BITSAT Physics Syllabus

How does acceleration due to gravity g vary with height h and depth d below Earth's surface?

At height: g_h = g(1 − 2h/R) for h << R; at depth: g_d = g(1 − d/R). g is maximum at the surface and zero at the centre.

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

Orbital velocity v_o = √(GM/r) = √(gR) near the surface (≈7.9 km/s); Escape velocity v_e = √(2GM/R) = √(2gR) ≈ 11.2 km/s = √2 × v_o.

State Kepler's three laws of planetary motion.

1) Orbits are ellipses with the Sun at one focus. 2) The line joining planet and Sun sweeps equal areas in equal times (constant areal velocity). 3) T² ∝ a³ (square of period proportional to cube of semi-major axis).

Define stress, strain, and Young's modulus.

Stress = force/area (N/m²); Strain = change in dimension/original dimension (dimensionless); Young's modulus Y = longitudinal stress/longitudinal strain.

State Hooke's law and define the elastic potential energy per unit volume.

Hooke's law: within the elastic limit, stress ∝ strain. Elastic PE per unit volume = ½ × stress × strain = ½ × Y × strain².

What are bulk modulus and shear (rigidity) modulus?

Bulk modulus B = −V(dP/dV) relates volumetric stress to volumetric strain (compressibility = 1/B). Shear modulus η relates shearing (tangential) stress to shear strain.

State Pascal's law and the principle of a hydraulic lift.

Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to every point. A hydraulic lift multiplies force: F2 = F1 × (A2/A1).

State Archimedes' principle and the condition for floating.

A body immersed in a fluid experiences an upward buoyant force equal to the weight of displaced fluid. A body floats when its weight equals the buoyant force (average density ≤ fluid density).

State Bernoulli's equation for streamline flow.

P + ½ρv² + ρgh = constant along a streamline, expressing conservation of energy per unit volume for an ideal incompressible fluid.

Define viscosity and state Stokes' law for terminal velocity.

Viscosity is the internal friction opposing relative motion between fluid layers (coefficient η). Stokes' law: viscous drag on a sphere F = 6πηrv; terminal velocity v_t = 2r²(ρ−σ)g/9η.

What is surface tension, and give the excess pressure inside a drop and a soap bubble?

Surface tension T is force per unit length along a liquid surface. Excess pressure inside a liquid drop = 2T/r; inside a soap bubble (two surfaces) = 4T/r.

Convert between Celsius, Kelvin, and Fahrenheit scales.

K = °C + 273.15; °F = (9/5)°C + 32. The relation is (C/5) = (F−32)/9 = (K−273)/5.

Give the formulas for linear, area, and volume thermal expansion and relate the coefficients.

ΔL = LαΔT; ΔA = AβΔT; ΔV = VγΔT, with β = 2α and γ = 3α for isotropic solids.

State the principle of calorimetry and define latent heat.

Calorimetry: heat lost by the hot body = heat gained by the cold body (no losses). Heat Q = mcΔT for temperature change; Q = mL for phase change, where L is latent heat (fusion or vaporization).

What are the three modes of heat transfer, and state Newton's law of cooling?

Conduction, convection, and radiation. Newton's law of cooling: the rate of cooling is proportional to the temperature difference with surroundings, dθ/dt ∝ (θ − θ_s).

Define simple harmonic motion and give its differential equation.

SHM is motion where restoring force is proportional to displacement and directed toward the mean position: F = −kx, giving d²x/dt² = −ω²x, with x = A sin(ωt + φ).

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

Simple pendulum: T = 2π√(L/g); Spring-mass: T = 2π√(m/k).

In SHM, write expressions for velocity and acceleration as functions of displacement.

v = ω√(A² − x²) (maximum at mean position, zero at extremes); a = −ω²x (maximum at extremes, zero at mean position).

How do energies vary in SHM?

KE = ½mω²(A² − x²), PE = ½mω²x²; total energy E = ½mω²A² is constant. KE is max at the mean position, PE is max at the extremes.

Give the speed of a transverse wave on a string and a longitudinal (sound) wave in a gas.

On a string: v = √(T/μ), where T is tension and μ is linear mass density. In a gas (Laplace): v = √(γP/ρ).

Distinguish transverse and longitudinal waves and relate wave speed, frequency, and wavelength.

In transverse waves particles vibrate perpendicular to propagation (light, string waves); in longitudinal waves parallel (sound). v = fλ.

What are beats, and what is the beat frequency?

Beats are periodic variations in loudness from superposition of two waves of slightly different frequencies. Beat frequency = |f1 − f2|.

State the Doppler effect formula for sound.

f' = f (v ± v_o)/(v ∓ v_s), where v is sound speed, v_o observer speed, v_s source speed; signs chosen so approach raises pitch and recession lowers it.

State the postulates of kinetic theory and the expression for pressure of an ideal gas.

Gas molecules are point particles in random motion with negligible intermolecular forces and perfectly elastic collisions. Pressure P = (1/3)(N/V) m v_rms² = (1/3)ρv_rms².

State the law of equipartition of energy and give the internal energy of monatomic and diatomic ideal gases.

Each degree of freedom carries average energy ½kT. Monatomic (3 dof): U = (3/2)nRT; diatomic (5 dof): U = (5/2)nRT.

Give the rms, average, and most probable speeds of gas molecules.

v_rms = √(3RT/M); average v_avg = √(8RT/πM); most probable v_mp = √(2RT/M). Ratio v_mp : v_avg : v_rms ≈ 1 : 1.13 : 1.22.

Relate Cp, Cv, and γ for an ideal gas (Mayer's relation).

Cp − Cv = R; γ = Cp/Cv. Monatomic γ = 5/3, diatomic γ = 7/5, polyatomic ≈ 4/3.

State the first law of thermodynamics with sign conventions.

ΔU = Q − W, where Q is heat added to the system, W is work done by the system, ΔU is change in internal energy. It is conservation of energy.

Give the work done and the key relation for isothermal and adiabatic processes.

Isothermal (T constant): W = nRT ln(V2/V1), PV = constant. Adiabatic (Q = 0): PV^γ = constant, W = (P1V1 − P2V2)/(γ−1).

State the second law of thermodynamics and the efficiency of a Carnot engine.

Heat cannot spontaneously flow from cold to hot (Clausius) / no engine can convert all heat to work (Kelvin-Planck). Carnot efficiency η = 1 − T_c/T_h, the maximum possible, with COP of a refrigerator = T_c/(T_h − T_c).

State Coulomb's law and give the value of the constant.

F = (1/4πε₀) q1 q2 / r² along the line joining charges. k = 1/4πε₀ ≈ 9 × 10⁹ N·m²/C²; ε₀ = 8.85 × 10⁻¹² C²/N·m².

State Gauss's law and give the field of an infinite line and infinite sheet of charge.

Gauss's law: Φ = ∮E·dA = q_enclosed/ε₀. Infinite line: E = λ/2πε₀r; infinite sheet: E = σ/2ε₀ (independent of distance).

Relate electric field and potential, and give the potential of a point charge.

E = −dV/dr (field is the negative gradient of potential). Potential of a point charge V = (1/4πε₀) q/r; potential energy of two charges U = (1/4πε₀) q1q2/r.

Give the capacitance of a parallel-plate capacitor and the effect of a dielectric.

C = ε₀A/d (vacuum); with a dielectric of constant K, C = Kε₀A/d. Energy stored U = ½CV² = ½ Q²/C = ½ QV.

How do capacitors combine in series and parallel?

Series: 1/C_eq = Σ(1/C_i) (charge same). Parallel: C_eq = ΣC_i (voltage same).

State Ohm's law and define resistivity and its temperature dependence.

V = IR. Resistance R = ρL/A, where ρ is resistivity. For metals ρ increases with temperature: ρ_t = ρ₀(1 + αΔT).

State Kirchhoff's two laws.

Junction (current) rule: ΣI = 0 at a node (charge conservation). Loop (voltage) rule: ΣV = 0 around a closed loop (energy conservation).

Give the condition for a balanced Wheatstone bridge.

P/Q = R/S; when balanced, no current flows through the galvanometer connecting the bridge midpoints.

How do resistors combine, and what is electrical power dissipated?

Series: R_eq = ΣR_i; Parallel: 1/R_eq = Σ(1/R_i). Power P = VI = I²R = V²/R.

Define EMF, terminal voltage, and internal resistance of a cell.

EMF (ε) is the work per unit charge by the source; terminal voltage V = ε − Ir when discharging (I is current, r internal resistance). Maximum power transfer occurs when external resistance equals r.

State the Biot-Savart law and give the field at the centre of a circular loop.

dB = (μ₀/4π)(I dl × r̂)/r². Field at the centre of a circular loop of radius R: B = μ₀I/2R; on the axis at distance x: B = μ₀IR²/2(R²+x²)^(3/2).

State Ampere's circuital law and give the field inside a long solenoid and a toroid.

∮B·dl = μ₀ I_enclosed. Inside a solenoid B = μ₀nI (n = turns per length); inside a toroid B = μ₀NI/2πr.

Give the force on a moving charge and on a current-carrying conductor in a magnetic field.

On a charge: F = qv × B (magnitude qvB sinθ). On a conductor: F = I L × B (magnitude BIL sinθ).

What is the radius and time period of a charged particle in a uniform magnetic field?

Radius r = mv/qB; time period T = 2πm/qB (independent of speed); used in cyclotrons.

Define magnetic dipole moment and classify dia-, para-, and ferromagnetic materials.

Magnetic moment m = NIA. Diamagnetic: weakly repelled, χ small negative; Paramagnetic: weakly attracted, χ small positive; Ferromagnetic: strongly attracted, χ large positive, shows hysteresis and a Curie temperature.

State Faraday's laws of electromagnetic induction and Lenz's law.

Induced EMF ε = −dΦ/dt; magnitude proportional to rate of change of flux. Lenz's law: the induced current opposes the change causing it (the minus sign), ensuring energy conservation.

Define self-inductance and mutual inductance, and give the energy stored in an inductor.

Self: ε = −L dI/dt; Mutual: ε₂ = −M dI₁/dt. Energy stored U = ½LI². Solenoid inductance L = μ₀n²Al.

In an AC circuit, define reactance for an inductor and a capacitor.

Inductive reactance X_L = ωL; capacitive reactance X_C = 1/ωC. Impedance Z = √(R² + (X_L − X_C)²).

State the resonance condition for a series LCR circuit and define power factor.

Resonance when X_L = X_C, i.e. f = 1/(2π√(LC)); impedance is minimum (=R) and current maximum. Power factor = cosφ = R/Z; average power P = V_rms I_rms cosφ.

What are rms and peak values of AC, and the transformer relation?

V_rms = V₀/√2, I_rms = I₀/√2. Ideal transformer: V_s/V_p = N_s/N_p = I_p/I_s (step-up/step-down).

State the properties of electromagnetic waves and give the speed of light relation.

EM waves are transverse, with E ⊥ B ⊥ direction of propagation, travel in vacuum at c = 1/√(μ₀ε₀) ≈ 3×10⁸ m/s. They carry energy and momentum; E₀/B₀ = c.

List the EM spectrum in order of increasing frequency.

Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays (increasing frequency, decreasing wavelength).

State the laws of reflection and the mirror formula with magnification.

Angle of incidence = angle of reflection, in the same plane. Mirror formula: 1/v + 1/u = 1/f; magnification m = −v/u = h'/h.

State Snell's law and define the critical angle for total internal reflection.

n₁ sinθ₁ = n₂ sinθ₂. Critical angle: sinθ_c = 1/n (light going from denser to rarer); beyond θ_c total internal reflection occurs.

Give the lens maker's formula and the lens formula with power.

Lens maker's: 1/f = (n−1)(1/R₁ − 1/R₂). Lens formula: 1/v − 1/u = 1/f; power P = 1/f (in dioptres, f in metres); combined power P = P₁ + P₂.

Explain dispersion through a prism and angular dispersion.

A prism splits white light into colours because refractive index varies with wavelength (violet bends most, red least). Deviation δ = (n−1)A for a thin prism; angular dispersion = (n_v − n_r)A.

State the conditions for constructive and destructive interference (Young's double slit).

Constructive (bright): path difference = nλ; Destructive (dark): path difference = (n+½)λ. Fringe width β = λD/d.

Give the condition for minima in single-slit diffraction.

Minima occur when a sinθ = nλ (n = 1,2,3...), where a is slit width. The central maximum is twice as wide as other maxima.

State Malus's law and Brewster's law for polarization.

Malus's law: transmitted intensity I = I₀ cos²θ through a polarizer. Brewster's law: at the polarizing angle, tanθ_p = n, and reflected and refracted rays are perpendicular.

State Einstein's photoelectric equation and define work function and threshold frequency.

K_max = hν − φ₀, where φ₀ = hν₀ is the work function (minimum energy to eject an electron) and ν₀ the threshold frequency. Below ν₀ no emission occurs regardless of intensity.

Give the de Broglie wavelength of a particle and that of an electron accelerated through V volts.

λ = h/p = h/mv. For an electron accelerated through potential V: λ = 12.27/√V Å (with V in volts).

State Bohr's postulates and give the radius and energy of the nth orbit in hydrogen.

Electrons occupy stationary orbits with quantized angular momentum L = nh/2π; energy is emitted/absorbed on transitions (E = hν). Radius r_n = 0.53 n² Å; energy E_n = −13.6/n² eV.

Give the Rydberg formula for hydrogen spectral lines and name the series.

1/λ = R(1/n₁² − 1/n₂²), R = 1.097×10⁷ m⁻¹. Series: Lyman (UV, n₁=1), Balmer (visible, n₁=2), Paschen, Brackett, Pfund (IR).

Define mass defect and binding energy, and the energy equivalent of 1 amu.

Mass defect Δm = (sum of nucleon masses) − (nuclear mass); binding energy = Δm c². 1 amu = 931.5 MeV. Higher binding energy per nucleon means a more stable nucleus (peak near iron, A≈56).

State the law of radioactive decay and define half-life and mean life.

N = N₀e^(−λt); activity A = λN. Half-life T½ = 0.693/λ; mean life τ = 1/λ = T½/0.693. Half-life is the time for half the nuclei to decay.

Distinguish alpha, beta, and gamma radiation.

Alpha: helium nucleus (⁴₂He), low penetration, high ionization; Beta: electron/positron, moderate penetration; Gamma: high-energy photon, highest penetration, no charge/mass change.

Distinguish nuclear fission and fusion.

Fission: a heavy nucleus splits into lighter nuclei releasing energy (e.g., U-235); Fusion: light nuclei combine into a heavier one (e.g., hydrogen to helium in the Sun), releasing even more energy per nucleon.

Distinguish intrinsic and extrinsic (n-type, p-type) semiconductors.

Intrinsic: pure semiconductor with equal electrons and holes. Extrinsic: doped — n-type (pentavalent donor, majority electrons), p-type (trivalent acceptor, majority holes).

Describe a p-n junction and forward vs reverse bias.

A p-n junction has a depletion region with a built-in potential barrier. Forward bias (p to +) lowers the barrier and conducts; reverse bias widens the depletion region and blocks current (allows only small leakage).

What is a rectifier, and how do half-wave and full-wave rectifiers differ?

A rectifier converts AC to DC using diodes. A half-wave rectifier uses one diode and conducts in one half-cycle (output frequency = input). A full-wave rectifier (two diodes/bridge) uses both half-cycles (output frequency = 2× input), giving more efficient DC.

What is a Zener diode and its main application?

A heavily doped diode operated in reverse breakdown at a sharp Zener voltage; the voltage stays constant over a range of currents, so it is used as a voltage regulator.

Give the logic outputs of AND, OR, and NOT gates and name the universal gates.

AND: output 1 only if all inputs 1; OR: output 1 if any input 1; NOT: inverts input. NAND and NOR are universal gates (any logic circuit can be built from them).