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Physics | 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 the work done by the force applied by the worker pulling the rope, and (2) the mechanical efficiency of the device. | （1）60W（2）80% |
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Physics | 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 between the brick clamp and the brick is f = 0.5. Determine the maximum value of distance b required to lift the brick using the clamp. | 11cm |
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Physics | 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 the semicylinder has velocity $v$, and the contact point P between the rod and the semicylinder is at an angular position $\theta$, determine the velocity of the vertical rod at that moment. | $\frac{v}{\cos(\theta)}$ |
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Physics | 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 well as between the wedge and the tabletop, is $\mu = 0.2$. Determine the range of values of $\theta$ for which the object slides down the incline while the wedge remains stationary. | $\tan(\theta)\geq \frac{12+\sqrt{69}}{5}$ or $\frac{1}{5} \leq \tan(\theta)\leq \frac{12-\sqrt{69}}{5}$ |
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Physics | 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 of the bowl, and point B on the rod lies along the rim of the bowl. When the rod AC moves within the vertical plane to the position shown—specifically when the angle θ is 30 degrees—the speed of end A is exactly half the speed of end C. Determine the ratio of the length of segment AB to that of segment BC. | 1/SQRT(5) |
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Physics | 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 out Book B. What is the minimum value of F required? | 1.17e3(N) |
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Physics | 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 shown in the figure, a viscous solid wall perpendicular to the direction of motion is located in front of point C. When ball C collides with the wall, it stops instantly. Determine the speed of ball A immediately after the collision. | v |
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Physics | 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 the direction of $CA$, and at the end of the impulse, particle $A$ has velocity $V$, while the other particles also acquire certain velocities. Given that $\angle BAD = 2\alpha$ (with $\alpha < \frac{\pi}{4}$), determine the total momentum of the particle system after the impulse. | $\frac{4mV}{1+2\sin^2 \alpha}$ |
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Physics | 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 perpendicular to itself. Find the velocity $v_P$ of their point of intersection P. | $\frac{1}{\sin(\varphi)} \sqrt{v_1^2+v_2^2-2v_1 v_2 \cos\varphi}$ |
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Physics | 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 in the figure. Due to a disturbance, the block begins to slide downward within the plane of the figure until it leaves the surface. Determine the work $W$ done by the normal force from the cylindrical surface on the block during this process. | $\frac{2mv\sqrt{6gR}}{9}$ |
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Physics | 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 DF is suddenly cut, find the tension in string AB at the instant immediately after the cut. | 8mg/3 |
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Physics | 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 member is subjected to either pure tension or pure compression. Determine the magnitude of the internal force (tension or compression) in member BC. | $\frac{2\sqrt{3}W}{9}$ |
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Physics | 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 cylinder and both the inclined plane and the stopper is 1/3, while the friction between the cylinders is negligible. Determine the maximum horizontal force $P$ that can be applied to the system such that it remains in equilibrium. | $\frac{R}{4l}((5+\sqrt{3})n+3(1+\sqrt{3}))mg$ |
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Physics | 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 inner surface of the bowl is $\mu = \tan\beta$. Determine the maximum angle between the rod and the horizontal plane such that the rod remains in equilibrium. Express your answer using tangent and arctangent functions. | $\arctan(\frac{\tan(\alpha+\beta)-\tan(\alpha-\beta)}{2})$ |
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Physics | 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 the rod is $\mu$. Assuming both rings have mass $m$, determine the maximum distance $x$ between rings A and B when the system is in static equilibrium. | $\frac{\mu l(1+\frac{2m}{M})}{\sqrt{1+\mu^2(1+\frac{2m}{M})^2}}$ |
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Physics | 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 axes of the cylinders, have the same length as the cylinders, and are spaced $4R$ apart, making contact with the cylinders without deformation, as shown in the figure. A third cylindrical rod, also of length equal to the first two, mass $m$, and radius $r$, is then placed symmetrically atop the two lower cylinders, aligned in the same axial direction. The coefficient of static friction between all contact surfaces—between cylinders and between the cylinders and the box—is $\mu$. If $r$ satisfies $0 < r \leq (\sqrt{2} - 1)R$, and the rigid box is gently lifted vertically upward, all three cylinders can be lifted together. Determine the minimum value of $\mu$ required for this to occur. | $\frac{3(3-\sqrt{2})}{7}$ |
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Physics | 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 rings. When the angle $\alpha = 30^\circ$, the velocity of point A is $v_A = 5.0\ \text{cm} \cdot \text{s}^{-1}$ and its acceleration is $a_A = 0$. Find the magnitude of the acceleration of the small ring M at this moment. | $10cm\cdot s^{-2}$ |
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Physics | 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 acceleration of the cart. | $\frac{4m-M\sin\alpha}{M+16m}g$ |
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Physics | 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 the velocity of point B at the end of rod AB at that instant. | 16cm/s |
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Physics | 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 along the same horizontal line constrained within horizontal tracks, determine the velocity of slider C at this instant. | 67.0cm/s |
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Physics | 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 $\theta = \frac{\pi}{3}$. Starting from time t = 0, ball A is subjected to a constant force F parallel to segment CB. Determine the tension in string $BC$ at the instant both strings have just become taut. | 79F/225 |
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Physics | 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 force P acts at joint C along the direction of rod CG. The system is in equilibrium. Determine the internal force in rod CG (expressed as a positive value for tension and a negative value for compression). | -P-SQRT(2)*Q |
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Physics | 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. | -SQRT(3) * Q |
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Physics | 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 angular configuration as shown in the figure. Determine the ratio of the initial angular accelerations of rod AB to rod BC at the moment of release. | 0.75 |
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Physics | 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 vertically downward (i.e., perpendicular to the ground), is suddenly applied at point $B$ on the edge of the disk. After the impulse, the disk undergoes pure rolling while remaining in contact with the ground. Determine the minimum impulse required to cause the disk to completely flip over. | 2.23M * \sqrt{gR} |
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Physics | 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 horizontal, determine the precession angular velocity. | $\frac{mgD}{I\omega_0}$ |
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Physics | 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 the wall is $\mu$. The horizontal distance between point $A$ and the wall is $a$, and it is given that $\sqrt{d^2 + a^2} > \frac{l}{2}$ and $d > \mu a$. Determine the magnitude of the support force exerted by the wall on the rod when the angle between the rod and the ground is minimized. | $$mg \cdot \frac{al\sqrt{d^2 - \mu^2 a^2}}{2d(d^2+a^2)}$$ |
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Physics | 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 "self-locking" of the latch. The structure of the latch-type door lock is shown in the diagram, where the movement of slider A controls the locking and unlocking of the door, and $\alpha$ is the angle between the inclined surface of slider A and its base. Given that the maximum coefficient of static friction (assumed equal to the kinetic friction coefficient) between slider A and the contact surfaces is $\mu$, what is the minimum value of angle $\alpha$ required to prevent self-locking of the slider? | $2 \arctan \mu$ |
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Physics | 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 attached at each of the points A, B, and C. The entire system lies on a smooth horizontal table with a fixed smooth vertical barrier. The system translates towards the barrier with the velocity shown in the figure. At a certain moment, ball C collides with the barrier; after the collision, its velocity component perpendicular to the barrier becomes zero, and it does not stick to the barrier. Determine the minimum value of angle $\alpha$ such that, after the collision of ball C, ball B hits the barrier before ball A. | $\arctan{\frac{3}{1+\pi}}$ |
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Physics | 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. What is the minimum initial speed $v_0$ required for the object to start moving upward without losing contact with the tube's surface? | $\dfrac{\sqrt{gr\cos\alpha}}{\sin\varphi}$ |
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Physics | 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 period of small oscillations of the heavy ball within the plane of the V-shaped frame. | $\pi\sqrt{\frac{2l}{g\sin\alpha}}$ |
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Physics | 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 water \( \rho \), and the acceleration due to gravity \( g \). | $\sqrt{\frac{2\gamma}{\rho g}}$ |
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Physics | 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. | $\frac{1}{2}(\frac{ab}{a+b}+\frac{ac}{a+c})$ |
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Physics | 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. | $\frac{r}{2}(1+\sqrt{\frac{r+4R}{r}})(1-\sqrt{\frac{r}{r+4R}})$ |
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Physics | 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 $R_2 = 60,\Omega$ respectively, are connected to form a circular loop that is coaxially placed outside the cylindrical region. Its cross-section is shown in the figure. A straight resistor MON with resistance $R_{MN} = 30,\Omega$ connects points M and N. Determine the resistance value (in ohms) that should be connected externally between points M and N such that the current through the straight resistor MON is zero. | 60 |
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Physics | 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 another part of the scale directly, without looking through the magnifying glass. Determine the range of markings on $M$ that the person cannot see. | 22.5~30, -30~-22.5 |
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Physics | 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. Determine the refractive index $n_A$ at point A. | $\sqrt{n_0^2 + \sin^2 \alpha}$ |
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Physics | 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 placed between the luminous point and the lens, perpendicular to the principal axis and at a distance of 2.00 cm from the lens; the refractive index of the wedge is n = 1.5 and the wedge angle $\alpha$ is 0.028 rad; on the opposite side of the lens, a plane mirror M is placed 46.25 cm from the center of the lens, with its reflective surface facing the lens and perpendicular to the principal axis. Question: How far from the optical axis is the final image of the luminous point formed? (Only paraxial rays are considered, and the small-angle approximation is applicable.) | 0.55cm |
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Physics | 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 light is incident on face AC, two regions can be observed on the screen: an illuminated region and a non-illuminated region. A line segment OD, connecting point D—the boundary between the two regions—and the optical center O of the lens, forms an angle of 30° with the optical axis OO'. Determine the refractive index n of the prism. The apex angle of the prism is given as $\alpha$ = 30°. | $\sqrt{5-2\sqrt{3}}$ |
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Physics | 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 OP is drawn from point P to the intersection edge O, forming angles $\alpha$ and $\beta$ with mirrors A and B, respectively. An observer is positioned between mirrors A and B. Question: When $\theta = \frac{\pi}{5}$, how many reflected images of the object can be observed? | 9 |
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Physics | 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 the double prism that results in the maximum number of observable interference fringes on the screen? | 19.6m |
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Physics | 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 direction of the prism (i.e., in the direction of $S_0M$), and the transmitted light is strictly linearly polarized. Any deviation of the incident light from the $S_0M$ direction, such as incidence along $S_1M$ or $S_2M$, may cause the Nicol prism to lose its polarizing function. Determine the maximum allowable deviation angle $\theta$ for each case. The principal refractive indices of calcite are $n_0 = 1.658$ and $n_e = 1.486$, and the refractive index of the Canada balsam used for cementing is $n = 1.550$. | 14° |
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Physics | 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. Initially, both the ring and the ball are at rest, with the ball positioned at the topmost point of the ring. After a slight disturbance, the ball begins to slide down the ring. Using Newtonian mechanics, determine the radius of curvature of the ball’s trajectory (relative to the ground) at point B shown in the figure. | $(\frac{M}{M+m})^2R$ |
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Physics | 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 cylinder is exactly equal to the pitch of the helix, meaning the ball completes one full turn around the cylinder as it descends to the bottom. Initially, both the ball and the cylinder are at rest. Determine the total distance traveled by the ball relative to the ground. | $\sqrt{h^2 + (\frac{2\pi M}{M+2m})^2 R^2}$ |
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Physics | 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. Given that \( \omega L = \frac{1}{\omega C} = R \), calculate the average power dissipated across the resistor \( R \). | $\frac{19{E_0}^2}{13R}$ |
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Physics | 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 opposite directions about their own central axes with the same angular speed \( \omega = 40\,\mathrm{rad/s} \). The coefficient of friction between the steel object and the rollers is \( \mu = 0.20 \). In order for the steel object to move at a constant linear speed \( v_0 = 0.050\,\mathrm{m/s} \) along the direction of the rollers' lengths, a horizontal force \( F \) must be applied in that direction. Calculate the magnitude of the force \( F \). | 2.0(N) |
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Physics | 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 a pulley, suspending object B vertically. Assume the pulley and string are massless, and there is no friction in the pulley’s axle. A horizontal force F is applied to block C. To ensure that objects A and B remain stationary relative to block C, what is the minimum value of force F required? | $\frac{1-\mu^2}{2\mu}(M+2m)g$ |
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Physics | 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 fixed peg located at a distance $r$ from the suspension point. Neglecting air resistance, determine the angle $\alpha$ required for the pendulum bob to make contact with the peg. | $\arccos(\frac{2r\cos\beta-\sqrt{3}(L-r)}{2L})$ |
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Physics | 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 friction along the wall and the ground, respectively. The rod begins to slide from rest in a vertical position and remains in the same vertical plane throughout the motion. Determine the distance from point $O$ (the initial contact point between the rod and the ground) to the point where the center $C$ of the rod touches the ground. | 12.5cm |
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Physics | 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 the same horizontal level as A, moving vertically downward with an initial speed $v_0$. There is another nail at point B, located on the left side of point A and also at the same horizontal level, with a distance of $l$ between A and B. When the string swings past point B, the ball begins to swing upward around point B. To ensure that the ball can eventually collide with the nail at point A, what is the minimum initial speed $v_0$ required? | $\sqrt{\frac{3\sqrt{3}}{2}gl}$ |
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Physics | 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 and BC as shown. An impulse $I$ is applied to particle C; determine the magnitude of the initial velocity of particle A at the moment it starts to move. | $\frac{Im_2 \cos\alpha}{(m_1+m_2+m_3)m_2+m_1 m_3 \sin^2 \alpha}$ |
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Physics | 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 is applied to the rod at a height h above the ground. What is the minimum value of h such that, regardless of the magnitude of the applied force F, the rod does not slip? | $\frac{L}{1+\mu\cot\theta}$ |
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Physics | 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 cylinders and the ground is $\mu_2$, determine the minimum values of $\mu_1$ and $\mu_2$ required to maintain the equilibrium of the three cylinders. | $\frac{1}{2+\sqrt{3}}$; $\frac{1}{3(2+\sqrt{3})}$ |
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Physics | 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 suspended from point C, and in equilibrium, point C is 7 meters vertically below the ceiling. Determine the value of m in kilograms. | 18 |
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Physics | 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 friction between the cylinder and the edge of the step is sufficiently large. Determine the maximum height $h$ of the step such that the cylinder can pivot about point $A$, roll up onto the step without losing contact at $A$, and continue moving forward. | 3R/7 |
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Physics | 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 horizontal impulse J, perpendicular to the rods, is applied simultaneously at one end of each rod. Determine the ratio of the kinetic energies acquired by the two rods. | 4:7 |
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Physics | 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 weight $G$ is laid flat across the rollers. The coefficient of friction between the board and the rollers is $\mu$. If the center of mass of the board is slightly displaced from the midpoint between the two roller axes, determine the period of oscillation of the board. | $2\pi\sqrt{\frac{l}{\mu g}}$ |
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Physics | 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. Assuming the object undergoes pure rolling motion on the two hollow cylinders, determine the period of oscillation. | $\pi \sqrt{\frac{2(M+m)}{k}}$ |
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Physics | 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, the instrument measures an ambient temperature of 700 K and a gravitational acceleration of 10 m/s² at the surface. The planet’s atmosphere is known to consist of carbon dioxide. Determine the falling speed of the instrument. | about 14.6m/s（14.3 to 14.9 are all correct） |
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Physics | 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 filled with chlorine gas at pressure p. Each chlorine molecule has a probability q (q < 1), which is constant, of undergoing a chemical reaction upon encountering a metal molecule. Assume the chlorine gas has equal density on both sides of the glass plate, and the decrease in gas pressure due to the chemical reaction is negligible. The mass of the glass plate is m, and relevant geometric parameters are given in the figure. It is observed that after the glass plate rotates by a very small angle around its vertical axis, it reaches an equilibrium state. Determine the magnitude of this angle. | (pqcb^2)/(mga) |
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Physics | 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 that connects them in the middle has a radius r. The edge of the circular membrane is bounded by a uniform, massless string. Given that the surface tension coefficient of the liquid is $\sigma$, gravity is negligible, and $\frac{r}{R}<0.8$, find the tension T in the string. | $2\sigma r\left(2\sqrt{1-\left(\frac{r}{R}\right)^2}-1\right)$ |
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Physics | 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 magnitude of the electric field at the center point $O$ of the semicircle. | 0 |
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Physics | 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 infinity. Consider dividing the current distribution into left and right halves. In the left half, a semi-infinite straight current I flows to the south pole of the left hemisphere, travels along the left hemispherical surface (where the current distribution matches that of the original sphere’s left half), and exits from the north pole through a semi-infinite straight wire. Determine the magnitude of the magnetic induction (magnetic field) at the center O of the sphere. | $\frac{\mu_0 I}{2\pi R}$ |
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Physics | 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 \( L \) from the straight wire. The directions of the currents are indicated in the figure. Determine the net force that the circular loop exerts on the straight wire (take the force as positive if it is attractive, and negative if it is repulsive). | $\mu_{0} I_{1} I_{2}\left(\frac{L}{\sqrt{L^{2}-R^{2}}}-1\right)$ |
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Physics | 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 = h, with its center on the z-axis and its plane parallel to the horizontal plane. A steady current flows through the ring, such that it is levitated and remains stationary at z = h. Determine the current required in the ring to achieve this levitation. | $\sqrt{\frac{2mgh}{\mu_0 r}}$ |
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Physics | 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 = 0 such that it exactly overlaps the boundary of the magnetic field region. After that, it rotates uniformly in the plane of the paper in a clockwise direction about its center with a period T, inducing an electric current in the loop ABC. The current is defined to be positive when flowing in the direction ABCA, and negative when flowing in the opposite direction. Given that the resistance of the loop ABC is R, find the magnitude of the average current over the time interval from t = 0 to t = T/2. | $\frac{\sqrt{3}a^2 B}{6RT}$ |
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Physics | 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 uniform magnetic field B with a magnitude of 1 T is directed perpendicularly into the plane of the loop, with its boundary parallel to segment de, as indicated by the dashed line. The loop is pulled out of the magnetic field region to the right at a constant velocity of 24 m/s. Calculate the work done by the pulling force during this process. | 8.0e-3(J) |
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Physics | 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 a and d are in contact with the two side edges of the conducting plate and can slide freely along them. The arc segments ae, eb, cf, and fd each correspond to 1/8 of a full circle, while the arc bc corresponds to 1/4 of a full circle. A voltmeter with internal resistance R_v = nR and negligible volume is placed at the center O of the circle and is connected to points b and c with ideal (resistance-free) wires. The entire setup is placed in a region with a uniform magnetic field B, which points vertically upward. While keeping the conducting plate stationary, the circular wire and the voltmeter move together at a constant velocity along the x-axis. Determine the electric potential difference between points e and f. | $(\sqrt{2}-\frac{2n+1}{3n+2})BLv$ |
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Physics | 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 moves leftward at a constant speed $v$, remaining in contact with the cross structure throughout its motion. A uniform magnetic field $B$ fills the region, directed perpendicularly into the plane of the cross and the loop, as indicated in the diagram. The resistance per unit length of each conducting rod is $r = 100\mathrm{\Omega/m}$, with $a = 0.1\mathrm{m}$, $v = 0.24\mathrm{m/s}$, and $B = 10^{-4}\mathrm{T}$. Let $t = 0$ correspond to the moment when the square loop is at the solid-line position in the figure. As the loop moves to the left, a current $I$ flows through the vertical rod of the cross, and to keep the loop moving at constant speed, an appropriate leftward force $F$ must be applied. Calculate the total charge $Q$ that flows through the vertical rod during the entire process. | 6.9e-8 (C) |
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Physics | 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. A uniform magnetic field B, perpendicular to the plane of the loop and directed into the page, exists in the same plane as the loop and decreases uniformly over time, with a known rate of change k. Given that 2r₁ = 3r₂, determine the potential difference between points A and B in the figure. | $-\frac{\sqrt{3}}{32}ka^2$ |
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Physics | 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. | 3R/4 |
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Physics | 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. | 5R/48 |
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Physics | 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. | $\frac{2r}{\sqrt{21}}$ |
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Physics | 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 triangle is a and the resistance per unit length of the metal wire is r, find the equivalent resistance between points A and B. | $\frac{\sqrt{7}-1}{3}ar$ |
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Physics | 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. | 15R/8 |
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Physics | 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. | 29R/24 |
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Physics | 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 $R_{AB}, R_{BC}, R_{CA}$ (forming a closed triangle with terminals A, B, and C). The transformation formulas are as follows: - **Delta to Star (Δ→Y)**: $R_a = \frac{R_{AB}R_{CA}}{R_{AB}+R_{BC}+R_{CA}}$, similarly for $R_b$ and $R_c$ (the numerator is the product of the two adjacent Δ resistors, and the denominator is the sum of all three Δ resistors). - **Star to Delta (Y→Δ)**: $R_{AB} = R_a + R_b + \frac{R_aR_b}{R_c}$, similarly for $R_{BC}$ and $R_{CA}$ (the sum of two Y resistors plus their product divided by the third Y resistor). Using the above star-delta transformation formulas, calculate the total resistance $R_{PQ}$ between points $P$ and $Q$ in the given circuit diagram. | 4 \Omega |
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Physics | 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. | 47R/22 |
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Physics | 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. | 24R/35 |
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Physics | 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 B? | $\frac{2}{3}\left(1-\frac{1}{2^n}\right)V$ |
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Physics | 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. | $2.9\mathrm{\mu F}$ |
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Physics | 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 $k_{1}$, $k_{2}$, and $k_{3}$ are first closed while $k_{4}$ is open to charge the three capacitors. Then, switches $k_{1}$, $k_{2}$, and $k_{3}$ are opened, and $k_{4}$ is closed to allow the capacitors to discharge. Calculate the total amount of heat generated across the resistor $R$ during the discharge process. | $\frac{2}{7}C_0\mathcal{E}^2$ |
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Physics | 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 capacitance $C$ are connected. Assume the distance between the positive and negative terminals of each battery is negligible, the internal resistance of the batteries can be ignored, and $\mathcal{E}_{1} = 2I_{0}R$, $\mathcal{E}_{2} = I_{0}R$. Find the current $I_{AB}$ through edge $AB$. | $\frac{3}{5}I_0$ |
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Physics | 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 of the line is equal to a, as shown in the diagram. Find the magnitude of the electric field at point P₄. | $\frac{2.45k\lambda}{a}$ |
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Physics | 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 $O$ intersect the sphere at points $A$ and $B$, as shown in the figure. If the surface charge density at point $A$ is $\sigma_{eA} = 0$, what is the value of $Q$ under this condition? | $q\frac{R^2(3d-R)}{d(d-R)^2}$ |
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Physics | 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 the work done by external forces in removing and separating the two point charges to an infinite distance apart. | $\frac{Q^2 \ln 2}{4\pi \epsilon_0 d}$ |
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Physics | 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 point A and exiting at point B, as shown in the figure. Determine the current density at point C on the surface of the sphere (i.e., the current per unit length flowing through a line segment perpendicular to the direction of current on the spherical surface at point C). | $\frac{\sqrt{2}I}{4\pi R}$ |
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Physics | 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 resistance. Determine the electromotive force V of this equivalent voltage source. | $\sum_{i = 1}^{n}\frac{V_{i}}{2^{i}}$ |
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Physics | 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 electromotive force $\varepsilon_2$ be increased? | 0.375 (V) |
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Physics | 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 current I flowing through the power source. (Use Y-Δ transformation to find the equivalent resistance $R_{AB}$, then solve for I.) | $\frac{24E}{29R+24r}$ |
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Physics | 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. | $\frac{1}{3}\left(r_1 + r_2 + \frac{r_3 r_4}{r_3 + r_4} \right)$ |
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Physics | As shown in the figure, each resistor in the circuit has a resistance of r. Find the equivalent resistance between points A and B. | 1.4r |
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Physics | 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. | 13r/7 |
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Physics | 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. | $\frac{\sqrt{3}r}{2}$ |
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Physics | 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 rotation axis \( AA' \). Calculate the magnitude of the torque exerted on the disk by the magnetic field. | $\frac{\pi}{4}\omega\sigma BR^4$ |
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Physics | 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 of magnetic induction $B$, directed vertically downward. If the ring rotates with a constant angular velocity $\omega$ about a vertical axis passing through its center in the direction shown, determine the additional tension generated in the ring due to its rotation. | $\frac{\omega R}{2\pi}\left(m\omega + BQ\right)$ |
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Physics | 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 current source (not shown in the figure) is connected in series along this side. The loop is placed in a uniform magnetic field with magnetic induction $B$ directed horizontally and perpendicular to the rotation axis, as shown in the top view. The current is gradually increased from zero. Determine the minimum current $I_{\text{min}}$ required for the loop to begin moving from its state of rest. | $\frac{mg}{2BL_1}$ |
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Physics | 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 placed in a uniform magnetic field with magnetic flux density $B$, directed upward and perpendicular to the surface of the incline. Determine the magnitude of the velocity of the block when it moves along the incline and reaches a steady state. | $\frac{mg}{qB}\cos\theta\sqrt{\tan^2 \theta -\mu^2}$ |
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Physics | 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 with mass $m$, electric charge $q$, and initial speed $v$ enters the magnetic field region through a small hole at point A on the ring, directed toward the center O of the ring. It is known that the charged particle moves on the tabletop, retains its charge after colliding with the ring, and that collisions with the ring are perfectly elastic. After a sequence of collisions with the ring, the particle does not pass beyond point A again, and exits directly through the hole at point A. Determine all possible values of the particle's initial speed $v$ that satisfy this condition. | $\frac{qBR}{m}\tan\frac{\pi}{n+3}$，式中$n\in\mathbb{N}$ |
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Physics | 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 boundary interface $O_1O_2$, to the left of which exists a region with a uniform horizontal magnetic induction of strength $B$, directed parallel to the interface and perpendicular to the plane of the ring, as shown in the figure. In order for the ring to roll without slipping on the table after it has fully entered the magnetic field region, what must be the total electric charge on the ring? | $\frac{\sqrt{2}mv_0}{RB}$ |
End of preview. Expand
in Data Studio
R-Bench-V
Introduction
In "R-Bench-V", R denotes reasoning, and V denotes vision-indispensable.
According to statistics on RBench-V, the benchmark spans 4 categories, which are math, physics, counting and game.
It features 803 questions centered on multi-modal outputs, which requires image manipulation, such as generating novel images and constructing auxiliary lines to support reasoning process.
Leaderboard
| Model | Source | Overall | w/o Math | Math | Physics | Counting | Game |
|---|---|---|---|---|---|---|---|
| Human Expert 👑 | / | 82.3 | 81.7 | 84.7 | 69.4 | 81.0 | 89.1 |
| OpenAI o3 🥇 | Link | 25.8 | 19.5 | 48.3 | 20.4 | 22.1 | 17.1 |
| OpenAI o4-mini 🥈 | Link | 20.9 | 14.6 | 43.2 | 12.7 | 17.4 | 13.8 |
| Gemini 2.5 pro 🥉 | Link | 20.2 | 13.9 | 42.6 | 9.6 | 19.0 | 12.7 |
| Doubao-1.5-thinking-pro-m | Link | 17.1 | 11.0 | 38.6 | 13.4 | 9.7 | 10.5 |
| OpenAI o1 | Link | 16.2 | 11.0 | 34.7 | 5.7 | 12.3 | 13.1 |
| Doubao-1.5-vision-pro | Link | 15.6 | 11.5 | 30.1 | 8.9 | 12.8 | 12.0 |
| OpenAI GPT-4o-20250327 | Link | 14.1 | 11.2 | 24.4 | 3.2 | 13.3 | 14.2 |
| OpenAI GPT-4.1 | Link | 13.6 | 11.7 | 20.5 | 5.7 | 11.3 | 15.3 |
| Step-R1-V-Mini | Link | 13.2 | 8.8 | 29.0 | 6.4 | 10.3 | 9.1 |
| OpenAI GPT-4.5 | Link | 12.6 | 11.0 | 18.2 | 2.5 | 11.8 | 15.3 |
| Claude-3.7-sonnet | Link | 11.5 | 9.1 | 19.9 | 3.8 | 8.7 | 12.4 |
| QVQ-Max | Link | 11.0 | 8.1 | 21.0 | 5.7 | 6.2 | 10.9 |
| Qwen2.5VL-72B | Link | 10.6 | 9.2 | 15.3 | 3.8 | 6.2 | 14.5 |
| InternVL-3-38B | Link | 10.0 | 7.2 | 20.5 | 0.6 | 5.1 | 12.4 |
| Qwen2.5VL-32B | Link | 10.0 | 6.4 | 22.7 | 2.5 | 4.1 | 10.2 |
| MiniCPM-2.6-o | Link | 9.7 | 7.5 | 17.6 | 1.3 | 3.6 | 13.8 |
| Llama4-Scout (109B MoE) | Link | 9.5 | 6.9 | 18.8 | 3.2 | 4.1 | 10.9 |
| MiniCPM-2.6-V | Link | 9.1 | 7.2 | 15.9 | 1.3 | 6.2 | 11.3 |
| LLaVA-OneVision-72B | Link | 9.0 | 8.9 | 9.1 | 4.5 | 4.6 | 14.5 |
| DeepSeek-VL2 | Link | 9.0 | 7.0 | 15.9 | 0.6 | 5.6 | 11.6 |
| LLaVA-OneVision-7B | Link | 8.5 | 6.8 | 14.2 | 2.5 | 4.6 | 10.9 |
| Qwen2.5VL-7B | Link | 8.3 | 7.0 | 13.1 | 2.5 | 3.6 | 12.0 |
| InternVL-3-8B | Link | 8.2 | 6.0 | 15.9 | 1.9 | 5.6 | 8.7 |
| InternVL-3-14B | Link | 8.0 | 7.0 | 11.4 | 1.3 | 5.1 | 11.6 |
| Qwen2.5-Omni-7B | Link | 7.7 | 4.5 | 11.4 | 1.9 | 2.1 | 7.7 |
The values in the table represent the Top-1 accuracy, in %
BibTeX
@inproceedings{
guo2025rbench-v,
title={RBench-V: A Primary Assessment for Visual Reasoning Models
with Multi-modal Outputs},
author={Meng-Hao Guo, Xuanyu Chu, Qianrui Yang, Zhe-Han Mo, Yiqing Shen,
Pei-Lin Li, Xinjie Lin, Jinnian Zhang, Xin-Sheng Chen, Yi Zhang, Kiyohiro Nakayama,
Zhengyang Geng, Houwen Peng, Han Hu, Shi-Min Hu},
year={2025},
eprint={},
archivePrefix={},
primaryClass={},
url={},
}
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