For an isotropic solid, volume expansion γ = 3α (cubical expansion is three times linear expansion). This arises because volume V = L³, so dV/V = 3dL/L, giving γ = 3α. Similarly area expansion β = 2α.

f-number (f-stop) = focal length/diameter. So f/4 means: focal length/diameter = 4. Focal length = 4 × diameter = 4 × 2.0 cm = 8.0 cm. The f-number system: f/4 means aperture diameter is focal length divided by 4.

Net force = Applied force - Friction = 140 - 40 = 100N. Using Newton's 2nd Law: a = F_net/m = 100/100 = 1 m/s². The acceleration of the body is 1 m/s².

In an AC circuit, power dissipated as heat (real power) P = I²R — it depends only on resistance. Inductors and capacitors store and release energy alternately (reactive components) but dissipate no net energy as heat. P = VI cosφ where cosφ is the power factor.

Swimming is an application of Newton's Third Law — a swimmer pushes water backward (action) and the water pushes the swimmer forward (reaction). The reaction force propels the swimmer forward. Newton's 3rd Law: every action has an equal and opposite reaction.

Introducing a dielectric (insulating) material between capacitor plates increases capacitance: C = κε₀A/d, where κ (dielectric constant) > 1. The dielectric reduces the electric field between plates by polarisation, allowing more charge to be stored at the same voltage.

Momentum p = mv — if v doubles, p doubles (2×). KE = ½mv² — if v doubles, KE = ½m(2v)² = 4×½mv² = 4 times original KE. So momentum doubles and kinetic energy quadruples.

When disconnected, charge Q is constant. C = ε₀A/d — as d increases, C decreases. V = Q/C — as C decreases, V increases. Energy = Q²/2C — as C decreases, energy increases. So voltage and electrostatic energy both increase, but energy stored increasing is the key correct answer here.

A vector can be multiplied by any scalar — dimensionless (e.g., 3v), dimensional scalar (e.g., mass×velocity giving momentum), or negative (reversing direction, e.g., -v). All three types of scalar multiplication are valid operations on vectors.

In intrinsic (pure) semiconductors, conductivity increases with temperature because thermal energy promotes more electrons from valence to conduction band, creating more electron-hole pairs. Both p-type and n-type doped semiconductors also show this but the question refers to intrinsic semiconductors as the clearest example.

Two protons have the same (positive) charge, so the electrostatic force between them is repulsive. Potential energy PE = kq₁q₂/r. As r decreases (brought closer), PE increases (becomes more positive). Work must be done against the repulsive force.

Chromatic aberration is caused by dispersion — different wavelengths (colours) of light are refracted by different amounts as they pass through a lens (because refractive index varies with wavelength). This causes different colours to focus at different points.

Magnetic flux Φ = B·A. Units: Weber (Wb) = T·m² = V·s = kg·m²·s⁻²·A⁻¹. The Henry (H) is the unit of inductance (L), not magnetic flux. So Henry is NOT a unit of magnetic flux.

For Newton's rings, nth dark ring: t = nλ/2, where t is air gap thickness. So λ = 2t/n = 2×(1.8×10⁻⁶)/6 = 3.6×10⁻⁶/6 = 6.0×10⁻⁷ m = 600 nm. This is in the visible (orange) light range.

Bulk modulus measures resistance to compression. Solids > Liquids > Gases. Liquids are nearly incompressible (high bulk modulus compared to gases) but much more compressible than solids. So liquid bulk modulus is higher than gas but lower than solid.

Two instruments playing the same note (same fundamental frequency) differ in timbre (tone quality) due to the different mixture of harmonics (overtones). The fundamental frequency and wavelength are the same — but the harmonic content (waveform) differs, giving each instrument its characteristic sound.

Time of flight T = 2u sinθ/g → u sinθ = gT/2. Max height H = (u sinθ)²/2g = (gT/2)²/2g = g²T²/8g = gT²/8. Therefore H = gT²/8.

Closed pipe first harmonic: f = v/4L1. Open pipe third harmonic: f = 3v/2L2. Setting equal: v/4L1 = 3v/2L2 → L1/L2 = 2/(12) = 1/6. Simplifying gives L1:L2 = 3:8.

Stress = Y × Strain = Y × (ΔL/L). Original length L, new length = 3L, so ΔL = 2L. Strain = 2L/L = 2. Stress = Y × 2 = 2Y. Force = Stress × Area = 2Y × 1 = 2Y (since area = 1 unit).

Using v = u + at: 20 = 10 + 2t → 2t = 10 → t = 5 hr. The particle takes 5 hours to accelerate from 10 km/hr to 20 km/hr at a uniform acceleration of 2 km/hr².

Stars generate energy through nuclear fusion of light nuclei — primarily hydrogen nuclei (protons) fusing to form helium in the proton-proton chain and CNO cycle. This process releases enormous energy per unit mass via E=mc². Chemical reactions are millions of times less energetic.

When acceleration is zero, velocity is constant — the body moves at the same speed in the same direction throughout. In this case, instantaneous velocity equals average velocity at every point. With uniform or variable acceleration the two differ.

The strong nuclear force is always attractive — it binds protons and neutrons together in the nucleus and overcomes the electrostatic repulsion between protons. The electrostatic force can be attractive or repulsive depending on charges. Magnetic force can be attractive or repulsive.

γ (gamma) is defined as the ratio of specific heat at constant pressure (Cp) to specific heat at constant volume (Cv): γ = Cp/Cv. This ratio is also called the adiabatic index. For monoatomic ideal gas γ = 5/3; for diatomic γ = 7/5.