index int64 0 999 | image stringlengths 4.4k 871k | question stringlengths 189 2.04k | answer stringclasses 4
values | category stringclasses 6
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values | reasoning_type stringclasses 20
values | embedding listlengths 4.1k 4.1k |
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600 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGWA1MDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A particle of mass $m$ and kinetic energy $E > 0$ approaches an abrupt potential drop $V_0$. When a free neutron enters a nucleus, it experiences a sudden drop in potential energy, from $V = 0$ outside to around $-12 \, \text{MeV}$ (million electron volts) inside. Suppose a neutron, emitted with kinetic energy $4 \, \t... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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601 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFOBGkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The Scattering Matrix. The theory of scattering generalizes in a pretty obvious way to arbitrary localized potentials. To the left (Region I), $V(x) = 0$, so $\psi(x) = Ae^{ikx} + Be^{-ikx}, \quad \text{where } k = \sqrt{\frac{2mE}{\hbar}}.$To the right (Region III), $V(x)$ is again zero, so$\psi(x) = Fe^{ikx} + Ge^{-i... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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603 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF0AtwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In a monovalent metal, one electron per atom is free to roam throughout the object. Evidently the energy of the composite structure must be less than the energy of the isolated atoms. This problem offers a crude but illuminating explanation for the cohesiveness of metals. When these atoms come together to form a metal,... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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604 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKwA0IDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The Boltzmann equation $$P(n) = \frac{1}{Z} e^{-eta E_n}, \quad Z = \sum_n e^{-eta E_n}, \quad eta = \frac{1}{k_B T},$$ gives the probability of finding a system in the state $n$ (with energy $E_n$), at temperature $T$ ($k_B$ is Boltzmann's constant). Note: The probability here refers to the random thermal distribut... | C | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
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u) \text{ betwee... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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606 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJBAosDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider three spin-1/2 particles arranged on the corners of a triangle and interacting via the Hamiltonian $$H = J (\mathbf{S}_1 \cdot \mathbf{S}_2 + \mathbf{S}_2 \cdot \mathbf{S}_3 + \mathbf{S}_3 \cdot \mathbf{S}_1),$$ where $J$ is a positive constant. This interaction favors opposite alignment of neighboring spins (... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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607 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADMA4wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An enemy spaceship is moving toward your starfighter with a speed, as measured in your frame, of $0.400c$. The missile is traveling at $0.700c$ relative to the enemy ship.You measure that the enemy ship is $8.00 \times 10^6$ km away from you when the missile is fired. How much time, measured in your frame, will it take... | A | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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608 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADeAXQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The symbol of the Denebian Empire is an ellipse whose major axis is 1.40 times longer than its minor axis.Its marking must be mistaken for that of a federation ship. How fast, relative to an observer, does an empire ship have to travel?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.... | A | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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609 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHOAYIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A magnetic field $\vec{B} = B \hat{k}$ is present. The electromagnetic field is $\vec{E} \perp \vec{B} = (0, \vec{B})$ in an inertial frame $S$, and then in another frame $S'$ moving at velocity $\vec{v}$ relative to $S$. What is the component of the magnetic field $\vec{B}'$, perpendicular to $\vec{v}$?Please directly... | A | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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610 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEmAVADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A fluorescent tube with length $L$ is fixed horizontally above a ticket window in a train station. At time $t = 0$ the tube lights up, changing color from white to bright yellow. After a duration $T$ the tube turns off, reverting to its white color. Events 1 and 2 correspond, respectively, to the right and left ends of... | A | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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612 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHCAdwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The work function of a material is examined using the apparatus shown schematically. The ammeter measures the photocurrent.The switch is returned to position $a$, and the wavelength of the light is reduced to 65.0 nm. The photocurrent increases. What is the minimum value of $R$ for which the photocurrent will cease?Ple... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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613 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFqAj4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A photon is incident on a stationary particle.The photon is annihilated while an electron–positron pair is produced.The target particle moves off in the original direction of the photon.The electron travels with respect to that direction.Owing to momentum conservation, the positron has the same speed as the electron. W... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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614 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGwAp4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An advanced civilization uses a fusion reactor to maintain a high temperature on a spherical blackbody whose radiation supplies energy for use on a spacecraft. The blackbody has radius $r = 1.23$ m. These capture all photons that have energy within 1.00\% of a central value $E_0$. The photocells are designed so that $E... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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615 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFUAU4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In a simple model for a radioactive nucleus, an alpha particle ($m = 6.64 imes 10^{-27}$ kg) is trapped by a square barrier that has height 30.0 MeV.The energy of the alpha particle is 10.0 MeV below the top of the barrier. What is the tunneling probability?Please directly answer the question and provide the correct O... | A | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
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616 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAICAzoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | $L = 1$ nm.If the left side is at a potential $V$ relative to the right side, then we can estimate the tunneling current as follows: The wires have diameter $d = 1$ mm, and copper has $n = 8.5 \times 10^{28}$ free electrons per m$^3$.Assume that the oxide gap provides a rectangular potential barrier of height 12 eV and... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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617 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFmAdADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a particle with mass $m$ and kinetic energy $E < U_0$ that is trapped in the well.The wave function must remain finite as $x \to \infty$.And it satisfy both the Schrödinger equation and this boundary condition at infinity. What must the form of the function $\psi(x)$ for $x > L$ be?Please directly answer the q... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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618 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADMAcIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | \({}^{232}_{92}\mathrm{U}\) (mass \(=232.037156\,\mathrm{u}\)) decays to \({}^{228}_{90}\mathrm{Th}\) (\(228.028741\,\mathrm{u}\)) with the emission of an \(\alpha\) particle. Calculate the disintegration energy.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A:... | C | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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619 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFUAZ4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A\(70\,\mathrm{kg}\) laboratory worker exposed to a \(40\,\mathrm{mCi}\) \({}^{60}_{27}\mathrm{Co}\) source, assuming the person's body has cross-sectional area \(1.5\,\mathrm{m^2}\) and is normally from the source for \(4.0\,\mathrm{h}\) per day. \({}^{60}_{27}\mathrm{Co}\) emits \(\gamma\) rays of energy \(1.33\,\mat... | C | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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620 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAOyAVwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | \(E\) and \(L\) for \(n=3\). Determine the energy.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -1.50eV B: -1.52eV C: -1.54eV D: -1.56eV | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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621 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEYASoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The rocket 2 is moving with respect to Earth. Calculate the speed of rocket 2.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.66c B: 0.77c C: 0.88c D: 0.99c | C | Modern Physics | Relativity | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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622 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADWAMQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A painting is hung on the side wall of a spaceship which is moving past the Earth at a speed of \(0.90c\). What are the dimensions as seen by an observer on the Earth?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.69m B: 0.67m C: 0.65m D: 0.62m | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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623 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFWAYADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Assume that the electrons's energy is low, \(\mathrm{KE}=100\,\mathrm{eV}\), so that they interact only with the surface layer of atoms. The smallest angle at which a diffraction maximum occurs is at \(24^\circ\). What is the separation \(d\) between the atoms on the surface?Please directly answer the question and pro... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.004058837890625,
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624 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADCAsgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An observer on Earth sees an alien vessel approach. The fictional starship *Enterprise* comes to the rescue, overtaking the aliens while moving directly toward Earth at a speed relative to Earth. What is the relative speed of one vessel as seen by the other?Please directly answer the question and provide the correct OP... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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625 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIgAfADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a monatomic solid with a weakly bound cubic lattice, with each atom connected to six neighbors, each bond having a binding energy of \(3.4 \times 10^{-3}\,\mathrm{eV}\). When this solid melts, its latent heat of fusion goes directly into breaking the bonds between the atoms. Estimate the latent heat of fusion ... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.043212890625,
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626 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADOAPQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A strip of silicon \(1.6\,\mathrm{cm}\) wide and \(1.0\,\mathrm{mm}\) thick is immersed in a magnetic field of strength \(1.5\,\mathrm{T}\) perpendicular to the strip.When a current of \(0.28\,\mathrm{mA}\) is run through the strip,there is a resulting Hall effect voltage of \(18\,\mathrm{mV}\) across the strip.The den... | D | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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627 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJ2AkIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The magnetic moment $\vec{\mu}$ of a spinning object with charge $Q$ and mass $M$ is proportional to its angular momentum $\vec{L}$ according to $\vec{\mu} = g(Q/2M)\vec{L}$. The dimensionless coefficient $g$ is known as the $g$-factor of the object. Consider a spherical shell uniform charge density $\sigma$. If the ch... | A | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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628 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAK6A+gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Our galaxy contains numerous molecular clouds, regions many light-years in extent in which the density is high enough and the temperature low enough for atoms to form into molecules. Most of the molecules are $H_2$, but a small fraction of the molecules are carbon monoxide ($CO$). Such a molecular cloud in the constell... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.00811767578125,
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629 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEyAkADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The circuit shown in figure, which is called a half-wave rectifier. The triangular symbol with the flat lower edge represents a diode, such that a forward bias drives the current downward. Use a typical value for the saturation current: $I_S = 5 \times 10^{-13}\ A$. Use a temperature of $300\ K$. What is the current $I... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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630 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHqA+wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A $p$-$n$ junction includes $p$-type silicon, with donor atom density $N_D$, adjacent to $n$-type silicon, with acceptor atom density $N_A$. Each depleted region has a constant charge density with magnitude equal to the corresponding donor atom density. Assume there is no net charge outside the depleted regions. Define... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02197265625,
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631 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKAbYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A colorless, odorless gas in a tank needs to be identified. The gas is $N_2$, $CO$, or $NO$. White light is passed through a sample to obtain an absorption spectrum. Among others, the following wavelengths present dark bands on the spectrum: $\lambda = 4.2680\ \mu m, 4.2753\ \mu m, 4.2826\ \mu m, 4.2972\ \mu m$, and $4... | A | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01708984375,
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632 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGiAdYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider the following hypothetical universe: The minuscule “flat” societies located at an angular separation of $\theta = 60^{\circ}$ on the surface of a two-dimensional spherical universe, as shown in figure. The radius of this universe was $R_0 = 500.0\ m$ upon its creation at time $t=0$, and it has been increasing ... | A | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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633 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJqAvwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Peggy is standing in a long, flat railroad car that has firecrackers tied to both ends. The car moves past Ryan, with velocity $v = 0.8c$. Flashes from the exploding firecrackers reach him simultaneously $1.0\;\mu s$ after the instant that Peggy passes him, and he later finds burn marks on the track $300\;m$ to either ... | B | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.020751953125,
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634 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIAAhIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An electron is fired between two electrodes that are $5.0\;mm$ apart. A potential difference $\Delta V$ between the electrodes establishes an electric field between them. A $3.0\;cm$-wide, $1.0\;mT$ magnetic field overlaps the electrodes and is perpendicular to the electric field. When $\Delta V = 0\;V$, the electron i... | B | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Spatial Relation Reasoning'] | [
0.045654296875,
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635 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAImAxgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An alpha particle is shot with a speed of $2.0 \times 10^7\;m/s$ directly toward the nucleus of a gold atom. What is the distance of closest approach to the nucleus?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $2.2 \times 10^{-14}\;m$ B: $2.7 \times 10^{-1... | B | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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636 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGmAp4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The cesium isotope $^{137}$Cs, with $Z=55$, is radioactive and decays by beta decay. A beta particle is observed in the laboratory with a kinetic energy of $300\;keV$. With what kinetic energy was the beta particle ejected from the $12.4\;fm$-diameter nucleus?Please directly answer the question and provide the correct ... | B | Modern Physics | Nuclear Physics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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637 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJcAoYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Fluorescence is the absorption of light at one wavelength followed by emission at a longer wavelength. Suppose a hydrogen atom in its ground state absorbs an ultraviolet photon with a wavelength of $95.10\;nm$. Immediately after the absorption, the atom undergoes a quantum jump with $\Delta n = 3$. What is the waveleng... | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01202392578125,
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638 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJ2AowDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A particle is described by the wave function $\psi(x)$ as shown in figure, where $L = 1\;nm$. If $10^6$ particles are detected, how many are expected to be found in the region $x \geq 1\;nm$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 125,000 B: 135,000 C... | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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639 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFAAsgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Electrons pass through the parallel electrodes shown in figure with a speed of $5.0 \times 10^6$ $m/s$. Assume that the magnetic field is confined to the region between the electrodes. What magnetic field strength will allow the electrons to pass through without being deflected?Please directly answer the question and p... | B | Modern Physics | Magnetism | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0439453125,
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640 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEsAr4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The two parallel electrodes in figure. A proton enters the plates from one end, an equal distance from both electrodes. A potential difference $\Delta$ across the electrodes deflects the proton so that it strikes the outer end of the lower electrode. Assume that both the electric and magnetic fields are confined to the... | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.043701171875,
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0.0098876953125,
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641 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGSAnQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An alpha particle approaches a nucleus with a speed of $1.50 \times 10^7$ $m/s$. As figure shows, the alpha particle is scattered at the slower speed of $1.49 \times 10^7$ $m/s$. With what speed does the $^{197}Au$ nucleus recoil?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B... | B | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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642 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF4AsgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure. How many photoelectrons are ejected per second in the experiment represented by the graph of figure?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $6.2 \times 10^{13}$ B: $6.25 \times 10^{13}$ C: $6.3 \times 10^{13}$ D: $6.35 \times 10^{1... | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.024169921875,
0.0155029296875,
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0.006896972656... |
643 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKAwIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An experiment was performed in which neutrons were shot through two slits spaced $0.10$ $nm$ apart and detected $3.5$ $m$ behind the slits. Figure shows the detector output. Notice the $100$ $\mu m$ scale on the figure. To one significant figure, what was the speed of the neutrons?Please directly answer the question an... | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0211181640625,
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0,
0.0011444091796875,
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644 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHkAjADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The energy levels of the fictitious element $X$ are shown in figure. What is the ionization energy of element $X$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -6.5 eV B: 6.5 eV C: -3 eV D: 3 eV | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning'] | [
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0.005523681640625,
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645 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHSAx4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the probability density for an electron that has passed through an experimental apparatus. If $1.0 \times 10^6$ electrons are used, what is the expected number that will land in a $0.010$-$mm$-wide strip at $2.000$ $mm$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A... | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.04248046875,
0.0027923583984375,
0.00823974609375,
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0.0286865234375,
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0.03125,
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646 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEwAfYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the spectrum of light emitted by a firefly. Determine the temperature of a blackbody that would emit radiation peaked at the same frequency.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 2\,500 \text{ K} \) B: \( 1\,700 \text{ K} \) C: \( 5\,... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.017822265625,
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0.02490234375,
0.00665283203125,
-0.02001953125,
0.020263671875,
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0.00799560546875,
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0.0252685546875,
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647 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGaAfIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of an electron. What is the probability that the electron is located between $x = -1.0$ $nm$ and $x = 1.0$ $nm$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.40 B: 0.80 C: 0.90 D: 0.60 | B | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0235595703125,
0.00531005859375,
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0.00012111663818359375,
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0.0115966796875,
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0.017822265625,
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0.01531982421875,
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648 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGgAhIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of a neutron. What is the probability that the neutron is located between $x = -1.0$ $mm$ and $x = 1.0$ $mm$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.75 B: 0.45 C: 0.25 D: 0.1 | C | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0234375,
0.01116943359375,
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0.0106201171875,
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649 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADOAi4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a pulse train. $\Delta t$ is the duration of each pulse. What is the maximum pulse-transmission rate (pulses per second) through an electronics system with a $200$ $kHz$ bandwidth?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $2.0 \times 10^5$ ... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0028839111328125,
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0.006195068359375,
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0.0250244140625,
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0.010009765625,
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0.024169921875,
0.00390625,
0.026611328125,
-0.025390625,
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-0.02... |
650 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGAAqQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An observer moving at a speed of \( 0.995c \) relative to a rod as shown in fig. What is the proper length of the rod?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 12.1 \text{ m} \) B: \( 17.4 \text{ m} \) C: \( 11.5 \text{ m} \) D: \( 13.3 \text{ m} \) | B | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.042236328125,
0.009765625,
-0.004180908203125,
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0.00872802734375,
0.021240234375,
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0.00830078125,
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0.04150390625,
0,
0.0081787109375,
0.0191650390625,
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0.03... |
651 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFEAiADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of a particle, the wave function is zero outside this region. Calculate the probability of finding the particle in the interval $0$ $nm$ $\le x \le 0.25$ $nm$.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.020 B: 0.024 C: 0.0... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.02880859375,
0.01031494140625,
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0.003265380859375,
0.006866455078125,
0.0294189453125,
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0.008056640625,
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0.015869140625,
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0.0115966796875,
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-0.02... |
652 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGOAfADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of a particle. The wave function is zero outside this region. Calculate the probability of finding the particle in the interval $-2.0$ $mm$ $\le x \le 2.0$ $mm$.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.08 B: 0.1 C: 0.12... | C | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.03076171875,
0.018310546875,
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0.0023345947265625,
0.0166015625,
0.0032806396484375,
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0.026123046875,
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-0.02258300781... |
653 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEOAeQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the probability density for finding a particle at position $x$. At what value of $x$ are you most likely to find the particle?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1 cm B: -1 cm C: 0 cm D: 2 cm | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning'] | [
0.0274658203125,
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0.01239013671875,
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0.00136566162109375,
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0,
0.008056640625,
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0.005218505859375,
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... |
654 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFUAjQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A small speck of dust with mass $1.0 \times 10^{-13}$ $g$ has fallen into the hole shown in figure and appears to be at rest. What is the deepest hole of this width from which it would have a good chance to escape?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: ... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.0263671875,
0.000690460205078125,
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0.01275634765625,
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0.0234375,
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0.016357421875,
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0.004913330078125,
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0.0267333984375,
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0.0164794921875,
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655 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHyAl4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows dust particles ($m = 1.0 \times 10^{-15}$ $kg$) in a vacuum chamber. The dust particles are released from rest above a hole, fall through the hole (there's just barely room for the particles to go through), and land on a detector at distance $d$ below. Quantum effects would be noticeable if the detection-c... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0220947265625,
0.00170135498046875,
-0.03076171875,
-0.00640869140625,
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0.01904296875,
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0.025634765625,
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0.00946044921875,
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0.03955078125,
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0.0224609375,
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656 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE0Aj4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of an electron in a rigid box. The electron energy is $6.0$ $eV$. How long is the box?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.5 nm B: 0.75 nm C: 1.0 nm D: 2.0 nm | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.024658203125,
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0.01177978515625,
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0.00567626953125,
-0.035400390625,
0.01019287109375,
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0.0341796875,
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657 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFEAkQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of an electron in a rigid box. The electron energy is $12.0$ $eV$. What is the energy of the electron's ground state?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.8 eV B: 1.1 eV C: 1.3 eV D: 1.7 eV | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0260009765625,
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0.0238037109375,
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0.000522613525390625,
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0.00830078125,
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0.02392578125,
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0.033203125,
0.0022125244140625,
... |
658 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADIAgwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. Figure is a one-dimensional model of a crystal lattice. The ions have mass $m$, charge $e$. Suppose this crystal consists of aluminum ions with an equilibrium ... | C | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01397705078125,
0.00616455078125,
0.007080078125,
-0.00244140625,
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0.03466796875,
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-0.0166015625,
0.00799560546875,
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0.0174560546875,
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0.0181884765625,
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0.020751953125,
-... |
659 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAL2AtoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a few energy levels of the mercury atom. What minimum speed must an electron have to excite the $492$-$nm$-wavelength blue emission line in the $Hg$ spectrum?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $1.40 \times 10^6$ $m/s$ B: $1.60 \times... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0172119140625,
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0.046142578125,
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0.0021514892578125,
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0.02490234375,
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0.050048828125,
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0.0133056640625,
0.0120849609375,
0.01153564453125,
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660 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF+AZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Alpha decay occurs when an alpha particle tunnels through the Coulomb barrier. Figure shows a simple one-dimensional model of the potential-energy well of an alpha particle in a nucleus with $A \approx 235$. The $15$ $fm$ width of this one-dimensional potential-energy well is the diameter of the nucleus. Further, to ke... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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661 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMOAn8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A valve has a cross-sectional area of $11 \, \text{cm}^2$ with a pressure of $735 \, \text{kPa}$ inside and $99 \, \text{kPa}$ outside. How large a force is needed to open the valve?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 836 N B: 70 N C: 634 N D: 700... | D | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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662 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE6AUADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A piston/cylinder with a cross-sectional area of $0.01 \, \text{m}^2$ has a piston mass of $100 \, \text{kg}$ resting on the stops, as shown in figure. With an outside atmospheric pressure of $100 \, \text{kPa}$, what should the water pressure be to lift the piston?Please directly answer the question and provide the co... | D | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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663 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAM/A4QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A steel cylinder has a cross-sectional area. At the bottom, is liquid water, on top of which is a layer of gasoline. This is shown in figure. The gasoline surface is exposed to atmospheric air at $101 \, \text{kPa}$. What is the highest pressure in the water?Please directly answer the question and provide the correct O... | D | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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664 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFuAvEDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A steel tank of cross-sectional area $3 \, \text{m}^2$ and height $16 \, \text{m}$ weighs $10\,000 \, \text{kg}$ and is open at the top, as shown in figure. We want to float it in the ocean so that it is positioned $10 \, \text{m}$ straight down by pouring concrete into its bottom. How much concrete should we use?Pleas... | D | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0189208984375,
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665 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHsAwYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Liquid water with density $\rho$ is filled on top of a thin piston in a cylinder with cross-sectional area $A$ and total height $H$, as shown in figure. Air is let in under the piston so that it pushes up, causing the water to spill over the edge. Derive the formula for the air pressure as a function of piston elevatio... | D | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00921630859375,
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666 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEuAWADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a frustum of a cone. Calculate the area of the curved surface.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \[ \3pi(r_1 + r_2)[h^{2} + (r_2 - r_1)^{2}]^{1/2} \] B: \[ \2pi(r_1 + r_2)[h^{2} + (r_2 - r_1)^{2}]^{1/2} \] C: \[ \pi(r_1 + r_2)[h^{2} ... | C | Mechanics | Statics | ['Spatial Relation Reasoning'] | [
0.02490234375,
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667 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEMAbADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A highway curve forms a section of a circle. A car goes around the curve as shown in the helicopter view of figure. Its dashboard compass shows that the car is initially heading due east. After it travels \( d = 840 \text{ m} \), it is heading \( \theta = 35.0^\circ \) south of east. Find the radius of curvature of its... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0172119140625,
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668 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC2Az4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | One drop of oil falls straight down onto the road from the engine of a moving car every \( 5 \text{ s} \). Figure shows the pattern of the drops left behind on the pavement. What is the average speed of the car over this section of its motion?Please directly answer the question and provide the correct OPTION LETTER ONL... | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Spatial Relation Reasoning'] | [
0.026123046875,
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669 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAYIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The position versus time for a certain particle moving along the \( x \) axis is shown in figure. Find the average velocity in the time intervals 0 to \( 8 \text{ s} \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \[ 6 \text{ m/s} \] B: \[ 10 \text{ m/s} \... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.044189453125,
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670 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE2AWwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A particle starts from rest and accelerates as shown in figure. Determine the distance traveled in the first \( 20.0 \text{ s} \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 178m B: 251m C: 263m D: 432m | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.027099609375,
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671 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEyAawDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A student drives a moped along a straight road as described by the velocity--time graph in figure. What is the moped's final position at \( t = 9.00 \text{ s} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 16m B: 14m C: 28m D: 32m | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.032470703125,
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672 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFKAfIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An object is at \( x = 0 \) at \( t = 0 \) and moves along the \( x \) axis according to the velocity--time graph in figure. Through what total distance has the object moved between \( t = 0 \) and \( t = 18.0 \text{ s} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D.... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.015869140625,
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0.01068115234375,
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673 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE+AToDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two objects, A and B, are connected by hinges to a rigid rod. The objects slide along perpendicular guide rails as shown in figure. Assume object A slides to the left with a constant speed. Find the velocity \( v_\text{B} \) of object B as a function of the angle \( \theta \).Please directly answer the question and pro... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0291748046875,
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674 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGyAgADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A blue car of length \( 4.52 \text{ m} \) is moving north on a roadway that intersects another perpendicular roadway as shown in figure. The blue car has a constant acceleration of magnitude \( 2.10 \text{ m/s}^2 \) directed south. The time interval required for the nose of the blue car to move from the near (south) ed... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00994873046875,
0.017822265625,
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675 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG2AZQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two thin rods are fastened to the inside of a circular ring as shown in figure. One rod is vertical, and the other makes an angle with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide without friction along the rods. Find an expression for the time interval required f... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0201416015625,
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676 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFOAhwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A surveyor measures the distance across a straight river by the following method as shown in figure. Starting directly across from a tree on the opposite bank, she walks \( d = 100 \text{ m} \) along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is \(... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning'] | [
0.01470947265625,
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677 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE4AVQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A force \( \vec{F}_1 \) of magnitude 6.00 units acts on an object at the origin in a direction \( \theta = 30.0^\circ \) above the positive \( x \) axis as shown in figure. A second force \( \vec{F}_2 \) of magnitude 5.00 units acts on the object. Find the magnitude the resultant force \( \vec{F}_1 + \vec{F}_2 \).Pleas... | C | Mechanics | Dynamics | ['Spatial Relation Reasoning'] | [
0.037109375,
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678 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGWAi4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A snow-covered ski slope makes an angle with the horizontal. When a ski jumper plummets onto the hill, a parcel of splashed snow is thrown up to a maximum displacement of \( 1.50 \text{ m} \) in the uphill direction as shown in figure. Find the components of its maximum displacement perpendicular to the surface.Please ... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.024169921875,
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0.00126647... |
679 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFMAtIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the \( x \) axis and at a fixed height of \( 7.60 \times 10^3 \text{ m} \). At time \( t = 0 \), the airplane is directly above you so that the vector leading from you to it is \( \vec{P}_0... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Predictive Reasoning'] | [
0.0201416015625,
0.0084228515625,
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680 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKAbYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The biggest stuffed animal in the world is a snake \( 420 \text{ m} \) long, constructed by Norwegian children. Suppose the snake is laid out in a park as shown in figure, forming two straight sides of a \( 105^\circ \) angle, with one side \( 240 \text{ m} \) long. Olaf and Inge run a race they invent. Inge runs direc... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0137939453125,
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681 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE8AZIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure a spider is resting after starting to spin its web. The gravitational force on the spider makes it exert a downward force of \( 0.150 \text{ N} \) on the junction of the three strands of silk. The junction is supported by different tension forces in the two strands above it so that the resultant force on the ... | C | Mechanics | Statics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.026123046875,
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682 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAH4AswDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A rectangular parallelepiped as shown in figure. Notice that \( \vec{R}_1 \), \( c\hat{k} \), and \( \vec{R}_2 \) make a right triangle. Obtain a vector expression for the body diagonal vector \( \vec{R}_2 \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \(... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.037109375,
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683 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGsAu4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A firefighter, a distance from a burning building, directs a stream of water from a fire hose as shown in figure. If the initial speed of the stream is \( v_i \), at what height \( h \) does the water strike the building?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. O... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.023681640625,
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... |
684 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGaAbIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A landscape architect is planning an artificial waterfall in a city park. Water flowing at \( 1.70 \text{ m/s} \) will leave the end of a horizontal channel at the top of a vertical wall \( h = 2.35 \text{ m} \) high, and from there it will fall into a pool as shown in figure. To sell her plan to the city council, the ... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01080322265625,
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0.0078125,
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685 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG0A6YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A playground is on the flat roof of a city school, \( 6.00 \text{ m} \) above the street below as shown in figure. The vertical wall of the building is \( h = 7.00 \text{ m} \) high, forming a 1-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an ... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0244140625,
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686 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJGAXoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of \( v_i = 18.0 \text{ m/s} \). The cliff is \( h = 50.0 \text{ m} \) above a body of water as shown in figure. With what speed does the stone land?Please directly answer the question and provide the correct OPTION LETTE... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0211181640625,
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0.01007080078125,
0.00408935546875,
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0.010009765625,
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0.04931640625,
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0.0361328125,
0.0159912109375,
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687 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFUA+YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The 20-g centrifuge at NASA's Ames Research Center in Mountain View, California, is a horizontal, cylindrical tube \( 58.0 \text{ ft} \) long and is represented in figure. Assume an astronaut in training sits in a seat at one end. Determine the rotation rate, in revolutions per second, required to give the astronaut a ... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.035888671875,
0.01422119140625,
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-0.0126953125,
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0.0162353515625,
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0.005706787109375,
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688 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFQAWoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure represents the total acceleration of a particle moving clockwise in a circle at a certain instant of time. For that instant, find its tangential acceleration.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 2.50 \text{ m/s}^2 \) B: \( 10.00 \text{ m/... | C | Mechanics | Rotational Motion | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.03125,
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0.024658203125,
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689 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG8A5gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A basketball player is standing on the floor as in figure. He shoots the ball at a angle with the horizontal from a height. At what speed must the player throw the basketball so that the ball goes through the hoop without striking the backboard?Please directly answer the question and provide the correct OPTION LETTER O... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.029541015625,
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0.038818359375,
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0.01068115234375,
0.0242919921875,
0.00909423828125,
-0.0299... |
690 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKOAuwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Towns A and B in figure are apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for \( 2.50 \text{ h} \) in the directions shown. Car 1 has a speed of \( 90.0 \text{ km/h} \). If the cars arrive simultaneously at the lake, wh... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0299072265625,
0.007293701171875,
-0.006378173828125,
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0.0089111328125,
0.0242919921875,
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0.04150390625,
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0.004730224609375,
0.0220947265625,
0.0162353515625,
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691 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEGAlQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As some molten metal splashes, one droplet flies off to the east, and another droplet flies off to the west as shown in figure. In terms of \( v_i \) and \( \theta_i \), find the distance between the two droplets as a function of time.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.,... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Predictive Reasoning'] | [
0.01483154296875,
0.00921630859375,
-0.0439453125,
0.001953125,
-0.007110595703125,
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0.0159912109375,
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0.01092529296875,
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0.008544921875,
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... |
692 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIcAXQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A pendulum with a cord of length \( r = 1.00 \text{ m} \) swings in a vertical plane as shown in figure. When the pendulum is in the two horizontal positions \( \theta = 90.0^{\circ} \) and \( \theta = 270^{\circ} \), its speed is \( 5.00 \text{ m/s} \). Calculate the magnitude of the total acceleration at these positi... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0218505859375,
0.004364013671875,
0.0028076171875,
-0.00762939453125,
0.0034332275390625,
0.0179443359375,
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0.0213623046875,
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0.022216796875,
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0.0164794921875,
0.0498046875,
0.0181884765625,
-0.010498046875,... |
693 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF0A3YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher as shown in figure, but that the ball's speed after the bounce is one-half of what it was before the bounce. Determine the ratio of the time interval for the one-bounce thr... | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Spatial Relation Reasoning'] | [
0.027587890625,
-0.021484375,
-0.00347900390625,
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0.006988525390625,
0.03466796875,
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0.00093841552734375,
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0.0281982421875,
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0.030029296875,
-0.02587890625,
0.0023956298828125,
0.0233154296875,
0.02880859375,
-0.0260009765625... |
694 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADEAnIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The spring constant is \(20\,\mathrm{N/m}\) and the surface is frictionless. What is the cube's launch speed, as it leaves the spring?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2.5m/s B: 3.1m/s C: 2.8m/s D: 3.4m/s | C | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0283203125,
-0.0028228759765625,
-0.0260009765625,
-0.003692626953125,
0.009033203125,
0.004638671875,
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0.01361083984375,
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0.0169677734375,
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0.0244140625,
-0.0194091796875,
0.0179443359375,
0.030517578125,
0.0009765625,
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... |
695 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEUAuwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The other end of the spring is anchored to a wall. Initially the box is at rest at the spring's equilibrium position. A rope with a constant tension of \(100\,\mathrm{N}\) then pulls the box away from the wall. The coefficient of friction between the box and the floor is \(0.30\). How much power is being supplied by t... | C | Mechanics | Work and Energy | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.018310546875,
-0.0003032684326171875,
-0.006622314453125,
-0.004638671875,
-0.00102996826171875,
0.00168609619140625,
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-0.02783203125,
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0.031005859375,
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0.002471923828125,
0.00933837890625,
0... |
696 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEaA0wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two balls are connected by a massless \(50\,\mathrm{cm}\)-long rod. They rotate about the center of mass at \(40\,\mathrm{rpm}\). What is the speed of the \(2.0\,\mathrm{kg}\) ball?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.76m/s B: 1.92m/s C: 1.68m/s... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.011962890625,
0.00689697265625,
-0.0147705078125,
-0.0029296875,
0.000896453857421875,
0.028076171875,
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-0.0245361328125,
-0.0302734375,
0.0113525390625,
-0.02587890625,
0.037841796875,
-0.01007080078125,
0.001312255859375,
0.0322265625,
0.015380859375,
-0.02160644531... |
697 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFOAx4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Find the center of mass of a thin, uniform rod of length \(L\) and mass \(M\). Use this result. A \(1.60\,\mathrm{m}\)-long rod rotates about its center of mass with an angular acceleration of \(6.0\,\mathrm{rad/s^2}\). Find the tangential acceleration of the rod.Please directly answer the question and provide the corr... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0400390625,
-0.00677490234375,
-0.0269775390625,
-0.00238037109375,
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0.0155029296875,
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... |
698 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGeArQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The three masses, held together by lightweight plastic rods, rotate in the plane of the page about an axle passing through the right-angle corner. At what angular velocity does the widget have \(100\,\mathrm{mJ}\) of rotational energy?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.,... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.024658203125,
0.0166015625,
-0.02001953125,
0.01202392578125,
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0.0185546875,
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0.0146484375,
0.00860595703125,
0.02197265625,
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0.037841796875,
0.0184326171875,
-0.01043701171875... |
699 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIoAqwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A rod is hinged at one end and connected to a wall. It is held out horizontally, then released. What is the speed of the tip of the rod as it hits the wall?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 5.2m/s B: 5.6m/s C: 5.4m/s D: 5.8m/s | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.032958984375,
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0.016845703125,
0.003692626953125,
0.01434326171875,
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0.006103515625,
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0.01129150390625,
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0.0234375,
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0.00946044921875,
0.0185546875,
0.02734375,
-0.0162353515625,
... |
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