³ This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: Q = V/t = 1.423×10^-5 m³/s This line is kept visible because it is the algebraic bridge to the final result.
4. Line 4: r = 0.013 m, L = 0.65 m, ΔP = 950 Pa This line is kept visible because it is the algebraic bridge to the final result.
5. Line 5: η = πr^4ΔP/(8LQ) ≈ 1.15 Pa s. This line is kept visible because it is the algebraic bridge to the final result.

Answer to Part (b)

Question demand: Castor oil, which has a density of 0.96 × 103 kg/m3 at room temperature, is forced (5) through a pipe of circular cross section by a pump that maintains a gauge pressure of 950 Pa. The pipe has a diameter of 2.6 cm and a length o f 65 cm. The castor oil emerging from the free end of — PAGE 2 — the pipe at atmospheric pressure is collected. After 90 s, a total of 1.23 kg has been collected. What is the coefficient of viscosity of the castor oil at this temperature?

Viscosity is internal friction in a fluid. It resists relative motion between adjacent layers. In liquids it normally decreases with temperature because cohesive forces weaken; in gases it usually increases because faster molecules transfer momentum more effectively.

A complete answer should include Newton’s law of viscosity: shear stress is proportional to velocity gradient. The coefficient of proportionality is the dynamic viscosity eta.

1. Begin with a one-sentence definition using correct physics terminology.
2. Write the standard mathematical relation if the concept has one.
3. Explain the symbols and physical meaning of the relation.
4. Add one example or application because CSS theory answers need illustration.

Answer to Part (c)

Question demand: A liquid flow through a horizontal pipe whose inner radius is 2.52 cm. The pipe (7) (20) bends upward through a height of 11.5 m where it widens and joins another horizontal pipe of inner radius 6.14 cm. What must the volume flux be if the pressure in the two horizontal pipes is the same?

For the rising pipe, use continuity A1v1 = A2v2 and Bernoulli P1 = P2: 0.5ρ(v1²-v2²)=ρgh. With v=Q/A, solve Q from (Q²/2)(1/A1²-1/A2²)=gh.

1. Identify the concept from fluids and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Calculation and Derivation Written Line by Line

Working Block 1

1. Poiseuille law: Q = π r^4 ΔP / (8ηL)
2. Collected volume V = m/rho = 1.23/(0.96×10^3) = 1.281×10^-3 m³
3. Q = V/t = 1.423×10^-5 m³/s
4. r = 0.013 m, L = 0.65 m, ΔP = 950 Pa
5. η = πr^4ΔP/(8LQ) ≈ 1.15 Pa s.

Subpart-by-Subpart Breakdown

1. Part (a) – Definition and explanation: Q. 5. What is viscosity? Explain in detail. What is the effect of temperature on viscosity? (8) Use: Poiseuille law: Q = π r^4 ΔP / (8ηL).
2. Part (b) – Definition and explanation: Castor oil, which has a density of 0.96 × 103 kg/m3 at room temperature, is forced (5) through a pipe of circular cross section by a pump that maintains a gauge pressure of 950 Pa. The pipe has a diameter of 2.6 cm and a length o f 65 cm. The castor oil emerging from the free end of — PAGE 2 — the pipe at atmospheric pressure is collected. After 90 s, a total of 1.23 kg has been collected. What is the coefficient of viscosity of the castor oil at this temperature? Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.
3. Part (c) – Direct answer: A liquid flow through a horizontal pipe whose inner radius is 2.52 cm. The pipe (7) (20) bends upward through a height of 11.5 m where it widens and joins another horizontal pipe of inner radius 6.14 cm. What must the volume flux be if the pressure in the two horizontal pipes is the same? Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.

What the Examiner Is Asking

This question belongs mainly to oscillations and waves. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

For waves and oscillations, begin with the standard equation and then identify amplitude, angular frequency, phase and speed. If energy is involved, remember that energy is proportional to amplitude squared. If interference is involved, write the path difference and the condition for maxima or minima. For grating or diffraction questions, define the order of spectrum and the number of illuminated lines before writing the resolving power.

Answer to Part (a)

Question demand: Q. 6. What is damped harmonic oscillator? Write its equation of motion and find its (10) solution.

A damped harmonic oscillator obeys m x” + b x’ + kx = 0. For light damping, x = A0 e^{-bt/2m} cos(ωd t + φ), where ωd = sqrt(k/m – b²/4m²).

A damped harmonic oscillator loses mechanical energy because a resistive force acts opposite to velocity. Its equation is m x double dot + b x dot + kx = 0. For light damping, the oscillation continues but the amplitude decays exponentially.

The standard solution has an exponential envelope multiplied by a cosine term. This tells the examiner both parts of the motion: decay of amplitude and periodic oscillation.

Working Block 1

1. Line 1: Amplitude falls by 3% per cycle: A2/A1 = 0.97. This line is kept visible because it is the algebraic bridge to the final result.
2. Line 2: Energy ∝ A², so E2/E1 = 0.97² = 0.9409. This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: Energy lost = 1 – 0.9409 = 0.0591 = 5.91%. This line is kept visible because it is the algebraic bridge to the final result.

Answer to Part (b)

Question demand: The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. (4) What percentage of the mechanical energy of the oscillator is lost in each cycle?

A damped harmonic oscillator loses mechanical energy because a resistive force acts opposite to velocity. Its equation is m x double dot + b x dot + kx = 0. For light damping, the oscillation continues but the amplitude decays exponentially.

The standard solution has an exponential envelope multiplied by a cosine term. This tells the examiner both parts of the motion: decay of amplitude and periodic oscillation.

Working Block 1

1. Line 1: Entropy change of water heated reversibly from 20 C to 100 C: This statement sets the physical condition used by the next line.
2. Line 2: ΔS = mc ln(T2/T1) This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: = 1.8 × 4186 × ln(373.15/293.15) This line is kept visible because it is the algebraic bridge to the final result.
4. Line 4: ≈ 1817 J/K. This statement sets the physical condition used by the next line.

Answer to Part (c)

Question demand: An insulating vessel containing 1.8 kg of water is placed on a hot plate, both the (6) (20) water and hot plate being initially at 20 oC. The temperature of the hot plate is raised very slowly to 100oC, at which point the water begins to boil. What is the e ntropy change of the water during this process? PHYSICS, PAPER-I

This subpart belongs to oscillations and waves. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Begin with a one-sentence definition using correct physics terminology.
2. Write the standard mathematical relation if the concept has one.
3. Explain the symbols and physical meaning of the relation.
4. Add one example or application because CSS theory answers need illustration.

Calculation and Derivation Written Line by Line

Working Block 1

1. Amplitude falls by 3% per cycle: A2/A1 = 0.97.
2. Energy ∝ A², so E2/E1 = 0.97² = 0.9409.
3. Energy lost = 1 – 0.9409 = 0.0591 = 5.91%.

Working Block 2

1. Entropy change of water heated reversibly from 20 C to 100 C:
2. ΔS = mc ln(T2/T1)
3. = 1.8 × 4186 × ln(373.15/293.15)
4. ≈ 1817 J/K.

Subpart-by-Subpart Breakdown

1. Part (a) – Numerical calculation: Q. 6. What is damped harmonic oscillator? Write its equation of motion and find its (10) solution. Use: Amplitude falls by 3% per cycle: A2/A1 = 0.97..
2. Part (b) – Direct answer: The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. (4) What percentage of the mechanical energy of the oscillator is lost in each cycle? Use: Entropy change of water heated reversibly from 20 C to 100 C:.
3. Part (c) – Definition and explanation: An insulating vessel containing 1.8 kg of water is placed on a hot plate, both the (6) (20) water and hot plate being initially at 20 oC. The temperature of the hot plate is raised very slowly to 100oC, at which point the water begins to boil. What is the e ntropy change of the water during this process? PHYSICS, PAPER-I Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.

What the Examiner Is Asking

This question belongs mainly to oscillations and waves. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

For waves and oscillations, begin with the standard equation and then identify amplitude, angular frequency, phase and speed. If energy is involved, remember that energy is proportional to amplitude squared. If interference is involved, write the path difference and the condition for maxima or minima. For grating or diffraction questions, define the order of spectrum and the number of illuminated lines before writing the resolving power.

Answer to Part (a)

Question demand: Q. 7. What are travelling waves? Find the rate at which energy is transported by a wave (5) travelling along a string.

This subpart belongs to oscillations and waves. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

Working Block 1

1. Line 1: μ = 0.525 kg/m, T = 45 N, f = 120 Hz, ym = 8.5 mm This line is kept visible because it is the algebraic bridge to the final result.
2. Line 2: v = sqrt(45/0.525) = 9.26 m/s This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: ω = 2πf = 754 rad/s This line is kept visible because it is the algebraic bridge to the final result.
4. Line 4: P_avg = 0.5(0.525)(754²)(0.0085²)(9.26) ≈ 99.8 W. This line is kept visible because it is the algebraic bridge to the final result.

Answer to Part (b)

Question demand: A string has linear density μ = 525 g/m and is under tension T = 45 N. We send a (5) sinusoidal wave with frequency f = 120 Hz and amplitude ym = 8.5 mm along the string. At what average rate does the wave transport energy?

For a sinusoidal wave y = ym sin(kx-ωt), the average power transported along a stretched string is P_avg = 0.5 μ ω² ym² v, where v = sqrt(T/μ).

Working Block 1

1. Line 1: A standing string is flat twice per period, so Δt = T/2 = 0.50 s => T = 1.0 s. This line is kept visible because it is the algebraic bridge to the final result.
2. Line 2: Given wave speed v = 10 cm/s, wavelength λ = vT = 10 cm. This line lists the data or converts the symbols into usable quantities.

Answer to Part (c)

Question demand: Two sinusoidal waves with the identical wavelengths and amplitudes travel in (10) (20) opposite directions along a string with a speed of 10 cm/s. If the time interval between instants when the string is flat is 0.50 s, what is the wavelength of the waves?

This subpart belongs to oscillations and waves. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Begin with a one-sentence definition using correct physics terminology.
2. Write the standard mathematical relation if the concept has one.
3. Explain the symbols and physical meaning of the relation.
4. Add one example or application because CSS theory answers need illustration.

Calculation and Derivation Written Line by Line

Working Block 1

1. μ = 0.525 kg/m, T = 45 N, f = 120 Hz, ym = 8.5 mm
2. v = sqrt(45/0.525) = 9.26 m/s
3. ω = 2πf = 754 rad/s
4. P_avg = 0.5(0.525)(754²)(0.0085²)(9.26) ≈ 99.8 W.

Working Block 2

1. A standing string is flat twice per period, so Δt = T/2 = 0.50 s => T = 1.0 s.
2. Given wave speed v = 10 cm/s, wavelength λ = vT = 10 cm.

Subpart-by-Subpart Breakdown

1. Part (a) – Numerical calculation: Q. 7. What are travelling waves? Find the rate at which energy is transported by a wave (5) travelling along a string. Use: μ = 0.525 kg/m, T = 45 N, f = 120 Hz, ym = 8.5 mm.
2. Part (b) – Direct answer: A string has linear density μ = 525 g/m and is under tension T = 45 N. We send a (5) sinusoidal wave with frequency f = 120 Hz and amplitude ym = 8.5 mm along the string. At what average rate does the wave transport energy? Use: A standing string is flat twice per period, so Δt = T/2 = 0.50 s => T = 1.0 s..
3. Part (c) – Definition and explanation: Two sinusoidal waves with the identical wavelengths and amplitudes travel in (10) (20) opposite directions along a string with a speed of 10 cm/s. If the time interval between instants when the string is flat is 0.50 s, what is the wavelength of the waves? Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.

What the Examiner Is Asking

This question belongs mainly to fluids. Treat it as a full CSS Physics answer, not as a short note. The examiner expects the definition or law, the relevant mathematical relation, the physical meaning of the symbols, and a clean final line. If the question has more than one part, solve the parts in the same order in which they appear in the paper.

1. Step 1: Identify the topic and write the governing principle before doing any calculation.
2. Step 2: List the given quantities and convert them into SI units wherever a numerical value is involved.
3. Step 3: Write the formula or theorem in its standard form and define every symbol used in it.
4. Step 4: Substitute values slowly, keeping powers of ten visible so the calculation can be checked.
5. Step 5: End with a boxed result, unit and one sentence explaining what the answer means physically.

For fluids, mention the assumptions before applying a formula. Bernoulli’s theorem assumes steady, incompressible, non-viscous flow along a streamline. Poiseuille flow assumes laminar flow through a circular tube. For pressure and capillarity, draw a simple force balance in words: upward surface-tension component versus weight, or pressure force versus external load. For numerical work, convert centimetres to metres, density to kg per cubic metre and pressure to pascals before substitution.

Answer to Part (a)

Question demand: Q. 8. Explain the volume and pressure corrections in ideal gas law as suggested by van (10) der Waals.

The van der Waals equation corrects ideal gas behavior by reducing free volume (V-nb) and adding pressure correction an²/V² for attractive forces.

Working Block 1

1. Line 1: Ideal: P = nRT/V = (1)(8.314)(50)/0.0224 = 1.856×10^4 Pa. This line is kept visible because it is the algebraic bridge to the final result.
2. Line 2: van der Waals: P = nRT/(V-nb) – an²/V² This line is kept visible because it is the algebraic bridge to the final result.
3. Line 3: = 415.7/(0.0224-3.18×10^-5) – 0.138/(0.0224²) This line is kept visible because it is the algebraic bridge to the final result.
4. Line 4: ≈ 1.831×10^4 Pa. This statement sets the physical condition used by the next line.

Answer to Part (b)

Question demand: For oxygen the van der Waals coefficients have been measured to be (5) a = 0.138 J .m3/mol2 and b = 3.18 × 10-5 m3/mol. Assume that 1.00 mol of oxygen at T = 50 K is confined to a box of volume 0.0224 m3. What pressure does the gas exert according to

This subpart belongs to fluids. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Identify the concept from fluids and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Answer to Part (a)

Question demand: the ideal gas law and

This subpart belongs to fluids. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Identify the concept from fluids and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Answer to Part (b)

Question demand: the van der Waals equation?

This subpart belongs to fluids. Start from the physical principle, then connect it directly to the command in the question. If the command is define, give the definition and one implication. If it is derive, show the starting equation, the assumption and the final expression. If it is calculate, show data, formula, substitution and final unit.

1. Identify the concept from fluids and state the relevant law.
2. Explain why that law is applicable to this exact subpart.
3. Use a labelled equation, example or diagram description where possible.
4. Finish with a direct answer to the wording of the question.

Answer to Part (c)

Question demand: State and explain the zeroth law of thermodynamics. (5) (20)

The zeroth law states that if A is in thermal equilibrium with B and B with C, then A is in thermal equilibrium with C; it defines temperature.

1. Begin with a one-sentence definition using correct physics terminology.
2. Write the standard mathematical relation if the concept has one.
3. Explain the symbols and physical meaning of the relation.
4. Add one example or application because CSS theory answers need illustration.

Calculation and Derivation Written Line by Line

Working Block 1

1. Ideal: P = nRT/V = (1)(8.314)(50)/0.0224 = 1.856×10^4 Pa.
2. van der Waals: P = nRT/(V-nb) – an²/V²
3. = 415.7/(0.0224-3.18×10^-5) – 0.138/(0.0224²)
4. ≈ 1.831×10^4 Pa.

Subpart-by-Subpart Breakdown

1. Part (a) – Conceptual explanation: Q. 8. Explain the volume and pressure corrections in ideal gas law as suggested by van (10) der Waals. Use: Ideal: P = nRT/V = (1)(8.314)(50)/0.0224 = 1.856×10^4 Pa..
2. Part (b) – Direct answer: For oxygen the van der Waals coefficients have been measured to be (5) a = 0.138 J .m3/mol2 and b = 3.18 × 10-5 m3/mol. Assume that 1.00 mol of oxygen at T = 50 K is confined to a box of volume 0.0224 m3. What pressure does the gas exert according to Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.
3. Part (a) – Direct answer: the ideal gas law and Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.
4. Part (b) – Direct answer: the van der Waals equation? Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.
5. Part (c) – Definition and explanation: State and explain the zeroth law of thermodynamics. (5) (20) Keep the answer conceptual, but support it with one formula, example or physical interpretation if possible.

How to Write This Answer in the CSS Exam

Write the answer in compact paragraphs, but do not skip the reasoning. Start with the law or definition, then show the algebra line by line. In a derivation, every new line should follow from the previous line. In a numerical part, the examiner should be able to see the data, the formula, the substitution and the final unit without searching through the answer.

If you are short of time, attempt the highest-mark subpart first, but keep all subparts under the same question heading. Use words such as therefore, hence and substituting the given values to make the flow clear. This is especially useful in CSS Physics Paper-I 2020 Solved, because the paper mixes conceptual physics with numerical reasoning.