MDCAT Physics Complete Formula Sheet & High-Yield Revision Blueprint

1. MDCAT Physics Syllabus Weightage & Cognitive Blueprint

• Current Electricity: 4 to 5 MCQs (~12% of Physics) — Highest single-chapter yield across all provincial boards.
• Mechanics & Kinematics: 4 to 5 MCQs covering equations of motion, momentum conservation, and projectile paths.
• Waves, Oscillations & Optics: 4 to 5 MCQs on SHM, Doppler frequency shifts, and lens equations.
• Electromagnetism & Induction: 3 to 4 MCQs evaluating Lorentz forces, Faraday's law, and Lenz's law.
• Modern & Nuclear Physics: ~3 MCQs on photoelectric thresholds, Bohr orbits, and radioactive half-lives.
• Cognitive Split: Approximately 65% to 75% formula-based numerical calculations and 25% to 35% conceptual and graphical questions.

2. Comprehensive High-Yield Physics Formula Matrix

Mechanics, Kinematics & Energy

• Equations of Constant Acceleration:

$$v = u + at$$

$$s = ut + \tfrac{1}{2}at^2$$

$$v^2 = u^2 + 2as$$

$$s = \frac{(u + v)t}{2}$$

• Dynamics & Momentum Conservation:

$$F = ma = \frac{\Delta p}{\Delta t}$$

$$p = mv$$

$$\text{Impulse} = F\Delta t = \Delta p$$

• Work, Energy & Power Relations:

$$W = Fs \cos\theta$$

$$KE = \tfrac{1}{2}mv^2, \quad PE = mgh$$

$$P = \frac{W}{t} = Fv$$

• Circular Motion, Gravity & Projectiles:

$$a_c = \frac{v^2}{r} = r\omega^2, \quad F_c = \frac{mv^2}{r}$$

$$v = r\omega, \quad T = \frac{2\pi r}{v}$$

$$F = \frac{G m_1 m_2}{r^2}, \quad g = \frac{GM}{R^2}$$

$$v_{\text{orbital}} = \sqrt{\frac{GM}{r}}, \quad v_{\text{escape}} = \sqrt{2gR}$$

$$\text{Projectile Range} = \frac{u^2 \sin(2\theta)}{g}, \quad H_{\text{max}} = \frac{u^2 \sin^2\theta}{2g}$$

Waves, Oscillations & Physical Optics

• Simple Harmonic Motion (SHM):
• Spring-Mass System: $T = 2\pi\sqrt{\frac{m}{k}}$
• Simple Pendulum: $T = 2\pi\sqrt{\frac{l}{g}}$
• Angular Frequency: $\omega = 2\pi f = \sqrt{\frac{k}{m}}$
• Maximum Velocity at Equilibrium: $v_{\text{max}} = A\omega = A\sqrt{\frac{k}{m}}$
• Wave Speed Mechanics:

$$v = f\lambda, \quad T = \frac{1}{f}$$

• Transverse Wave on Stretched String: $v = \sqrt{\frac{T}{\mu}}$
• Longitudinal Wave in Fluid: $v = \sqrt{\frac{B}{\rho}}$
• Longitudinal Wave in Solid: $v = \sqrt{\frac{Y}{\rho}}$
• Speed of Sound in Gas (Laplace Formula): $v = \sqrt{\frac{\gamma P}{\rho}}$
• The Doppler Effect:

$$f' = f\left(\frac{v \pm v_o}{v \mp v_s}\right)$$

• Geometrical & Physical Optics:
• Thin Lens / Spherical Mirror Formula: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
• Optical Linear Magnification: $m = \frac{v}{u} = \frac{h'}{h}$
• Snell's Law of Refraction: $n_1 \sin\theta_1 = n_2 \sin\theta_2$
• Critical Angle for Total Internal Reflection: $\sin\theta_c = \frac{n_2}{n_1} = \frac{1}{n}$

Current Electricity & Electromagnetism

• Ohm's Law, Resistivity & Microscopic Current:

$$V = IR, \quad R = \frac{\rho L}{A}$$

$$\text{Drift Velocity Equation: } I = nA e v_d$$

• Electrical Power Dissipation:

$$P = VI = I^2R = \frac{V^2}{R}$$

• Resistor Combinations:
• Series Circuit: $R_{\text{eq}} = R_1 + R_2 + \dots$
• Parallel Circuit: $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \implies R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2} \text{ (for 2 resistors)}$
• Kirchhoff's Laws & Circuit Analysis:
• Kirchhoff's Current Law (Junction Rule): $\sum I_{\text{in}} = \sum I_{\text{out}}$ (Conservation of Charge)
• Kirchhoff's Voltage Law (Loop Rule): $\sum \text{EMF} = \sum IR$ (Conservation of Energy)
• Terminal Potential Difference: $V = \mathcal{E} - Ir \text{ (discharging)}, \quad V = \mathcal{E} + Ir \text{ (charging)}$
• Balanced Wheatstone Bridge Condition: $\frac{P}{Q} = \frac{R}{S} \quad (\text{Galvanometer Current } I_g = 0)$
• Magnetic Fields & Lorentz Forces:
• Magnetic Force on Current-Carrying Conductor: $F = BIL \sin\theta$
• Magnetic Force on Moving Charge: $F = qvB \sin\theta$
• Magnetic Field of Long Straight Wire: $B = \frac{\mu_0 I}{2\pi r}$
• Electromagnetic Induction:
• Faraday's Law of Induction: $\mathcal{E} = -N\frac{\Delta \Phi}{\Delta t}, \quad \Phi = BA \cos\theta$
• Motional EMF in Moving Rod: $\mathcal{E} = BvL \sin\theta$
• Lenz's Law: Induced current creates a magnetic flux that opposes the initial flux change (Conservation of Energy).

Modern Physics & Nuclear Reactions

• Photons & Photoelectric Effect:

$$E = hf = \frac{hc}{\lambda} = mc^2$$

$$hf = \Phi + KE_{\text{max}} \implies KE_{\text{max}} = h(f - f_0) = eV_s$$

$$\text{Threshold Frequency: } f_0 = \frac{\Phi}{h}$$

$$\text{de Broglie Matter Wavelength: } \lambda = \frac{h}{p} = \frac{h}{mv}$$

• Bohr Hydrogen Model:
• Quantized Energy Levels: $E_n = -\frac{13.6}{n^2}\text{ eV}$
• Quantized Orbital Radii: $r_n = 0.529 \times n^2\text{ \AA}$
• Photon Emission Energy: $\Delta E = E_{\text{final}} - E_{\text{initial}} = hf$
• Radioactivity & Nuclear Transmutations:
• Radioactive Decay Law: $N = N_0 e^{-\lambda t}$
• Activity Rate: $A = \lambda N$
• Nuclear Half-Life: $t_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}$
• Alpha ($\alpha$) Decay: Mass number decreases by 4; Atomic number decreases by 2.
• Beta ($\beta^-$) Decay: Mass number unchanged; Atomic number increases by 1 ($n \rightarrow p + e^- + \bar{\nu}_e$).

3. The 15-Second Elimination Shortcut: No-Calculator Speed Hacks

4. The White Coat Preview: Clinical Medical Biophysics

In 1st-year MBBS Physiology and Cardiology, electrical circuit physics explains Electrocardiography (ECG). The human heart functions as a rotating electrical dipole generating ionic volume-conductor currents through thoracic interstitial fluid. Einthoven's Triangle models limb leads (Leads I, II, and III) based directly on Kirchhoff's Voltage Law:

$$\text{Lead II Potential} = \text{Lead I Potential} + \text{Lead III Potential}$$

In Diagnostic Radiology and Oncology, understanding ionizing radiation kinetics dictates Positron Emission Tomography (PET) scanning. Fluorodeoxyglucose ($^{18}\text{F-FDG}$) undergoes $\beta^+$ positron decay inside metabolically hyperactive tumor cells. The emitted positron travels 1 to 2 mm before colliding with a tissue electron, undergoing particle-antiparticle annihilation to emit two collinear $511\text{ keV}$ gamma photons at $180^\circ$ detected by external scintillation rings.

Frequently Asked Questions

Q: Why does stretching a wire to double its length quadruple its electrical resistance?

Stretching a wire increases its length while keeping total metal volume constant. Doubling the length ($2L$) forces the cross-sectional area to halve ($A/2$). Because resistance is directly proportional to length and inversely proportional to area ($R \propto L/A$), the new resistance is $(2L) / (A/2) = 4R$.

Q: How do you solve Doppler effect frequency shift MCQs without confusing the plus and minus signs?

Use relative distance intuition: when the source and observer are moving closer together (approaching), the observed frequency must increase ($f' > f$), so use the plus sign in the numerator and minus sign in the denominator. When moving apart (receding), frequency must decrease ($f' < f$), so use the minus sign in the numerator and plus sign in the denominator.

Q: Why is terminal potential difference greater than electromotive force (EMF) when a battery is being recharged?

During discharging, internal resistance causes an internal voltage drop, yielding $V = \mathcal{E} - Ir$. During charging, current is forced backward into the positive terminal by an external charger, reversing the internal IR drop and yielding $V = \mathcal{E} + Ir$, making terminal potential difference strictly greater than the EMF.