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values | question stringlengths 39 1.54k | image imagewidth (px) 74 4.95k ⌀ | answer stringlengths 1 103 |
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Physics | As shown in the figure, in the coordinate system Oxyz, the x-axis and z-axis lie in the plane of the paper, while the y-axis is perpendicular to the paper, pointing inward. Two infinitely large metal plates P and Q are located at x = -d and x = d, respectively. A uniform magnetic field of magnitude B lies in the Oxz pl... | $\frac{qBd}{2m\cos\alpha}$ | |
Physics | As shown in the figure, triangle Oab is a right-angled triangle with its two perpendicular sides formed by insulated dielectric rods, and the hypotenuse ab formed by a thin metallic rod. The length of Ob is equal to ab/2 = l. The triangle is placed in a uniform magnetic field with magnetic induction B, which is perpend... | $Bl^2\omega$ | |
Physics | As shown in the figure, a closed wire loop consists of 12 straight segments, each of length l. Except for segments 1-8, 2-9, and 3-4 (represented by dashed lines), which have negligible resistance, the remaining nine segments each have a resistance of r. A uniform magnetic field B is directed perpendicular to the plane... | $\frac{2B^2 l^3 v}{r}$ | |
Physics | A straight conductor MN and a metal ring with radius r are placed overlapping on a smooth horizontal surface. The straight conductor MN is fixed and located at a distance of r/2 from the center O of the stationary metal ring, and there is good electrical contact at the point where the ring intersects the conductor. A u... | $\frac{27}{32\pi + 72\sqrt{3}} \cdot \frac{rB_{0}^{2}}{2\pi m_{0}r_{0}}$ | |
Physics | A thin wire forms a loop along the edges of one face of a cube, with its self-inductance denoted as L₁, as shown in diagram (a). Using the same wire, a loop is formed along the edges of the cube, yielding a self-inductance of L₂, as shown in diagram (b). Determine the self-inductance of a loop formed using the same wir... | 3(L_2 - L_1) | |
Physics | A uniformly thick and homogeneous conductive wire with a nonzero constant resistivity is bent into an equilateral triangular loop with side length \( a \). The triangle rotates at a constant angular velocity \( \omega \) about one of its sides, AB, which serves as the axis of rotation. A uniform magnetic field with mag... | $\frac{\sqrt{3}}{12}B\omega a^2\sin\omega t$ | |
Physics | As shown in the figure, two identical metal rings each have a radius R, mass m, and resistance r. They are both placed in the same uniform magnetic field, with the field direction perpendicular to the plane of the rings and pointing into the page. The magnetic flux density is $B_0$. The contact points A and C between t... | $\frac{9\sqrt{3}R^3B_0^2}{10mr}$ | |
Physics | As shown in the diagram, the circuit contains two resistors each with resistance \( R_1 = R_2 = R \), and one capacitor with capacitance \( C \); two ideal AC ammeters, \( A_1 \) and \( A_2 \), measure currents of 0.3 A and 0.2 A respectively. The circuit is connected to an AC power supply with an RMS voltage of 36 V a... | $13.5\mathrm{\mu F}$ | |
Physics | As shown in the figure, the inductances of the two coils are $L_1 = 10,\mathrm{mH}$ and $L_2 = 20,\mathrm{mH}$; the capacitances of the two capacitors are $C_1 = 10,\mathrm{nF}$ and $C_2 = 5,\mathrm{nF}$; the resistor has resistance $R = 100,\mathrm{k\Omega}$. The switch $S$ has been closed for a long time. It is then ... | -0.1 (A) | |
Physics | A U-shaped glass capillary tube with uniform thickness and open ends is placed in a vertical plane in an atmosphere with pressure \( p_0 \). The two vertical arms of the tube each have a height of \( h \), and the horizontal section connecting them has a length of \( 2h \). The tube has a radius \( r \) (where \( r << ... | $\sqrt{\dfrac{3(3p_0 + 2\rho gh)}{35\rho h^2}}$ | |
Physics | (Multiple Choice) The diagram shows a vertical cross-section of a circular pool. AB is the diameter of the water surface, MN is the diameter of the pool bottom, and O is the center of the circular pool bottom. It is known that ON is 11.4 m, AM and BN are sloped edges, the water depth is 5.0 m, the refractive index of w... | c，d | |
Physics | The diagram shows a tank filled with a liquid of refractive index \( n \), with a symmetric, ridge-shaped thin transparent cover ADB placed over its central part. The cover has a vertex angle of \( 2\varphi \), encloses air inside, and is fully submerged in the liquid. A bright point C is located at the midpoint of the... | $\sqrt{n^2 -1}-1$ | |
Physics | As shown in the figure, in a vacuum, there is a small sphere with a uniform texture, radius \( r \), and refractive index \( n \) (where \( n > n_0 \), and \( n_0 \) is the refractive index of vacuum). A narrow laser beam with frequency \( \nu \) travels in a straight line BC through the vacuum. The line segment CD pas... | $\frac{lh\nu}{r^{2}}\left[n-\sqrt{1-\frac{(n^{2}-1)l^{2}}{r^{2}-l^{2}}}\right]$ | |
Physics | As shown in the figure, L₁ and L₂ are two coaxial thin convex lenses with a common principal axis OO’. Lens L₁ has a focal length of f₁ = 10 cm and an aperture (diameter) of d₁ = 4.0 cm; lens L₂ has a focal length of f₂ = 5.0 cm and an aperture of d₂ = 2.0 cm. The distance between the two lenses is a = 30 cm. AB is a u... | 2.0 (cm) | |
Physics | A slender rod ABC rests against a step in a vertical plane, with end A free to slide along the horizontal ground toward the step, while the rod remains in contact with the edge of the step. When the angle between the rod and the horizontal ground is $\phi$ (as shown in the figure), point B is exactly at the edge of the... | $\frac{\sqrt{4-\cos^2 \phi}}{\sin\phi}$ | |
Physics | Two rods, each of length $l$, are connected by a hinge at point $P$, as shown in the figure. One end of the first rod is fixed at point $O$ via a hinge, while the free end $Q$ of the second rod begins to move with a constant velocity $v$ in both magnitude and direction. At the initial moment, the velocity $v$ is direct... | $\dfrac{v^2}{4l\sin^2 \alpha \cos \alpha}$ | |
Physics | Two motorboats are towing a barge, with their velocities given by $v_1$ and $v_2$, respectively. The angle between the two velocity vectors is $\alpha$, and at this moment, the velocity vectors $v_1$ and $v_2$ are aligned with the directions in which the motorboats are moving, as shown in the figure. Determine the magn... | $\dfrac{\sqrt{v_1^2+v_2^2-2v_1 v_2 \cos\alpha}}{\sin \alpha}$ | |
Physics | As shown in the figure, a light rope of length l has identical small balls of mass m attached to both ends, and a third ball of mass M attached at the center; all three balls are initially at rest on a smooth horizontal surface, with the rope fully stretched. Now, the central ball M is given an impulse, resulting in an... | $\dfrac{M^2mv^2}{(M+2m)^2l}$ | |
Physics | As shown in the figure, a prism ABC with a triangular cross-section is constrained to move along a smooth track such that its edge AB can only slide along the smooth rail DE. A smooth small ball, having the same mass m as the prism ABC, moves in the same horizontal plane along a direction perpendicular to the rail DE a... | $\dfrac{2v_0}{3}$ | |
Physics | As shown in the figure, a uniform solid cylinder of mass m and radius R is wedged between a wooden plank and a vertical wall. The coefficient of kinetic friction between the cylinder and both the wall and the plank is 0.75. The plank is very light and its mass can be neglected. One end of the plank, point O, is connect... | $\dfrac{25Rm}{4L}$ | |
Physics | A uniform thin wooden rod of length $l$ is suspended vertically by a fine thread and positioned above the horizontal surface of water in a bucket, as shown in the figure. As the bucket is slowly raised, the rod gradually becomes submerged in water. When the submerged depth of the rod exceeds a certain value $h$, the ro... | $l\left(1-\sqrt{1-\dfrac{\rho}{\rho_0}}\right)$ | |
Physics | Rod AB is placed inside a cylindrical container. Point A of the rod is hinged at the junction between the cylinder wall and the bottom, while point C of the rod rests against the edge of the cylinder. Both points A and C lie in a vertical plane that passes through the axis of the cylinder, as shown in the figure. The r... | $\frac{\tan\frac{\varphi}{2}}{\sqrt{1+\cot^{2}\alpha\cos^{2}\frac{\varphi}{2}}}$ | |
Physics | Three strings are floating on the water surface with their endpoints connected, as shown in the figure. Strings 1 and 2 are each 1.5 cm long, and string 3 is 1 cm long. A certain impurity is dropped at point A inside the circular region, causing the surface tension coefficient of the water at that point to decrease by ... | 0(N); 1.67e-4(N); 1.67e-4(N) | |
Physics | Mercury is poured onto a clean, horizontal, flat glass plate, and due to gravity and surface tension, it approximately forms a circular disk shape (with its sides bulging outward). A vertical cross-section through the axis of the disk is shown in the figure. Given the density of mercury $\rho = 13.6 \times 10^3 \mathrm... | 3e-3 (m) | |
Physics | In the figure, object a is a fixed uniformly charged sphere with radius R, and O is its center. Given that the electric potential on the sphere's surface is U = 1000 V when the potential at infinity is taken to be zero, an electron b is located near a point O' far from the center O. The electron is moving toward sphere... | $\dfrac{\sqrt{6}}{2}R$ | |
Physics | A square network made of uniform resistive wires, as shown in the figure, consists of 9 identical small squares, with each side of a small square having a resistance of $r = 8\,\Omega$. A battery with an electromotive force of $E = 5.7\,\mathrm{V}$ and negligible internal resistance is connected to the network. If poin... | 0.267 (A) | |
Physics | As shown in the figure, $R_1 = 2\Omega$, $R_2 = R_3 = 6\Omega$, the total resistance of $R_4$ is $6\Omega$, and the internal resistance of the power supply is $r = 1\Omega$. When switch K is moved to the upper position, the voltmeter reads 5V. When the sliding contact is set at a certain position, the power consumed by... | 2 (W) | |
Physics | In the circuit shown, all power sources have zero internal resistance, and points B and C are connected to the right to an infinite network composed of alternating $1.0\Omega$ and $2.0\Omega$ resistors; determine the amount of charge on the plate of the $10\mathrm{\mu F}$ capacitor that is connected to point D. | 1.3e-4 (C) | |
Physics | As shown in the left diagram, the resistors $R_1$ and $R_2$ each have a resistance of $1\mathrm{k\Omega}$, and the electromotive force is $E = 6\,\mathrm{V}$. Two identical diodes $D$ are connected in series within the circuit, and the $I_D$-$U_D$ characteristic curve of diode $D$ is provided in the right diagram. Calc... | 16 (mW) | |
Physics | Modern material growth and microfabrication techniques have enabled the creation of microstructured semiconductor devices that confine the motion of electrons within a single plane (two-dimensional), allowing electrons to travel through the device like bullets, unaffected by scattering from impurity atoms. This propert... | $\frac{mv}{3qR}$ | |
Physics | As shown in the figure, two plane mirrors A and B have their reflecting surfaces perpendicular to the plane of the paper, and the line of intersection between the two mirrors passes through point O in the diagram. The angle between the two mirror surfaces is $\alpha = 15^\circ$. From point C on mirror A, a light ray is... | 9.1e-9 (s) | |
Physics | A thick glass tank has a bottom thickness of 5 cm and contains water to a depth of 4 cm, as shown in the figure. Given that the refractive indices of glass and water are 1.8 and 1.33 respectively, what is the apparent distance from the water surface to the bottom surface of the glass tank when viewed vertically from ab... | 6.34 (cm) | |
Physics | A horizontal parallel-plane glass plate H, 3.0 cm thick and with a refractive index of n = 1.5, has a small object S located 2.0 cm below its bottom surface. Above the glass plate is a thin convex lens L with a focal length f = 30 cm, and its principal axis is perpendicular to the surface of the glass plate. The object... | 1.0 (cm) | |
Physics | A black sphere with radius R is placed inside a cylindrical tube whose inner surface reflects but does not absorb light. A point light source S is located at a distance 2R from the center of the sphere O, with both O and S lying along the axis of the cylinder, as shown in the figure. To ensure that all light emitted by... | $\dfrac{2\sqrt{3}}{3}R$ | |
Physics | As shown in the figure, a narrow monochromatic light beam is incident on two parallel glass plates. The beam is parallel to the optical axis $OO_1$, which is perpendicular to the glass plates and passes through their center. The beam is at a distance $R = 3\,\mathrm{cm}$ from the axis, and the thickness of the glass pl... | 1.91° | |
Physics | As shown in the figure, in a Lloyd's mirror experiment, a point light source S is located 2 mm above the mirror plane; the mirror is positioned midway between the light source and the screen. The length of the mirror is l = 40 cm, the distance between the screen and the light source is D = 1.5 m, and the wavelength of ... | 12.25 | |
Physics | Three identical capacitors are connected as shown in the diagram. Initially, capacitor 1 carries a charge Q with its upper plate positively charged, while capacitors 2 and 3 are uncharged. A wire is used to connect points a and b; then a and b are disconnected, and points a and c are connected; after disconnecting a an... | Q/12 | |
Physics | In the network shown in the figure, the current values and directions on some branches, certain component parameters, and the electric potentials at junction points are known (all relevant values and parameters are marked in the figure). Using the given data and parameters, determine the magnitude of the current in the... | 2 (A) | |
Physics | The cross-section of a thermometer is shown in the diagram. It is known that the thin mercury column A is located at a distance of 2R from the vertex O of the cylindrical surface, where R is the radius of the cylindrical surface. Point C represents the position of the central axis of the cylinder. The refractive index ... | 3 | |
Physics | A smooth horizontal circular table has a radius R = 1.00 m and a vertical post fixed near its center O. The intersection between the post and the tabletop forms a convex, smooth, closed curve C, as shown in the figure. A soft, light, inextensible string has one end fixed to a point on curve C, and the other end is tied... | 2.5 (m) | |
Physics | In certain heavy machinery and lifting equipment, a double-block electromagnetic brake is commonly used. Its simplified schematic diagram is shown in the figure, with $O_1$ and $O_2$ as fixed hinges. When the power is on, the lever A is pressed downward, pulling spring S through hinges $C_1$, $C_2$, and $C_3$, causing ... | 1.49e4 (N/m) | |
Physics | A cylinder A with radius R rests stationary on a horizontal surface and is in contact with a vertical wall. Another thinner cylinder B, having the same mass as A and radius r, is placed on top of cylinder A such that it also touches the wall, as shown in the figure. Cylinder A is held in place by hand while placing B, ... | 0.289940828402367 | |
Physics | A pendulum with a string of length l (with the bob considered a point mass and the string's mass negligible) is set up such that a fixed peg is placed at point C on the vertical line passing through the pivot point O, at a distance x below O (where x < l), as shown in the figure. As the pendulum swings, the string may ... | 0.464l | |
Physics | A rigid, uniform, thin circular ring with radius R and mass $m_0$ is initially at rest on a smooth horizontal table. There is a small hole $P_0$ on the ring, and a particle of mass m located on the table can freely pass through this hole. Initially, the particle enters the ring through hole $P_0$ with velocity v and un... | $\dfrac{2m}{m+m_0}v\sin\dfrac{\pi}{N+1}$ | |
Physics | Three identical, smooth-surfaced small balls labeled A, B, and C are involved in the setup. Balls B and C are suspended from the ceiling by two massless, inextensible strings, each with a length of L = 2.00 m, such that the two balls just touch each other. A right-handed coordinate system Oxyz is established with the p... | 1.13 (m) | |
Physics | Three uniform rigid rods, each 2.00 meters in length, form an equilateral triangular frame ABC. Point C is suspended from a frictionless horizontal axis, allowing the entire frame to rotate about this axis. Rod AB serves as a track on which an electric toy squirrel can move, as shown in the figure. It is observed that ... | 2.64 (s) | |
Physics | A massless inextensible string passes through a bead of mass m (considered as a particle). The lower end of the string is fixed at point A, while the upper end is attached to a light ring that can slide along a fixed horizontal rod (the mass of the ring and the friction between the ring and the rod are negligible). The... | $\sqrt{2gL\left(1-\dfrac{mg}{2T}\right)}$ | |
Physics | Three steel balls A, B, and C are connected by two light, rigid rods of length l, standing vertically on a horizontal surface as shown in the figure. The mass of ball A is 2m, and the masses of balls B and C are each m. There is a vertical wall located at a horizontal distance $a = \dfrac{5\sqrt{2}}{8}l$ from the rods.... | $\dfrac{1}{8}\sqrt{(38+45\sqrt{2})gl}$ | |
Physics | As shown in the figure, an n-layer bracket is composed of identical triangular plates connected by hinges, with two forces of magnitude P applied at the top; neglecting the weight of the triangular plates, determine the magnitude of the horizontal component of the reaction force at the fixed hinge support A. | 0.5P | |
Physics | Twenty identical resistors, each with resistance R, are connected as shown in the diagram; determine the equivalent resistance between points A and B. | 2R | |
Physics | A tetrahedral framework is composed of uniform wires made of the same material and having identical cross-sectional areas, with each edge having a resistance of a, b, or c as shown in the diagram. Determine the equivalent resistance between points A and B. | $\dfrac{1}{2}\left(\dfrac{ab}{a+b}+\dfrac{ac}{a+c}\right)$ | |
Physics | As shown in the figure, a smooth hemispherical container with diameter a has its edge just touching a smooth vertical wall. A uniform straight rod AB has its end A resting against the wall and end B in contact with the bottom of the container. When the rod is inclined at an angle of 60° to the horizontal, it remains in... | $a\left(1+\dfrac{\sqrt{13}}{13}\right)$ | |
Physics | A uniform rod AB is placed on two inclined planes that are perpendicular to each other, as shown in the figure. Assuming the angle of friction at each contact surface is $\varphi$, determine the possible range of the angle $\theta$ between the rod AB and the inclined plane AO when the system is in equilibrium. It is gi... | $\alpha - 2\varphi \leq \theta \leq \alpha + 2\varphi$ | |
Physics | As shown in the left diagram, it is a common-emitter single-stage amplifier circuit, where \( E = 6\,\mathrm{V} \), \( R_b = 270\,\mathrm{k\Omega} \), and \( R_c = 2\,\mathrm{k\Omega} \); given that the transistor's output characteristic curves are shown in the right diagram, determine the collector voltage \( U_c \). | Approximately 3.2 (V) (3.1 to 3.3 are all correct) | |
Physics | The correct way to use a pressure cooker (as shown in the left diagram) is as follows: after sealing the cooker with its lid, heat it until the water inside begins to boil, then attach the pressure regulator weight. At this point, it can be assumed that all the air inside has been expelled and only saturated steam rema... | about 114.5°C (114°C to 115°C are all correct) | |
Physics | A toy train is composed of many connected cars and moves at a constant speed along a horizontal track before entering a vertical loop-the-loop (as shown in the figure). The total length of the train is \( L \), and the radius of the loop is \( R \), where \( R \) is much larger than the length of an individual car, but... | $\sqrt{gR\left(3+\dfrac{4\pi R}{L}\right)}$ | |
Physics | Three steam trains are moving at constant speeds along a straight railway track. Three streams of steam rings blown from the trains are photographed from above, as shown in the image. The first train is traveling at 50 km/h, and the second at 70 km/h, with their directions of motion indicated by arrows in the image. De... | 40 (km/h) | |
Counting | How many triangles are there in the given figure? | 24 | |
Counting | In the figure, there are six circles whose outlines divide the space into multiple regions, with each region lying inside a certain number of circles. What is the maximum number of circles that cover a single region in the diagram? | 5 | |
Counting | Which of the four colors covers the largest area? | Yellow | |
Counting | How many unit squares does the line segment pass through in the given grid diagram? | 16 | |
Counting | The figure shows a polygon on a grid diagram; please calculate how many grid cells are completely contained within the polygon. | 7 | |
Counting | How many bricks are missing from the wall? | 6 | |
Counting | How many 2×2 squares are there in this figure? | 8 | |
Counting | How many lines in the figure will each of the segments AB, AC, AD, and AE intersect respectively? | 3, 4, 3, 2 | |
Counting | First, draw a line segment connecting points A and C in the figure (the segment passes through point B). How many triangles are formed in the new figure? (Note: A large triangle can consist of several smaller triangles.) | 10 | |
Counting | How many quadrilaterals are there in the picture in total? | 150 | |
Counting | In the figure, there are a total of ( ) triangles. | 10 | |
Counting | How many rectangles are there in the figure? | 8 | |
Counting | How many circles are there in the image? | 5 | |
Counting | In the picture, there are ( ) rectangles and ( ) circles. | 10；4 | |
Counting | There are ( ) rectangles, ( ) triangles, and ( ) circles in the picture. | 7；9；5 | |
Counting | In the picture, there are ( ) triangles and ( ) parallelograms. | 10；4 | |
Counting | In the picture, there are ( ) rectangles and ( ) triangles. | 9；12 | |
Counting | How many different routes are there from Xiaoqiang's home to the sports stadium? | 5 | |
Counting | The diagram shows a floor made up of three different types of tiles labeled Type 1, Type 2, and Type 3. How many tiles of each type are used in total? | 12,16,8 | |
Counting | If the area of each square is 1 cm², what is the total area of the shaded region? | 35 | |
Counting | How many bricks are missing in the diagram? | 9 | |
Counting | How many "X" symbols are there in the image in total? | 120 | |
Counting | Given triangle ABC, two points D and E are chosen on line segment BC, and lines AD and AE are drawn; two points F and G are chosen on line segment AC, and lines BF and BG are drawn. How many quadrilaterals are there in the resulting figure? | Not supported with pagination yet | 9 |
Counting | Given triangle ABC, two points D and E are selected on line segment BC (with D being closer to point B), and lines AD and AE are drawn. Two points F and G are selected on line segment AC (with F being closer to point C), and lines BF and BG are drawn. Line BF intersects AD at point H and AE at point J; line BG intersec... | Not supported with pagination yet | 4, 4, 4, 4 |
Counting | Given triangle AHK, point B lies on segment AH, points I and J lie on segment HK, and point E lies on segment AK. Lines AI and BE intersect at point C, and lines HE and AI intersect at point G. Similarly, lines AJ and BE intersect at point D, and lines AJ and HE intersect at point F. How many triangles are there in the... | Not supported with pagination yet | 24 |
Counting | How many triangles can be found in the figure? | 29 | |
Counting | How many triangles are there in the figure? | 35 | |
Counting | How many triangles are there in the diagram? | 15 | |
Counting | As shown in the figure, there are 20 game pieces placed on graph paper (each red dot represents one piece). Using these pieces as vertices, how many distinct squares can be formed? | 21 | |
Counting | How many triangles are there in the diagram? | 15 | |
Counting | In triangle ABC, points G and H are selected on side AB, and point D is selected on side AC. Lines CG and CH intersect BD at points E and F, respectively. How many triangles are there in the figure? | Not supported with pagination yet | 15 |
Counting | The square in the diagram is divided into 9 equal smaller squares, forming a total of 16 vertices. By selecting any 3 non-collinear points among these vertices, triangles can be formed. Among all such triangles, how many have the same area as the shaded triangle? | 48 | |
Counting | How many triangles are there in the diagram? | 45 | |
Counting | There are 16 points arranged in a 4×4 grid forming a square on a plane, with equal spacing between adjacent points along each row and column, and a nail is placed at each point. Using these points as vertices and connecting them with lines to form squares, how many distinct squares can be formed in total? | Not supported with pagination yet | 20 |
Counting | Xiao Wang places several identical equilateral triangle paper pieces on a table. In the first round, he places 1 piece; in the second round, he places 3 more pieces around the first triangle; in the third round, he places additional pieces around the shape formed in the second round, and so on. The placement rule is: e... | Not supported with pagination yet | 571 |
Counting | How many trapezoids are there in the diagram in total? | 28 | |
Counting | What is the maximum number of regions into which a rectangle can be divided by drawing three circles entirely inside it (the circles may be tangent to the rectangle)? | Not supported with pagination yet | 15 |
Counting | How many triangles are there in the diagram? | 15 | |
Counting | How many triangles are there in the figure? | 76 | |
Counting | Given a regular pentagon with points A, B, C, D, and E as the midpoints of its five sides, if every pair of these points is connected by a line segment, how many trapezoids are formed in the resulting figure? | Not supported with pagination yet | 35 |
Counting | Given a regular pentagon with points A, B, C, D, and E being the midpoints of its sides, how many trapezoids are formed by connecting the following pairs of points: AC, AD, BD, BE, and CE? | Not supported with pagination yet | 15 |
Counting | As shown in the figure, the three large triangles are all equilateral triangles; how many triangles are there in total in the figure? | 30 | |
Counting | How many triangles are there in the diagram? | 17 |
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