data_source stringclasses 1
value | prompt listlengths 1 1 | images images listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|---|
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is shown. Evaluate each $\\int_0^2 f(x) d x$ by interpreting it in terms of areas.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"gt_answer": "4",
"id": "scibench_multimodal--100",
"mc_options": null,
"original_question": "<image>The graph of $f$ is shown. Evaluate each $\\int_0^2 f(x) d x$ by interpreting it in terms of areas."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is shown. Evaluate each $\\int_0^5 f(x) d x$ by interpreting it in terms of areas.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"gt_answer": "10",
"id": "scibench_multimodal--101",
"mc_options": null,
"original_question": "<image>The graph of $f$ is shown. Evaluate each $\\int_0^5 f(x) d x$ by interpreting it in terms of areas."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is shown. Evaluate each $\\int_5^7 f(x) d x$ by interpreting it in terms of areas.",
"role": "user"
}
] | {
"ground_truth": "-3",
"style": "rule"
} | {
"gt_answer": "-3",
"id": "scibench_multimodal--102",
"mc_options": null,
"original_question": "<image>The graph of $f$ is shown. Evaluate each $\\int_5^7 f(x) d x$ by interpreting it in terms of areas."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is shown. Evaluate each $\\int_0^9 f(x) d x$ by interpreting it in terms of areas.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"gt_answer": "2",
"id": "scibench_multimodal--103",
"mc_options": null,
"original_question": "<image>The graph of $f$ is shown. Evaluate each $\\int_0^9 f(x) d x$ by interpreting it in terms of areas."
} | |
scibench_multimodal | [
{
"content": "<image>Shown is the power consumption in the province of Ontario, Canada, for December 9, 2004 ( $P$ is measured in megawatts; $t$ is measured in hours starting at midnight). Using the fact that power is the rate of change of energy, estimate the energy used on that day.",
"role": "user"
}
] | {
"ground_truth": "$4.75 \\times 10^5$ megawatt-hours",
"style": "rule"
} | {
"gt_answer": "$4.75 \\times 10^5$ megawatt-hours",
"id": "scibench_multimodal--104",
"mc_options": null,
"original_question": "<image>Shown is the power consumption in the province of Ontario, Canada, for December 9, 2004 ( $P$ is measured in megawatts; $t$ is measured in hours starting at midnight). Using t... | |
scibench_multimodal | [
{
"content": "<image>Use the given graph of $f$ to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.",
"role": "user"
}
] | {
"ground_truth": "8",
"style": "rule"
} | {
"gt_answer": "8",
"id": "scibench_multimodal--105",
"mc_options": null,
"original_question": "<image>Use the given graph of $f$ to find the Riemann sum with six subintervals. Take the sample points to be left endpoints."
} | |
scibench_multimodal | [
{
"content": "<image>Use the given graph of $f$ to find the Riemann sum with six subintervals. Take the sample points to be midpoints.",
"role": "user"
}
] | {
"ground_truth": "5.7",
"style": "rule"
} | {
"gt_answer": "5.7",
"id": "scibench_multimodal--106",
"mc_options": null,
"original_question": "<image>Use the given graph of $f$ to find the Riemann sum with six subintervals. Take the sample points to be midpoints."
} | |
scibench_multimodal | [
{
"content": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 3^{-}} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"gt_answer": "1",
"id": "scibench_multimodal--107",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 3^{-}} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>A population of honeybees increased at a rate of $r(t)$ bees per week, where the graph of $r$ is as shown. Use the Midpoint Rule with six subintervals to estimate the increase in the bee population during the first 24 weeks.",
"role": "user"
}
] | {
"ground_truth": "72400",
"style": "rule"
} | {
"gt_answer": "72400",
"id": "scibench_multimodal--108",
"mc_options": null,
"original_question": "<image>A population of honeybees increased at a rate of $r(t)$ bees per week, where the graph of $r$ is as shown. Use the Midpoint Rule with six subintervals to estimate the increase in the bee population during ... | |
scibench_multimodal | [
{
"content": "<image>Find the area of the shaded region.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{32}{3}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{32}{3}$",
"id": "scibench_multimodal--109",
"mc_options": null,
"original_question": "<image>Find the area of the shaded region."
} | |
scibench_multimodal | [
{
"content": "<image>Find the area of the shaded region.",
"role": "user"
}
] | {
"ground_truth": "$e-(1 / e)+\\frac{10}{3}$",
"style": "rule"
} | {
"gt_answer": "$e-(1 / e)+\\frac{10}{3}$",
"id": "scibench_multimodal--110",
"mc_options": null,
"original_question": "<image>Find the area of the shaded region."
} | |
scibench_multimodal | [
{
"content": "<image>Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten secon... | {
"ground_truth": "117 \\frac{1}{3} ft",
"style": "rule"
} | {
"gt_answer": "117 \\frac{1}{3} ft",
"id": "scibench_multimodal--111",
"mc_options": null,
"original_question": "<image>Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use th... | |
scibench_multimodal | [
{
"content": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_1$ about $O A$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{\\pi}{3}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{\\pi}{3}$",
"id": "scibench_multimodal--112",
"mc_options": null,
"original_question": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_1$ about $O A$."
} | |
scibench_multimodal | [
{
"content": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_1$ about $A B$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{\\pi}{3}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{\\pi}{3}$",
"id": "scibench_multimodal--113",
"mc_options": null,
"original_question": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_1$ about $A B$."
} | |
scibench_multimodal | [
{
"content": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_2$ about $O A$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{\\pi}{3}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{\\pi}{3}$",
"id": "scibench_multimodal--114",
"mc_options": null,
"original_question": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_2$ about $O A$."
} | |
scibench_multimodal | [
{
"content": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_2$ about $A B$ about the specified line.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{13\\pi}{45}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{13\\pi}{45}$",
"id": "scibench_multimodal--115",
"mc_options": null,
"original_question": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_2$ about $A B$ about the specified line."
} | |
scibench_multimodal | [
{
"content": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_3$ about $O A$ about the specified line.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{\\pi}{3}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{\\pi}{3}$",
"id": "scibench_multimodal--116",
"mc_options": null,
"original_question": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_3$ about $O A$ about the specified line."
} | |
scibench_multimodal | [
{
"content": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_3$ about $B C$ about the specified line.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{17\\pi}{45}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{17\\pi}{45}$",
"id": "scibench_multimodal--117",
"mc_options": null,
"original_question": "<image>Refer to the figure and find the volume generated by rotating the $\\mathscr{R}_3$ about $B C$ about the specified line."
} | |
scibench_multimodal | [
{
"content": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 3^{+}} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"gt_answer": "4",
"id": "scibench_multimodal--118",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 3^{+}} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>If the region shown in the figure is rotated about the $x$-axis to form a solid, use the Midpoint Rule with $n=4$ to estimate the volume of the solid.",
"role": "user"
}
] | {
"ground_truth": "196",
"style": "rule"
} | {
"gt_answer": "196",
"id": "scibench_multimodal--119",
"mc_options": null,
"original_question": "<image>If the region shown in the figure is rotated about the $x$-axis to form a solid, use the Midpoint Rule with $n=4$ to estimate the volume of the solid."
} | |
scibench_multimodal | [
{
"content": "<image>Estimate the volume if the region is rotated about the $y$-axis. Again use the Midpoint Rule with $n=4$.",
"role": "user"
}
] | {
"ground_truth": "838",
"style": "rule"
} | {
"gt_answer": "838",
"id": "scibench_multimodal--120",
"mc_options": null,
"original_question": "<image>Estimate the volume if the region is rotated about the $y$-axis. Again use the Midpoint Rule with $n=4$."
} | |
scibench_multimodal | [
{
"content": "<image>Find the average value of $f$ on $[0, 8]$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{9}{8}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{9}{8}$",
"id": "scibench_multimodal--121",
"mc_options": null,
"original_question": "<image>Find the average value of $f$ on $[0, 8]$."
} | |
scibench_multimodal | [
{
"content": "<image>Use the Midpoint Rule and the given data to estimate the value of the integral $\\int_1^5 f(x) d x$.",
"role": "user"
}
] | {
"ground_truth": "14.4",
"style": "rule"
} | {
"gt_answer": "14.4",
"id": "scibench_multimodal--122",
"mc_options": null,
"original_question": "<image>Use the Midpoint Rule and the given data to estimate the value of the integral $\\int_1^5 f(x) d x$."
} | |
scibench_multimodal | [
{
"content": "<image>If it is known that $-2 \\leqslant f^{\\prime \\prime}(x) \\leqslant 3$ for all $x$, estimate the error involved in using the Midpoint Rule for an approximation of the integral $\\int_1^5 f(x) d x$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{1}{2}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{1}{2}$",
"id": "scibench_multimodal--123",
"mc_options": null,
"original_question": "<image>If it is known that $-2 \\leqslant f^{\\prime \\prime}(x) \\leqslant 3$ for all $x$, estimate the error involved in using the Midpoint Rule for an approximation of the integral $\\int_1^5 f(x) d x... | |
scibench_multimodal | [
{
"content": "<image>A graph of the temperature in New York City on September 19, 2009 is shown. Use Simpson's Rule with $n=12$ to estimate the average temperature on that day.",
"role": "user"
}
] | {
"ground_truth": "$64.4^{\\circ} \\mathrm{F}$ \\mathrm{F}",
"style": "rule"
} | {
"gt_answer": "$64.4^{\\circ} \\mathrm{F}$ \\mathrm{F}",
"id": "scibench_multimodal--124",
"mc_options": null,
"original_question": "<image>A graph of the temperature in New York City on September 19, 2009 is shown. Use Simpson's Rule with $n=12$ to estimate the average temperature on that day."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of the acceleration $a(t)$ of a car measured in $\\mathrm{ft} / \\mathrm{s}^2$ is shown. Use Simpson's Rule to estimate the increase in the velocity of the car during the 6-second time interval.",
"role": "user"
}
] | {
"ground_truth": "37.73 ft/s",
"style": "rule"
} | {
"gt_answer": "37.73 ft/s",
"id": "scibench_multimodal--125",
"mc_options": null,
"original_question": "<image>The graph of the acceleration $a(t)$ of a car measured in $\\mathrm{ft} / \\mathrm{s}^2$ is shown. Use Simpson's Rule to estimate the increase in the velocity of the car during the 6-second time inte... | |
scibench_multimodal | [
{
"content": "<image>The table (supplied by San Diego Gas and Electric) gives the power consumption $P$ in megawatts in San Diego County from midnight to 6:00 AM on a day in December. Use Simpson's Rule to estimate the energy used during that time period. (Use the fact that power is the derivative of energy.)",... | {
"ground_truth": "10177 megawatt-hours",
"style": "rule"
} | {
"gt_answer": "10177 megawatt-hours",
"id": "scibench_multimodal--126",
"mc_options": null,
"original_question": "<image>The table (supplied by San Diego Gas and Electric) gives the power consumption $P$ in megawatts in San Diego County from midnight to 6:00 AM on a day in December. Use Simpson's Rule to esti... | |
scibench_multimodal | [
{
"content": "<image>Use Simpson's Rule with $n=8$ to estimate the volume of the solid obtained by rotating the region shown in the figure about the $x$-axis.",
"role": "user"
}
] | {
"ground_truth": "190",
"style": "rule"
} | {
"gt_answer": "190",
"id": "scibench_multimodal--127",
"mc_options": null,
"original_question": "<image>Use Simpson's Rule with $n=8$ to estimate the volume of the solid obtained by rotating the region shown in the figure about the $x$-axis."
} | |
scibench_multimodal | [
{
"content": "<image>Use Simpson's Rule with $n=8$ to estimate the volume of the solid obtained by rotating the region shown in the figure about the $y$-axis.",
"role": "user"
}
] | {
"ground_truth": "828",
"style": "rule"
} | {
"gt_answer": "828",
"id": "scibench_multimodal--128",
"mc_options": null,
"original_question": "<image>Use Simpson's Rule with $n=8$ to estimate the volume of the solid obtained by rotating the region shown in the figure about the $y$-axis."
} | |
scibench_multimodal | [
{
"content": "<image>For the function $f$ whose graph is given, state the value of $f(3)$.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"gt_answer": "3",
"id": "scibench_multimodal--129",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state the value of $f(3)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of the concentration function $c(t)$ is shown after a 7-mg injection of dye into a heart. Use Simpson's Rule to estimate the cardiac output.",
"role": "user"
}
] | {
"ground_truth": "5.77 $\\mathrm{L}/\\mathrm{min}$",
"style": "rule"
} | {
"gt_answer": "5.77 $\\mathrm{L}/\\mathrm{min}$",
"id": "scibench_multimodal--130",
"mc_options": null,
"original_question": "<image>The graph of the concentration function $c(t)$ is shown after a 7-mg injection of dye into a heart. Use Simpson's Rule to estimate the cardiac output."
} | |
scibench_multimodal | [
{
"content": "<image>The magnitude of the acceleration vector a is $10 \\mathrm{~cm} / \\mathrm{s}^2$. Use the figure to estimate the normal components of $\\mathbf{a}$.\r\n",
"role": "user"
}
] | {
"ground_truth": "9 $\\mathrm{cm}/\\mathrm{s^2}$",
"style": "rule"
} | {
"gt_answer": "9 $\\mathrm{cm}/\\mathrm{s^2}$",
"id": "scibench_multimodal--131",
"mc_options": null,
"original_question": "<image>The magnitude of the acceleration vector a is $10 \\mathrm{~cm} / \\mathrm{s}^2$. Use the figure to estimate the normal components of $\\mathbf{a}$.\r\n"
} | |
scibench_multimodal | [
{
"content": "<image>In Fig. 21-26, particle 1 of charge $+1.0 \\mu \\mathrm{C}$ and particle 2 of charge $-3.0 \\mu \\mathrm{C}$ are held at separation $L=$ $10.0 \\mathrm{~cm}$ on an $x$ axis. If particle 3 of unknown charge $q_3$ is to be located such that the net electrostatic force on it from particles 1 a... | {
"ground_truth": "$-14$ cm",
"style": "rule"
} | {
"gt_answer": "$-14$ cm",
"id": "scibench_multimodal--132",
"mc_options": null,
"original_question": "<image>In Fig. 21-26, particle 1 of charge $+1.0 \\mu \\mathrm{C}$ and particle 2 of charge $-3.0 \\mu \\mathrm{C}$ are held at separation $L=$ $10.0 \\mathrm{~cm}$ on an $x$ axis. If particle 3 of unknown ch... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 23-49, a small, nonconducting ball of mass $m=1.0 \\mathrm{mg}$ and charge $q=2.0 \\times$ $10^{-8} \\mathrm{C}$ (distributed uniformly through its volume) hangs from an insulating thread that makes an angle $\\theta=30^{\\circ}$ with a vertical, uniformly charged nonconducting shee... | {
"ground_truth": "$5.0$ $\\mathrm{nC} / \\mathrm{m}^2$",
"style": "rule"
} | {
"gt_answer": "$5.0$ $\\mathrm{nC} / \\mathrm{m}^2$",
"id": "scibench_multimodal--133",
"mc_options": null,
"original_question": "<image>In Fig. 23-49, a small, nonconducting ball of mass $m=1.0 \\mathrm{mg}$ and charge $q=2.0 \\times$ $10^{-8} \\mathrm{C}$ (distributed uniformly through its volume) hangs from... | |
scibench_multimodal | [
{
"content": "<image>Fig. 23-31 shows a Gaussian surface in the shape of a cube with edge length $1.40 \\mathrm{~m}$. What is the net flux $\\Phi$ through the surface if $\\vec{E}=(3.00 y \\hat{j}) \\mathrm{N} / \\mathrm{C}$, with $y$ in meters?",
"role": "user"
}
] | {
"ground_truth": "$8.23$ $\\mathrm{~N} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$8.23$ $\\mathrm{~N} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"id": "scibench_multimodal--134",
"mc_options": null,
"original_question": "<image>Fig. 23-31 shows a Gaussian surface in the shape of a cube with edge length $1.40 \\mathrm{~m}$. What is the net flux $\\Phi$ through the surface if $\\v... | |
scibench_multimodal | [
{
"content": "<image>Figure 22-47 shows two parallel nonconducting rings with their central axes along a common line. Ring 1 has uniform charge $q_1$ and radius $R$; ring 2 has uniform charge $q_2$ and the same radius $R$. The rings are separated by distance $d=3.00 R$. The net electric field at point $P$ on th... | {
"ground_truth": "$0.506$",
"style": "rule"
} | {
"gt_answer": "$0.506$",
"id": "scibench_multimodal--135",
"mc_options": null,
"original_question": "<image>Figure 22-47 shows two parallel nonconducting rings with their central axes along a common line. Ring 1 has uniform charge $q_1$ and radius $R$; ring 2 has uniform charge $q_2$ and the same radius $R$. T... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 21-23, three charged particles lie on an $x$ axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If $L_{23}=L_{12}$, what is the ratio $q_1 / q_2$ ?\r\n",
"role": "user"
}
] | {
"ground_truth": "-4.00",
"style": "rule"
} | {
"gt_answer": "-4.00",
"id": "scibench_multimodal--136",
"mc_options": null,
"original_question": "<image>In Fig. 21-23, three charged particles lie on an $x$ axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero.... | |
scibench_multimodal | [
{
"content": "<image>Find $\\iint_S \\mathbf{F} \\cdot \\mathbf{n} d S$, where $\\mathbf{F}(x, y, z)=x \\mathbf{i}+y \\mathbf{j}+z \\mathbf{k}$ and $S$ is the outwardly oriented surface shown in the figure (the boundary surface of a cube with a unit corner cube removed).",
"role": "user"
}
] | {
"ground_truth": "21",
"style": "rule"
} | {
"gt_answer": "21",
"id": "scibench_multimodal--137",
"mc_options": null,
"original_question": "<image>Find $\\iint_S \\mathbf{F} \\cdot \\mathbf{n} d S$, where $\\mathbf{F}(x, y, z)=x \\mathbf{i}+y \\mathbf{j}+z \\mathbf{k}$ and $S$ is the outwardly oriented surface shown in the figure (the boundary surface o... | |
scibench_multimodal | [
{
"content": "<image>Figure 23-51 shows a cross section through a very large nonconducting slab of thickness $d=9.40 \\mathrm{~mm}$ and uniform volume charge density $\\rho=5.80$ $\\mathrm{fC} / \\mathrm{m}^3$. The origin of an $x$ axis is at the slab's center. What is the magnitude of the slab's electric field... | {
"ground_truth": "$0$",
"style": "rule"
} | {
"gt_answer": "$0$",
"id": "scibench_multimodal--138",
"mc_options": null,
"original_question": "<image>Figure 23-51 shows a cross section through a very large nonconducting slab of thickness $d=9.40 \\mathrm{~mm}$ and uniform volume charge density $\\rho=5.80$ $\\mathrm{fC} / \\mathrm{m}^3$. The origin of an ... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 22-69, particle 1 of charge $q_1=1.00 \\mathrm{pC}$ and particle 2 of charge $q_2=-2.00 \\mathrm{pC}$ are fixed at a distance $d=5.00 \\mathrm{~cm}$ apart. In unit-vector notation, what is the net electric field at point $A$?",
"role": "user"
}
] | {
"ground_truth": "$-1.80$ $\\mathrm{~N} / \\mathrm{C} \\hat{\\mathrm{i}} $",
"style": "rule"
} | {
"gt_answer": "$-1.80$ $\\mathrm{~N} / \\mathrm{C} \\hat{\\mathrm{i}} $",
"id": "scibench_multimodal--139",
"mc_options": null,
"original_question": "<image>In Fig. 22-69, particle 1 of charge $q_1=1.00 \\mathrm{pC}$ and particle 2 of charge $q_2=-2.00 \\mathrm{pC}$ are fixed at a distance $d=5.00 \\mathrm{~cm... | |
scibench_multimodal | [
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 0^{-}} g(t)$.",
"role": "user"
}
] | {
"ground_truth": "-1",
"style": "rule"
} | {
"gt_answer": "-1",
"id": "scibench_multimodal--140",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 0^{-}} g(t)$."
} | |
scibench_multimodal | [
{
"content": "<image>In Fig. 21-28a, particles 1 and 2 have charge $20.0 \\mu \\mathrm{C}$ each and are held at separation distance $d=1.50$ $\\mathrm{m}$. What is the magnitude of the electrostatic force on particle 1 due to particle 2? In Fig. 21-28b, particle 3 of charge $20.0 \\mu \\mathrm{C}$ is positioned... | {
"ground_truth": "$35$ $\\mathrm{~N}$",
"style": "rule"
} | {
"gt_answer": "$35$ $\\mathrm{~N}$",
"id": "scibench_multimodal--141",
"mc_options": null,
"original_question": "<image>In Fig. 21-28a, particles 1 and 2 have charge $20.0 \\mu \\mathrm{C}$ each and are held at separation distance $d=1.50$ $\\mathrm{m}$. What is the magnitude of the electrostatic force on par... | |
scibench_multimodal | [
{
"content": "<image>Figure 22-49 shows three circular arcs centered on the origin of a coordinate system. On each arc, the uniformly distributed charge is given in terms of $Q=2.00 \\mu \\mathrm{C}$. The radii are given in terms of $R=10.0 \\mathrm{~cm}$. What is the magnitude of the net electric field at the ... | {
"ground_truth": "$1.62$ $10^6 \\mathrm{~N} / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$1.62$ $10^6 \\mathrm{~N} / \\mathrm{C}$",
"id": "scibench_multimodal--142",
"mc_options": null,
"original_question": "<image>Figure 22-49 shows three circular arcs centered on the origin of a coordinate system. On each arc, the uniformly distributed charge is given in terms of $Q=2.00 \\mu \\ma... | |
scibench_multimodal | [
{
"content": "<image>Figure 22-37 shows two charged particles on an $x$ axis: $-q=$ $-3.20 \\times 10^{-19} \\mathrm{C}$ at $x=-3.00 \\mathrm{~m}$ and $q=3.20 \\times 10^{-19} \\quad \\mathrm{C}$ at $x=+3.00 \\mathrm{~m}$. What is the magnitude of the net electric field produced at point $P$ at $y=4.00 \\mathrm... | {
"ground_truth": "$1.38$ $10^{-10} \\mathrm{~N} / \\mathrm{C} $",
"style": "rule"
} | {
"gt_answer": "$1.38$ $10^{-10} \\mathrm{~N} / \\mathrm{C} $",
"id": "scibench_multimodal--143",
"mc_options": null,
"original_question": "<image>Figure 22-37 shows two charged particles on an $x$ axis: $-q=$ $-3.20 \\times 10^{-19} \\mathrm{C}$ at $x=-3.00 \\mathrm{~m}$ and $q=3.20 \\times 10^{-19} \\quad \\m... | |
scibench_multimodal | [
{
"content": "<image>Figure 23-35 shows a closed Gaussian surface in the shape of a cube of edge length $2.00 \\mathrm{~m}$, with one corner at $x_1=5.00 \\mathrm{~m}, y_1=4.00$ $\\mathrm{m}$. The cube lies in a region where the electric field vector is given by $\\vec{E}=-3.00 \\hat{i}-4.00 y^2 \\hat{j}+3.00 \... | {
"ground_truth": "$-1.70$ $\\mathrm{nC}$",
"style": "rule"
} | {
"gt_answer": "$-1.70$ $\\mathrm{nC}$",
"id": "scibench_multimodal--144",
"mc_options": null,
"original_question": "<image>Figure 23-35 shows a closed Gaussian surface in the shape of a cube of edge length $2.00 \\mathrm{~m}$, with one corner at $x_1=5.00 \\mathrm{~m}, y_1=4.00$ $\\mathrm{m}$. The cube lies i... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 23-56, a nonconducting spherical shell of inner radius $a=2.00 \\mathrm{~cm}$ and outer radius $b=2.40 \\mathrm{~cm}$ has (within its thickness) a positive volume charge density $\\rho=A / r$, where $A$ is a constant and $r$ is the distance from the center of the shell. In addition,... | {
"ground_truth": "$1.79$ $10^{-11} \\mathrm{C} / \\mathrm{m}^2$",
"style": "rule"
} | {
"gt_answer": "$1.79$ $10^{-11} \\mathrm{C} / \\mathrm{m}^2$",
"id": "scibench_multimodal--145",
"mc_options": null,
"original_question": "<image>In Fig. 23-56, a nonconducting spherical shell of inner radius $a=2.00 \\mathrm{~cm}$ and outer radius $b=2.40 \\mathrm{~cm}$ has (within its thickness) a positive v... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 23-33, a proton is a distance $d / 2$ directly above the center of a square of side $d$. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge $d$.",
"role": "user"
}
] | {
"ground_truth": "$3.01$ $\\mathrm{nN} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$3.01$ $\\mathrm{nN} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"id": "scibench_multimodal--146",
"mc_options": null,
"original_question": "<image>In Fig. 23-33, a proton is a distance $d / 2$ directly above the center of a square of side $d$. What is the magnitude of the electric flux through the sq... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 22-35, the four particles form a square of edge length $a=5.00 \\mathrm{~cm}$ and have charges $q_1=+10.0 \\mathrm{nC}, \\quad q_2=-20.0 \\mathrm{nC}, \\quad q_3=$ $+20.0 \\mathrm{nC}$, and $q_4=-10.0 \\mathrm{nC}$. In unitvector notation, what net electric field do the particles pr... | {
"ground_truth": "$1.02$ $\\mathrm{~N} / \\mathrm{C} \\hat{\\mathrm{j}}$",
"style": "rule"
} | {
"gt_answer": "$1.02$ $\\mathrm{~N} / \\mathrm{C} \\hat{\\mathrm{j}}$",
"id": "scibench_multimodal--147",
"mc_options": null,
"original_question": "<image>In Fig. 22-35, the four particles form a square of edge length $a=5.00 \\mathrm{~cm}$ and have charges $q_1=+10.0 \\mathrm{nC}, \\quad q_2=-20.0 \\mathrm{nC... | |
scibench_multimodal | [
{
"content": "<image>Figure 23-42 is a section of a conducting rod of radius $R_1=1.30 \\mathrm{~mm}$ and length $L=$ $11.00 \\mathrm{~m}$ inside a thin-walled coaxial conducting cylindrical shell of radius $R_2=10.0 R_1$ and the (same) length $L$. The net charge on the rod is $Q_1=+3.40 \\times 10^{-12} \\math... | {
"ground_truth": "$0.214$ $\\mathrm{~N} / \\mathrm{C} $",
"style": "rule"
} | {
"gt_answer": "$0.214$ $\\mathrm{~N} / \\mathrm{C} $",
"id": "scibench_multimodal--148",
"mc_options": null,
"original_question": "<image>Figure 23-42 is a section of a conducting rod of radius $R_1=1.30 \\mathrm{~mm}$ and length $L=$ $11.00 \\mathrm{~m}$ inside a thin-walled coaxial conducting cylindrical she... | |
scibench_multimodal | [
{
"content": "<image>A graph of the temperature in New York City on September 19, 2009 is shown. Use Simpson's Rule with $n=12$ to estimate the average temperature on that day.",
"role": "user"
}
] | {
"ground_truth": "64.4 $^{\\circ} \\mathrm{F}$",
"style": "rule"
} | {
"gt_answer": "64.4 $^{\\circ} \\mathrm{F}$",
"id": "scibench_multimodal--149",
"mc_options": null,
"original_question": "<image>A graph of the temperature in New York City on September 19, 2009 is shown. Use Simpson's Rule with $n=12$ to estimate the average temperature on that day."
} | |
scibench_multimodal | [
{
"content": "<image>In Fig. 22-51, two curved plastic rods, one of charge $+q$ and the other of charge $-q$, form a circle of radius $R=$ $8.50 \\mathrm{~cm}$ in an $x y$ plane. The $x$ axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. If $q=15.0 \\mathrm{... | {
"ground_truth": "$23.8$ $\\mathrm{~N} / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$23.8$ $\\mathrm{~N} / \\mathrm{C}$",
"id": "scibench_multimodal--150",
"mc_options": null,
"original_question": "<image>In Fig. 22-51, two curved plastic rods, one of charge $+q$ and the other of charge $-q$, form a circle of radius $R=$ $8.50 \\mathrm{~cm}$ in an $x y$ plane. The $x$ axis pass... |
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