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Quizzes > Science > Physics

Ultimate Hard Physics Questions Quiz - Are You Up for the Challenge?

Ready to tackle difficult physics questions? Take the quiz now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Teal background paper art showing physics symbols equations and atoms with text inviting a free challenging physics quiz

Use this free quiz to practice hard physics questions and see how you think under time. You'll work problems from mechanics to quantum in a timed practice quiz , spot gaps before the exam, and handle quick estimates and multi-step setups.

What is the relationship among distance (d), velocity (v), and time (t) in uniform motion?
d = v / t
v = d × t
t = v / d
d = v × t
In uniform motion, velocity is defined as the rate of change of distance with respect to time, so distance traveled equals velocity multiplied by time. This is a fundamental kinematic relationship used in many physics problems. If you know how fast and for how long you travel, you can directly compute the distance. .
According to Newton's second law, what is the net force (F) acting on an object of mass m undergoing acceleration a?
F = m / a
F = a / m
F = m + a
F = m × a
Newton's second law states that the net force on an object is the product of its mass and acceleration. It forms the basis for dynamics and allows you to calculate motion under a wide range of forces. This law applies only when mass is constant and acceleration is the result of net external forces. .
What is the kinetic energy of an object with mass m moving at velocity v?
m v / 2
m v²
½ m v²
2 m v²
The kinetic energy for a non-relativistic object is given by one-half times mass times velocity squared. This expression derives from integrating the work done by a force accelerating the mass from rest to velocity v. It shows how energy scales quadratically with speed. .
Which law states that the angle of incidence equals the angle of reflection for a light ray striking a mirror?
Law of Reflection
Snell's Law
Law of Refraction
Law of Diffraction
The law of reflection specifies that when a light ray hits a reflective surface, the angle it makes with the normal before reflection equals the angle after reflection. This principle underlies mirror optics and is used in periscopes and telescopes. It applies to smooth surfaces where the wavefronts remain coherent. .
For a wave, what equation relates its speed v, frequency f, and wavelength ??
v = ? / f
v = f × ?
v = f + ?
v = f / ?
A wave's speed equals the product of its frequency and wavelength, linking temporal oscillations to spatial patterning. This fundamental wave relationship holds for sound, light, and water waves. If you increase frequency while holding speed constant, wavelength must decrease proportionally. .
What is the potential energy stored in a spring with force constant k and extension x?
½ k x²
k x³
k x
½ k / x
Hooke's law indicates that the force needed to extend or compress a spring is proportional to its displacement. Integrating this force over the displacement gives the stored potential energy as one-half k times x squared. This formula is used in mechanics and oscillatory systems. .
What is the horizontal range R of a projectile launched at speed v and angle ? in a uniform gravitational field?
v² sin ? / g
2 v² sin ? cos ? / g
v² sin(2?) / g
g / (v² sin(2?))
Assuming no air resistance, the maximum horizontal distance is v² sin(2?) divided by g. This arises by decomposing the motion into independent horizontal and vertical components and finding time of flight. The range is maximized when ? = 45°. .
For a thin lens, which equation relates the focal length f to the object distance do and image distance di?
1/f = 1/do + 1/di
f = do + di
f = do × di
1/f = do + di
The thin-lens formula links the distances of the object and its image to the focal length. It derives from similar triangles in ray-tracing diagrams and holds when the lens thickness is negligible. This equation is fundamental in optical design. .
What is the period T of a simple pendulum of length L under gravitational acceleration g (for small angles)?
2 ?(L/g)
2? L / g
? ?(L/g)
2? ?(L/g)
For small oscillations, a pendulum behaves like a simple harmonic oscillator. The period is independent of mass and amplitude (for small angles), depending only on length and gravity. This formula is derived by linearizing the restoring torque. .
How is electrical power P in a circuit related to voltage V and current I?
P = I / V
P = V² × I
P = V / I
P = V × I
Electrical power is the rate of energy transfer per unit time, given by the product of voltage and current. It reflects how much work is done by the circuit per second. This relation is foundational in circuit analysis. .
In special relativity, what is the time dilation formula relating proper time ?t? to dilated time ?t at speed v?
?t = ?t? / (1 - v²/c²)
?t = ?t? (1 - v²/c²)²
?t = ?t? / ?(1 - v²/c²)
?t = ?t? × ?(1 - v²/c²)
Time dilation arises because moving clocks tick slower compared to stationary ones. The Lorentz factor, 1/?(1 - v²/c²), quantifies this effect in special relativity. As v approaches the speed of light c, time dilation becomes very large. .
For an ideal gas undergoing an adiabatic process, which quantity remains constant?
P × V^?
P / T
P × V
V / T
In an adiabatic process, no heat is exchanged with the environment. For an ideal gas, the pressure - volume relationship follows P·V^? = constant, where ? is the heat capacity ratio. This condition describes rapid compressions and expansions. .
What are the energy levels for a particle in a one-dimensional infinite potential well of width L?
E? = n²h² / (2mL)
E? = n²h² / (8mL²)
E? = nh² / (8mL²)
E? = n²h / (8mL²)
Quantum confinement in an infinite well leads to discrete energy levels proportional to n². The derivation solves the Schrödinger equation with zero boundary conditions at the walls. This model illustrates basic quantum behavior of particles. .
Faraday's law of induction states the induced emf ? in a loop is given by which expression?
? = -d?/dt
? = -dQ/dt
? = d?/dt
? = ? / dt
Faraday's law relates changing magnetic flux ? through a circuit to the induced electromotive force ?. The negative sign indicates Lenz's law, showing the induced emf opposes the change in flux. This principle underpins transformers and electric generators. .
What is the Schwarzschild radius r? for a non-rotating mass M in general relativity?
r? = GM / c²
r? = GM / (2c²)
r? = 2GM / c²
r? = 2G M² / c²
The Schwarzschild radius defines the event horizon of a non-rotating black hole, derived from the Schwarzschild solution to Einstein's field equations. It is directly proportional to mass and inversely to the square of the speed of light. Objects compressed within this radius become black holes. .
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Study Outcomes

  1. Solve Challenging Problems -

    Apply advanced techniques to tackle hard physics questions and difficult physics questions, building confidence in approaching complex scenarios.

  2. Apply Fundamental Principles -

    Use core laws of mechanics, electromagnetism, and thermodynamics to break down and solve the toughest physics questions with clarity.

  3. Analyze Problem-Solving Strategies -

    Compare different methods for solving the hardest physics question examples, identifying the most efficient approach for each problem type.

  4. Evaluate Solution Accuracy -

    Critically assess each solution step to ensure precision and reduce errors when working through tough physics questions.

  5. Enhance Critical Thinking -

    Develop logical reasoning skills by confronting a variety of problem formats and applying systematic thought processes.

  6. Sharpen Conceptual Understanding -

    Reinforce key concepts and interconnections across topics to excel at future quizzes and real-world physics challenges.

Cheat Sheet

  1. Conservation Laws in Complex Collisions -

    Hard physics questions often revolve around simultaneous conservation of momentum and energy. For an elastic collision of two masses m₝ and m₂, set m₝v₝ + m₂v₂ = m₝v₝′ + m₂v₂′ and ½m₝v₝² + ½m₂v₂² = ½m₝v₝′² + ½m₂v₂′² (MIT OpenCourseWare). A mnemonic like "Momentum first, Energy next" helps keep the two equations distinct.

  2. Symmetry & Gauss's Law -

    In difficult physics questions on electrostatics, exploit symmetry to simplify ∮E·dA = Qₑₙc/ε₀ (HyperPhysics, Georgia State University). For spherical or cylindrical charge distributions, choose Gaussian surfaces that match the geometry to make the electric field constant across the surface. Remember "sphere: r², cylinder: r" to recall how field strength falls off with distance.

  3. Solving the Schrödinger Equation in a Box -

    Hardest physics questions in quantum mechanics often ask for wavefunctions in an infinite square well of width L. The solutions ψₙ(x)=√(2/L)·sin(nπx/L) yield quantized energy levels Eₙ = n²π²ħ²/(2mL²) (MIT OpenCourseWare). A quick mnemonic is "sine waves in a box," emphasizing the standing-wave boundary conditions.

  4. Lorentz Transformations & Time Dilation -

    Tough physics questions in relativity test your use of t′=γ(t - vx/c²) and x′=γ(x - vt) with γ=1/√(1 - v²/c²) (Einstein Papers Project). Apply time dilation Δt=γΔτ to predict muon lifetimes in Earth's atmosphere as a classic example. Think "slower clocks" to recall that moving clocks tick more slowly.

  5. Maxwell's Equations & Wave Propagation -

    Tough physics questions on electromagnetism combine ∇·E=ϝ/ε₀, ∇·B=0, ∇×E= - ∂B/∂t, and ∇×B=μ₀J+μ₀ε₀∂E/∂t to derive the wave equation ∇²E=μ₀ε₀∂²E/∂t² (Griffiths, University of Illinois). Recognize that electric and magnetic fields propagate as perpendicular oscillations in vacuum at speed c=1/√(μ₀ε₀). Use the phrase "divergence, divergence, curl, curl" to recall the order of Maxwell's equations.

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