id string | media images list | messages string | answer string | question_type string | catagory string |
|---|---|---|---|---|---|
rbench_v_full_00000 | [{"role": "user", "question": "As shown in the diagram, a worker applies a force of 150 N to move object A at a constant speed along a horizontal surface for 12 meters over the course of 1 minute; during this motion, object A is subjected to a 240 N horizontal pulling force directed to the left. Find: (1) the power of ... | （1）60W（2）80% | open | Physics | |
rbench_v_full_00001 | [{"role": "user", "question": "The width of the brick clamp is 25 cm, and the curved rods AGB and GCED are hinged at point G, with dimensions as shown in the figure. Suppose the weight of the brick is Q=120N and the force P that lifts the brick acts along the centerline of the brick clamp. The coefficient of friction b... | 11cm | open | Physics | |
rbench_v_full_00002 | [{"role": "user", "question": "As shown in the figure, a semicylindrical body with radius $R$ undergoes uniformly accelerated motion with acceleration $a$ in the horizontal direction perpendicular to its axis. A vertical rod is placed on the cylindrical surface, constrained to move only in the vertical direction. When ... | $\frac{v}{\cos(\theta)}$ | open | Physics | |
rbench_v_full_00003 | [{"role": "user", "question": "A wedge with an inclination angle of $\\theta$ is placed on a horizontal tabletop, as shown in the figure. An object of mass $m$ is placed on the inclined surface of the wedge, and the wedge itself also has a mass of $m$. The coefficient of friction between the object and the wedge, as we... | $\tan(\theta)\geq \frac{12+\sqrt{69}}{5}$ or $\frac{1}{5} \leq \tan(\theta)\leq \frac{12-\sqrt{69}}{5}$ | open | Physics | |
rbench_v_full_00004 | [{"role": "user", "question": "A bowl is placed on a horizontal table, and the inner surface of the bowl is shaped like a hemisphere with a radius of R. In a vertical plane, as shown in the figure, there is a thin, straight rod AC (mass assumed negligible). One end of the rod, point A, is in contact with the inner wall... | 1/SQRT(5) | open | Physics | |
rbench_v_full_00005 | [{"role": "user", "question": "As shown in the figure, two books are interleaved page by page, with a coefficient of static friction of 0.3 between the sheets of paper. Each page has a mass of m = 5 grams, and each book contains 200 pages. Book A is fixed in place. A horizontal force F is applied to the right to pull o... | 1.17e3(N) | open | Physics | |
rbench_v_full_00006 | [{"role": "user", "question": "Four small balls A, B, C, and D, each with the same mass, are connected by smooth hinges using massless rigid rods of equal length to form a rhombus. Initially, the rhombus is shaped as a square and moves with a constant velocity v along its diagonal AC on a smooth horizontal surface. As ... | v | mcq | Physics | |
rbench_v_full_00007 | [{"role": "user", "question": "As shown in the figure, four particles each of mass $m$ are connected by inextensible, massless strings of equal length to form a rhombus $ABCD$, and the system is initially at rest on a smooth horizontal table. Suppose particle $A$ is given an impulsive force of very short duration along... | $\frac{4mV}{1+2\sin^2 \alpha}$ | open | Physics | |
rbench_v_full_00008 | [{"role": "user", "question": "As shown in the figure, two straight lines AB and CD lie in a plane and intersect at an angle $\\varphi$. Line AB is moving within the plane at a speed $v_1$ in the direction perpendicular to itself, while line CD is also moving within the plane at a speed $v_2$ in the direction perpendic... | $\frac{1}{\sin(\varphi)} \sqrt{v_1^2+v_2^2-2v_1 v_2 \cos\varphi}$ | open | Physics | |
rbench_v_full_00009 | [{"role": "user", "question": "A heavy cart moves with constant velocity $v$ on a horizontal surface. Inside the cart, there is a fixed, smooth semicylindrical surface of radius $R$, and a block of mass $m$ is initially placed at the top of the semicylinder, remaining momentarily at rest relative to the cart, as shown ... | $\frac{2mv\sqrt{6gR}}{9}$ | open | Physics | |
rbench_v_full_00010 | [{"role": "user", "question": "As shown in the figure, two light rigid rods CD and EF each have a length of $2l$, with point masses of mass $m$ attached to their endpoints. Inextensible strings CE and DF each have a length of $l$. The midpoint B of rod CD is suspended from a ceiling point A using a string AB. If string... | 8mg/3 | open | Physics | |
rbench_v_full_00011 | [{"role": "user", "question": "A truss consists of 11 members of equal length, with joints labeled A, B, ..., G, as shown in the diagram. Point A is rigidly fixed, and point G is supported only in the vertical direction. The weights of the members are negligible. A load with weight W is suspended at point E. Each membe... | $\frac{2\sqrt{3}W}{9}$ | open | Physics | |
rbench_v_full_00012 | [{"role": "user", "question": "As shown in the figure, n (n > 3) identical homogeneous cylinders, each of mass m and radius R, are placed in sequence on an inclined plane with an angle of 30°, and are blocked by a vertically hinged stopper. The length of the stopper is l, and the coefficient of friction between each cy... | $\frac{R}{4l}((5+\sqrt{3})n+3(1+\sqrt{3}))mg$ | open | Physics | |
rbench_v_full_00013 | [{"role": "user", "question": "A uniform straight rod is placed obliquely inside a hemispherical bowl in the vertical plane that passes through the center of the sphere. The two ends of the rod subtend a central angle of $2\\alpha$ at the center of the sphere. The coefficient of static friction between the rod and the ... | $\arctan(\frac{\tan(\alpha+\beta)-\tan(\alpha-\beta)}{2})$ | open | Physics | |
rbench_v_full_00014 | [{"role": "user", "question": "Two small rings A and B are placed on a horizontal rod MN. A massless, inextensible string of length $l$ has its two ends attached to rings A and B, with a mass $M$ suspended from the midpoint of the string, as shown in the figure. The coefficient of static friction between each ring and ... | $\frac{\mu l(1+\frac{2m}{M})}{\sqrt{1+\mu^2(1+\frac{2m}{M})^2}}$ | open | Physics | |
rbench_v_full_00015 | [{"role": "user", "question": "Two identical cylindrical rods, each of radius $R$ and mass $m$, are placed side by side in contact on a horizontal tabletop. An open, rigid, lidless, and endless box—consisting only of the top, left, and right panels—is inverted over the two cylinders. The side panels are parallel to the... | $\frac{3(3-\sqrt{2})}{7}$ | open | Physics | |
rbench_v_full_00016 | [{"role": "user", "question": "As shown in the figure, two large circular rings with centers at A and B and equal radii R = 5.0 cm lie in the same plane. Ring B is fixed, while ring A moves toward ring B along the line connecting points A and B. A small ring M is simultaneously linked to and constrained by both large r... | $10cm\cdot s^{-2}$ | open | Physics | |
rbench_v_full_00017 | [{"role": "user", "question": "In the diagram, the mass of the cart M, the mass of the hanging object m, and the angle of inclination \\(\\alpha\\) of the fixed slope are all known; the rope is inextensible, and the masses of the rope and pulley, as well as all friction in the system, can be neglected—determine the acc... | $\frac{4m-M\sin\alpha}{M+16m}g$ | open | Physics | |
rbench_v_full_00018 | [{"role": "user", "question": "The mechanism shown in the figure moves in a vertical plane, with the dimensions of each component indicated. At a certain moment, when rod OA is in the horizontal position and rotating about point O with an angular velocity of $\\Omega = 2\\, \\text{rad/s}$, determine the magnitude of th... | 16cm/s | open | Physics | |
rbench_v_full_00019 | [{"role": "user", "question": "As shown in the figure, crank OA rotates about a fixed axis at point O with an angular velocity of $\\omega = 4\\ \\mathrm{s^{-1}}$; the angle between OA and DC is 60°, and BD is perpendicular to OA. Given that OA = AB = AD = a = 30 cm and BC = b = 40 cm, and that sliders C and D move alo... | 67.0cm/s | open | Physics | |
rbench_v_full_00020 | [{"role": "user", "question": "Three small balls A, B, and C, each of mass m, are connected by two inextensible strings of equal length l and initially placed on a smooth horizontal surface, with their positions arranged as shown in the figure, where the strings are fully stretched and the angle $\\theta = \\frac{\\pi}... | 79F/225 | open | Physics | |
rbench_v_full_00021 | [{"role": "user", "question": "Rods BC, BD, CD, CE, CG, and DG are connected by hinges and are positioned along the edges and diagonals of a cube, as shown in the diagram. Hinges at points B, E, and G are fixed, and the rods are assumed to be massless. A force Q acts at joint D along the diagonal direction ED, and a fo... | -P-SQRT(2)*Q | open | Physics | |
rbench_v_full_00022 | [{"role": "user", "question": "As shown in the figure, a truss structure is subjected to a set of loads; assuming all members are massless and connected by smooth hinges, determine the internal force in member DE.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | -SQRT(3) * Q | open | Physics | |
rbench_v_full_00023 | [{"role": "user", "question": "Two identical uniform rods AB and BC, each of mass m, are connected at point B via a smooth hinge; end A is attached to a fixed point through a smooth hinge as well. The rods are constrained to move within a vertical plane, and points A and C are initially aligned horizontally, with the a... | 0.75 | numeric | Physics | |
rbench_v_full_00024 | [{"role": "user", "question": "A homogeneous semicircular disk with finite thickness, radius $R$, and mass $M$ is placed on a horizontal ground such that the plane of the disk is perpendicular to the ground. The coefficient of friction between the disk and the ground is $\\mu$. An impulse of magnitude $K$, directed ver... | 2.23M * \sqrt{gR} | open | Physics | |
rbench_v_full_00025 | [{"role": "user", "question": "A rigid, square, massless frame contains four rotating disks, as shown in the figure. Each disk has mass $m$, moment of inertia $I$, and angular velocity $\\omega_0$. When one corner of the frame is mounted on a pivot and the frame is free to rotate about the support while remaining horiz... | $\frac{mgD}{I\omega_0}$ | open | Physics | |
rbench_v_full_00026 | [{"role": "user", "question": "As shown in the figure, a rod of length $l$ leans against a short wall of height $d$. The rod has mass $m$, and the coefficient of friction between the rod and the ground is sufficiently large to ensure no slipping at the contact point $A$. The coefficient of friction between the rod and ... | $$mg \cdot \frac{al\sqrt{d^2 - \mu^2 a^2}}{2d(d^2+a^2)}$$ | open | Physics | |
rbench_v_full_00027 | [{"role": "user", "question": "Most of the door locks in our home are of the latch type, which automatically locks the door when it is gently closed, providing convenience and ease of use. However, over time, a problem may occur where the latch fails to retract automatically when closing the door, a phenomenon known as... | $2 \arctan \mu$ | open | Physics | |
rbench_v_full_00028 | [{"role": "user", "question": "As shown in the figure, two rigid, lightweight rods AB and BC are firmly connected at point B, forming a rigid system. The extension of rod AB and rod BC form an acute angle $\\alpha$, with rod BC of length $l$ and rod AB of length $l\\cos\\alpha$. A small ball of mass $m$ is rigidly atta... | $\arctan{\frac{3}{1+\pi}}$ | open | Physics | |
rbench_v_full_00029 | [{"role": "user", "question": "A smooth, long cylindrical tube with radius $r$ is inclined at an angle $\\alpha$ to the horizontal, as shown in the figure. A small object is projected upward from point A along the inner surface of the tube, with its initial velocity making an angle $\\varphi$ with the straight line AB.... | $\dfrac{\sqrt{gr\cos\alpha}}{\sin\varphi}$ | open | Physics | |
rbench_v_full_00030 | [{"role": "user", "question": "Two smooth, thin rods form a V-shaped frame with an angle $\\alpha$ between them. A massless string of length $l$ is looped over the apex of the frame, with both ends of the string attached to the same heavy ball, as shown in the figure. The frame is placed vertically. Determine the perio... | $\pi\sqrt{\frac{2l}{g\sin\alpha}}$ | open | Physics | |
rbench_v_full_00031 | [{"role": "user", "question": "In a clean glass container, the water surface forms the shape of a concave lens, as shown in the figure. Calculate the height difference \\( h \\) between the center and the edge of the concave meniscus. Given are the surface tension coefficient of water \\( \\gamma \\), the density of wa... | $\sqrt{\frac{2\gamma}{\rho g}}$ | open | Physics | |
rbench_v_full_00032 | [{"role": "user", "question": "A tetrahedral framework is formed from uniform wires made of the same material and having equal cross-sectional areas, with each edge having a resistance of a, b, or c, as shown in the figure. Determine the equivalent resistance between points A and B.", "hint": "", "options": {}, "choice... | $\frac{1}{2}(\frac{ab}{a+b}+\frac{ac}{a+c})$ | open | Physics | |
rbench_v_full_00033 | [{"role": "user", "question": "An infinite resistor network is constructed using resistors with resistances $r$ and $R$, as shown in the figure. Determine the equivalent resistance between two nodes that are very far apart.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | $\frac{r}{2}(1+\sqrt{\frac{r+4R}{r}})(1-\sqrt{\frac{r}{r+4R}})$ | open | Physics | |
rbench_v_full_00034 | [{"role": "user", "question": "A uniform magnetic field $B$ inside a cylindrical region of radius $r = 20,\\mathrm{cm}$ varies linearly with time according to $B = kt$, where $k = \\frac{225}{\\pi},\\mathrm{T/s}$. Two semicircular resistors, MPN and MQN, with resistances $R_1 = 30,\\Omega$ and $R_2 = 60,\\Omega$ respec... | 60 | numeric | Physics | |
rbench_v_full_00035 | [{"role": "user", "question": "As shown in the figure, at a certain moment, a person’s eye is at point $E$, observing a scale $M$ through a magnifying glass $L$. Points $F_1$ and $F_2$ are the two focal points of the lens $L$. At this moment, the person can see part of the scale $M$ through the lens, and can also see a... | 22.5~30, -30~-22.5 | open | Physics | |
rbench_v_full_00036 | [{"role": "user", "question": "Given a parallel-sided plate of thickness $d$ whose refractive index varies according to the equation $$n(x) = \\frac{n_0}{1 - \\frac{x}{r}},$$ a light beam enters the plate perpendicularly from air at point O and exits at point A with an angle $\\alpha$, as shown in the diagram. Determin... | $\sqrt{n_0^2 + \sin^2 \alpha}$ | open | Physics | |
rbench_v_full_00037 | [{"role": "user", "question": "As shown in the figure, a luminous point S is located on the principal axis of a thin convex lens L with a focal length of 20.00 cm, at a distance of 30.00 cm from the center of the lens; a light wedge C (a prism with a very small apex angle $\\alpha$), whose thickness is negligible, is p... | 0.55cm | open | Physics | |
rbench_v_full_00038 | [{"role": "user", "question": "To measure the refractive index n of a glass prism, an experimental setup as shown in the figure is used. The prism is placed in front of a converging lens, with face AB perpendicular to the optical axis of the lens. A screen is positioned on the focal plane of the lens. When scattered li... | $\sqrt{5-2\sqrt{3}}$ | open | Physics | |
rbench_v_full_00039 | [{"role": "user", "question": "As shown in the figure, two plane mirrors A and B are inclined to each other, intersecting along the edge O, with an angle $\\theta$ between them. The reflective surfaces of the mirrors face each other, and there is an object point P located between the two mirrors. A perpendicular line O... | 9 | numeric | Physics | |
rbench_v_full_00040 | [{"role": "user", "question": "A parallel laser beam with a wavelength of $\\lambda = 632.8\\,\\mathrm{nm}$ is perpendicularly incident on a double prism with an apex angle of $\\alpha = 3'30''$, a width of $W = 4.0\\,\\mathrm{cm}$, and a refractive index of $n = 1.5$. What is the distance $L$ between the screen and th... | 19.6m | open | Physics | |
rbench_v_full_00041 | [{"role": "user", "question": "As shown in the diagram, a Nicol prism is made from a calcite crystal, with angles $\\angle CAC' = 90^\\circ$ and $\\angle ACC' = 68^\\circ$ in its principal section, and the optical axis forms an angle of 48° with line AC. Under normal operation, natural light enters along the lengthwise... | 14° | open | Physics | |
rbench_v_full_00042 | [{"role": "user", "question": "As shown in the figure, a hollow circular ring of radius R is fixed to a block which rests on a smooth horizontal surface. The total mass of the block and ring is M. A small ball of mass m (treated as a point mass) is free to move without friction along the inner surface of the ring. Init... | $(\frac{M}{M+m})^2R$ | open | Physics | |
rbench_v_full_00043 | [{"role": "user", "question": "As shown in the figure, a vertical cylinder with mass M and radius R is placed on a smooth horizontal surface. A small ball of mass m starts from rest at the top of the cylinder and slides down without friction along a helical groove on the inner wall of the cylinder. The height h of the ... | $\sqrt{h^2 + (\frac{2\pi M}{M+2m})^2 R^2}$ | open | Physics | |
rbench_v_full_00044 | [{"role": "user", "question": "In the circuit shown in the figure, the electromotive forces of the three power sources are given by \\( E_1 = E_0 \\cos\\left(\\frac{1}{2}\\omega t + 30^\\circ\\right) \\), \\( E_2 = E_0 \\cos(\\omega t + 45^\\circ) \\), and \\( E_3 = E_0 \\cos(2\\omega t + 60^\\circ) \\), respectively. ... | $\frac{19{E_0}^2}{13R}$ | open | Physics | |
rbench_v_full_00045 | [{"role": "user", "question": "As shown in the figure, a symmetric steel object with a mass of \\( m = 20\\,\\mathrm{kg} \\) is placed across two identical, parallel, and infinitely long cylindrical rollers. The rollers lie in the same horizontal plane and have a radius \\( r = 0.025\\,\\mathrm{m} \\). They rotate in o... | 2.0(N) | open | Physics | |
rbench_v_full_00046 | [{"role": "user", "question": "As shown in the figure, a block C with mass M is placed on a frictionless horizontal table. Two objects, A and B, each with mass m, are connected by a light string; object A lies flat on top of block C, with a coefficient of friction $\\mu<1$ between A and C, while the string passes over ... | $\frac{1-\mu^2}{2\mu}(M+2m)g$ | open | Physics | |
rbench_v_full_00047 | [{"role": "user", "question": "As shown in the figure, a simple pendulum has a length $L$ and a bob of mass $m$. It is released from rest on the left side at an angle $\\alpha$ from the vertical. On the right side, along the direction that makes an angle $\\beta$ (with $\\beta < \\alpha$) with the vertical, there is a ... | $\arccos(\frac{2r\cos\beta-\sqrt{3}(L-r)}{2L})$ | open | Physics | |
rbench_v_full_00048 | [{"role": "user", "question": "As shown in the figure, a massless rod of length $2r = 20,\\mathrm{cm}$ has a fixed particle of mass $m$ attached at its center point $C$. One end of the rod, point $A$, rests against a vertical wall, while the other end, point $B$, rests on the ground. Both ends are free to slide without... | 12.5cm | open | Physics | |
rbench_v_full_00049 | [{"role": "user", "question": "As shown in the figure, a light, inextensible string of length $2l$ has one end fixed at a nail at point A, and a small ball is attached to the other end. The ball can move within the vertical plane, pivoting about point A. Initially, the ball is on the right side of point A and lies at t... | $\sqrt{\frac{3\sqrt{3}}{2}gl}$ | open | Physics | |
rbench_v_full_00050 | [{"role": "user", "question": "As shown in the figure, three particles A, B, and C are initially at rest on a smooth horizontal surface. Their respective masses are indicated in the diagram. They are connected by soft, inextensible, and negligible-mass strings that are pulled taut, with the angle between segments AB an... | $\frac{Im_2 \cos\alpha}{(m_1+m_2+m_3)m_2+m_1 m_3 \sin^2 \alpha}$ | open | Physics | |
rbench_v_full_00051 | [{"role": "user", "question": "As shown in the figure, a uniform, slender rod of mass m and length L is placed vertically, with its lower end in contact with the ground where the coefficient of friction is $\\mu$. The upper end of the rod is held by a rope forming an angle $\\theta$ with the rod. A horizontal force F i... | $\frac{L}{1+\mu\cot\theta}$ | open | Physics | |
rbench_v_full_00052 | [{"role": "user", "question": "As shown in the figure, three identical cylinders with the same radius and mass are stacked on the ground in the configuration illustrated, making contact with one another. Given that the coefficient of friction between the cylinders is $\\mu_1$ and the coefficient of friction between the... | $\frac{1}{2+\sqrt{3}}$; $\frac{1}{3(2+\sqrt{3})}$ | open | Physics | |
rbench_v_full_00053 | [{"role": "user", "question": "As shown in the diagram, AB, BC, CD, and DE are massless strings of equal length, with points A and E suspended from a horizontal ceiling; the length relationships are indicated in the diagram. Points B and D each support identical spheres with a mass of 7 kg. An object with mass m is sus... | 18 | numeric | Physics | |
rbench_v_full_00054 | [{"role": "user", "question": "As shown in the figure, a uniform solid cylinder is undergoing pure rolling on a horizontal surface, with its radius and the velocity of its center O indicated. As it rolls forward, the cylinder encounters a step and undergoes a completely inelastic collision. Assume the coefficient of fr... | 3R/7 | open | Physics | |
rbench_v_full_00055 | [{"role": "user", "question": "As shown in the figure, two uniform slender rods, each of mass m and length l, are initially at rest on a frictionless horizontal surface. One of the rods consists of two identical segments connected by a smooth hinge, allowing the segments to bend at the joint without separating. A horiz... | 4:7 | open | Physics | |
rbench_v_full_00056 | [{"role": "user", "question": "As shown in the figure, two identical cylindrical rollers are placed parallel to each other on a horizontal surface. Each roller rotates about its own axis with the same angular velocity in the directions indicated. The distance between the two axes is $2l$. A uniform wooden board of weig... | $2\pi\sqrt{\frac{l}{\mu g}}$ | open | Physics | |
rbench_v_full_00057 | [{"role": "user", "question": "As shown in the figure, an object of mass M is placed on two identical thin-walled hollow cylinders, each of mass m. Identical springs with spring constant k are attached to both sides of the object, with their other ends fixed, and both springs are at their natural lengths initially. Ass... | $\pi \sqrt{\frac{2(M+m)}{k}}$ | open | Physics | |
rbench_v_full_00058 | [{"role": "user", "question": "An instrument released from a spaceship falls vertically at a constant speed toward the surface of a certain planet. The graph shows how the atmospheric pressure P, recorded in standardized units by the instrument, changes over time t as it descends. Upon reaching the planet’s surface, th... | about 14.6m/s（14.3 to 14.9 are all correct） | open | Physics | |
rbench_v_full_00059 | [{"role": "user", "question": "As shown in the figure, a flat and thin rectangular homogeneous glass plate is suspended using two massless strings of equal length. One half of each side of the glass plate is symmetrically coated with a layer of chemically active metal. The entire setup is placed inside a container fill... | (pqcb^2)/(mga) | open | Physics | |
rbench_v_full_00060 | [{"role": "user", "question": "After two spherical films of the same liquid collide, they form a symmetrical conjoined film as shown in the figure. The two spherical surfaces of the conjoined film (each being a partial spherical surface greater than a hemisphere) have an identical radius R, and the circular membrane th... | $2\sigma r\left(2\sqrt{1-\left(\frac{r}{R}\right)^2}-1\right)$ | open | Physics | |
rbench_v_full_00061 | [{"role": "user", "question": "An infinitely long uniformly charged thin wire is bent into the planar shape shown in the diagram, where $\\overparen{AB}$ is a semicircular arc, and $AA'$ and $BB'$ are two parallel straight segments extending infinitely to the right from points $A'$ and $B'$, respectively. Determine the... | 0 | numeric | Physics | |
rbench_v_full_00062 | [{"role": "user", "question": "As shown in the figure, a direct current of strength 2I flows through a semi-infinite straight wire to the south pole of a metallic spherical surface with radius R, passes along the surface to the north pole, and then continues through another semi-infinite straight wire extending to infi... | $\frac{\mu_0 I}{2\pi R}$ | open | Physics | |
rbench_v_full_00063 | [{"role": "user", "question": "As shown in the figure, an infinitely long straight wire carries a current \\( I_1 \\), and a circular loop of radius \\( R \\) placed next to it carries a current \\( I_2 \\). Both the straight wire and the circular loop lie in the same plane, with the center of the loop at a distance \\... | $\mu_{0} I_{1} I_{2}\left(\frac{L}{\sqrt{L^{2}-R^{2}}}-1\right)$ | open | Physics | |
rbench_v_full_00064 | [{"role": "user", "question": "In the right-handed Cartesian coordinate system Oxyz as shown, the xy-plane is horizontal and there is a superconducting flat plate located at z = 0. The z-axis points vertically upward. A homogeneous metallic circular ring with mass m and radius r (where r >> h) is positioned at height z... | $\sqrt{\frac{2mgh}{\mu_0 r}}$ | open | Physics | |
rbench_v_full_00065 | [{"role": "user", "question": "As shown in the figure, there is a uniform magnetic field B perpendicular to the plane of the paper and pointing outward, confined within an equilateral triangular region with side length a. An equilateral triangular conducting loop ABC, also with side length a, is positioned at time t = ... | $\frac{\sqrt{3}a^2 B}{6RT}$ | open | Physics | |
rbench_v_full_00066 | [{"role": "user", "question": "As shown in the figure, there is a closed conducting wire loop with segments of equal length: ab = bc = cd = de = ef = fa = 0.1 m. The resistances of segments ab, cf, and de are all 3 Ω; the resistances of segments cd and fe are 1.5 Ω each; and segments bc and af have zero resistance. A u... | 8.0e-3(J) | open | Physics | |
rbench_v_full_00067 | [{"role": "user", "question": "As shown in the figure, a long, thin conducting plate of width L is placed horizontally along the x-axis, and its resistance is negligible. The arc-shaped uniform wire aebcfd in the figure has a total resistance of 3R. The plane of the arc is perpendicular to the x-axis, and its endpoints... | $(\sqrt{2}-\frac{2n+1}{3n+2})BLv$ | open | Physics | |
rbench_v_full_00068 | [{"role": "user", "question": "As shown in the figure, two long, straight conducting rods—one horizontal and one vertical—intersect and are fixed together to form a rigid cross-shaped structure. A square loop composed of four conducting rods, each of length $a$, starts at the solid-line position shown in the figure and... | 6.9e-8 (C) | open | Physics | |
rbench_v_full_00069 | [{"role": "user", "question": "As shown in the figure, a circuit is formed by a uniformly dense thin wire bent into a circular loop with radius a, and a resistive wire shaped as an equilateral triangle inscribed within the loop. The resistance values of the different segments of the circuit are indicated in the figure.... | $-\frac{\sqrt{3}}{32}ka^2$ | open | Physics | |
rbench_v_full_00070 | [{"role": "user", "question": "In a regular tetrahedral framework-shaped resistor network as shown in the figure, each segment has a resistance of R. Determine the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 3R/4 | open | Physics | |
rbench_v_full_00071 | [{"role": "user", "question": "Three identical uniform metallic rings are connected in pairs to form a network as shown in the diagram. Given that the resistance of each metallic ring is R, calculate the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 5R/48 | open | Physics | |
rbench_v_full_00072 | [{"role": "user", "question": "As shown in the figure, an infinite resistor network is formed by identical resistive wires, each with resistance r. Determine the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | $\frac{2r}{\sqrt{21}}$ | open | Physics | |
rbench_v_full_00073 | [{"role": "user", "question": "An infinite network of equilateral triangles is formed by connecting identical uniform metal wires, as shown in the diagram, where the midpoints of the sides of each outer triangle serve as the vertices of the next inner triangle. Given that the side length of the outermost equilateral tr... | $\frac{\sqrt{7}-1}{3}ar$ | open | Physics | |
rbench_v_full_00074 | [{"role": "user", "question": "Ten resistive wires, each with resistance R, are connected to form a resistor network as shown in the diagram. Determine the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 15R/8 | open | Physics | |
rbench_v_full_00075 | [{"role": "user", "question": "As shown in the diagram, the resistor wire network consists of segments, each with a resistance of R. Determine the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 29R/24 | open | Physics | |
rbench_v_full_00076 | [{"role": "user", "question": "In a complex resistor network, resistors connected in star (Y) or delta (Δ) configurations can be simplified using equivalent transformations. Let the star resistors be $R_a, R_b, R_c$ (with a common center node and terminals A, B, and C), and let the delta resistors be $R_{AB}, R_{BC}, R... | 4 \Omega | open | Physics | |
rbench_v_full_00077 | [{"role": "user", "question": "As shown in the figure, the network is composed of resistive wires, each segment having a resistance of R; using the Y-Δ transformation formulas and the symmetry of the circuit, calculate the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_im... | 47R/22 | open | Physics | |
rbench_v_full_00078 | [{"role": "user", "question": "As shown in the figure of the cube-shaped resistor network, where each small segment has a resistance of R, use the Y-Δ transformation and circuit symmetry to determine the equivalent resistance between points P and Q.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 24R/35 | open | Physics | |
rbench_v_full_00079 | [{"role": "user", "question": "Several resistors are connected to form the circuit shown in the diagram, in which the grounding resistance between points A and B is fixed. The input voltages V₁, V₂, ..., Vₙ can only take values of either 1V or 0V, where 0V represents ground. What is the maximum output voltage at point ... | $\frac{2}{3}\left(1-\frac{1}{2^n}\right)V$ | open | Physics | |
rbench_v_full_00080 | [{"role": "user", "question": "In the capacitor network shown in the figure, it is given that $C_1 = C_2 = C_3 = C_9 = 1\\ \\mathrm{\\mu F}$, $C_4 = C_5 = C_6 = C_7 = 2\\ \\mathrm{\\mu F}$, and $C_8 = C_{10} = 3\\ \\mathrm{\\mu F}$. Determine the equivalent capacitance between points A and B.", "hint": "", "options": {... | $2.9\mathrm{\mu F}$ | open | Physics | |
rbench_v_full_00081 | [{"role": "user", "question": "In the circuit shown, which consists of capacitors and a DC power source, the capacitances are given as $C_{1} = 4C_{0}$, $C_{2} = 2C_{0}$, and $C_{3} = C_{0}$, and the power source has an electromotive force of $\\mathcal{E}$ with negligible internal resistance. As illustrated, switches ... | $\frac{2}{7}C_0\mathcal{E}^2$ | open | Physics | |
rbench_v_full_00082 | [{"role": "user", "question": "As shown in the figure, twelve resistive wires, each with resistance $R$, are connected to form a cube. Two of these wires are connected to ideal batteries with electromotive forces $\\mathcal{E}_{1}$ and $\\mathcal{E}_{2}$, respectively. In five other wires, identical capacitors of capac... | $\frac{3}{5}I_0$ | open | Physics | |
rbench_v_full_00083 | [{"role": "user", "question": "An infinitely long straight line, along which charges cannot move freely, is uniformly charged with a linear charge density of $\\lambda$ and bent at point A to form a right angle. In the plane of the bent line, there is a point P₄ located such that its perpendicular distance to both arms... | $\frac{2.45k\lambda}{a}$ | open | Physics | |
rbench_v_full_00084 | [{"role": "user", "question": "A conducting sphere of radius $R$ carries a total charge $Q$ and is electrically isolated (not grounded). A point charge $q$ is located outside the sphere at a distance $d$ from the center of the sphere. Let the line connecting the point charge $q$ and the center of the sphere $O$ interse... | $q\frac{R^2(3d-R)}{d(d-R)^2}$ | open | Physics | |
rbench_v_full_00085 | [{"role": "user", "question": "Two infinite grounded parallel conducting plates are separated by a distance of 4d, with two point charges +Q and -Q placed between them; the +Q charge is located a distance d from one plate, and the -Q charge is located a distance 3d from the same plate, as shown in the figure. Determine... | $\frac{Q^2 \ln 2}{4\pi \epsilon_0 d}$ | open | Physics | |
rbench_v_full_00086 | [{"role": "user", "question": "A thin spherical conducting shell with radius R has its center at point O. Points A, B, and C lie on the surface of the sphere, and the radii OA, OB, and OC are mutually perpendicular. A and B are connected by thin wires to a power source, with an electric current I entering the sphere at... | $\frac{\sqrt{2}I}{4\pi R}$ | open | Physics | |
rbench_v_full_00087 | [{"role": "user", "question": "As shown in the diagram, the network consists of batteries with electromotive forces $V_1$, $V_2$, ..., $V_n$, all having negligible internal resistance. When terminals A and B are taken as the output terminals, the entire network can be equivalent to a single voltage source with internal... | $\sum_{i = 1}^{n}\frac{V_{i}}{2^{i}}$ | open | Physics | |
rbench_v_full_00088 | [{"role": "user", "question": "In the circuit shown in the figure, the electromotive force $\\varepsilon_1$ of battery 1 decreases by $1.5\\ \\text{V}$, resulting in changes in the current through various parts of the circuit; to keep the current through battery $\\varepsilon_2$ unchanged, by how much must the electrom... | 0.375 (V) | open | Physics | |
rbench_v_full_00089 | [{"role": "user", "question": "A resistor network composed of resistive metal wires is shown in the figure, where each small segment of wire has a resistance R. A power source with electromotive force E and internal resistance r is connected across two points A and B on the network. Determine the expression for the cur... | $\frac{24E}{29R+24r}$ | open | Physics | |
rbench_v_full_00090 | [{"role": "user", "question": "Connect three of each resistor \\( r_1 \\), \\( r_2 \\), \\( r_3 \\), and \\( r_4 \\) to form a complete cubic network as shown in the diagram; determine the equivalent resistance \\( R_{AB} \\) between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | $\frac{1}{3}\left(r_1 + r_2 + \frac{r_3 r_4}{r_3 + r_4} \right)$ | open | Physics | |
rbench_v_full_00091 | [{"role": "user", "question": "As shown in the figure, each resistor in the circuit has a resistance of r. Find the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 1.4r | open | Physics | |
rbench_v_full_00092 | [{"role": "user", "question": "As shown in the figure, a resistive metal wire network is given, where each segment of the metal wire has a resistance of r; determine the equivalent resistance between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 13r/7 | open | Physics | |
rbench_v_full_00093 | [{"role": "user", "question": "As shown in the figure, consider an infinite resistor network where each resistor has a resistance of $r$; determine the equivalent resistance $R_{AB}$ between points A and B.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | $\frac{\sqrt{3}r}{2}$ | open | Physics | |
rbench_v_full_00094 | [{"role": "user", "question": "As shown in the figure, a flat plastic disk with radius $R$ is uniformly charged with a surface charge density $\\sigma$. The disk rotates about its central axis \\( AA' \\) with an angular velocity \\( \\omega \\). A uniform magnetic field \\( B \\) is applied perpendicular to the rotati... | $\frac{\pi}{4}\omega\sigma BR^4$ | open | Physics | |
rbench_v_full_00095 | [{"role": "user", "question": "As shown in the figure, a thin circular ring with uniformly distributed mass has a radius of $R$ and a mass of $m$. The ring is uniformly charged with a total positive charge $Q$ and is placed flat on a smooth, insulating horizontal table. It is also subjected to a uniform magnetic field ... | $\frac{\omega R}{2\pi}\left(m\omega + BQ\right)$ | open | Physics | |
rbench_v_full_00096 | [{"role": "user", "question": "A rectangular conducting wire loop of length $L_1$, width $L_2$, and mass $m$ is made of rigid rods with uniformly distributed mass. It is initially at rest on a non-conducting horizontal table and can rotate about a smooth fixed axis $ab$ that coincides with one of its sides. A variable ... | $\frac{mg}{2BL_1}$ | open | Physics | |
rbench_v_full_00097 | [{"role": "user", "question": "As shown in the figure, a small insulating inclined plane with an angle of inclination $\\theta$ has a small block of mass $m$ and positive charge $q$ ($q>0$) placed on it. The coefficient of friction between the block and the incline is $\\mu$ ($\\mu < \\tan\\theta$). The entire setup is... | $\frac{mg}{qB}\cos\theta\sqrt{\tan^2 \theta -\mu^2}$ | open | Physics | |
rbench_v_full_00098 | [{"role": "user", "question": "As shown in the figure, an insulating circular ring of radius $R$ is fixed on a smooth, horizontal, and insulating tabletop. Within the region enclosed by the ring, there exists a uniform magnetic field perpendicular to the tabletop, with a magnetic induction magnitude of $B$. A particle ... | $\frac{qBR}{m}\tan\frac{\pi}{n+3}$，式中$n\in\mathbb{N}$ | open | Physics | |
rbench_v_full_00099 | [{"role": "user", "question": "A non-conductive dielectric ring with radius $R$, mass $m$, and uniformly distributed electric charge moves on a frictionless horizontal table within its own vertical plane. Initially, the ring translates from right to left at a velocity $v_0$ without any rotation. Above the table lies a ... | $\frac{\sqrt{2}mv_0}{RB}$ | open | Physics |
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