{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"専門的な科学課題を解く能力を評価するベンチマークです。公開データはolympiadとresearchに分かれ、競技問題と研究課題を区別して扱います。\n\nFrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex"},"task_id":"aa8b584e-33a2-512f-a69c-ebb2107d637a","task_key":"olympiad--test--f10254b9~2df0a1~2d407f~2d8af9~2d3169e23eee5e","task_revision_id":"1","upstream_id":"f10254b9-f0a1-407f-8af9-3169e23eee5e","short_description":"Consider a cylinder with a radius `\\(R\\)` and a length `\\(L\\)`, with a mass of…","config":"olympiad","split":"test","body":"{\"problem\":\"Consider a cylinder with a radius `\\\\(R\\\\)` and a length `\\\\(L\\\\)`, with a mass of `\\\\(m\\\\)`, in a fluid with a density `\\\\(\\\\rho\\\\)`. At the beginning (`\\\\(t=0\\\\)`), the cylinder is parallel to the `\\\\(y\\\\)`-axis and its center of mass is located at `\\\\(x=z=0\\\\)`, with its center of mass stationary but rotating with an angular velocity `\\\\( \\\\vec{\\\\omega}=-\\\\omega \\\\hat{y}\\\\)`. The entire system is in a uniform gravitational field `\\\\( \\\\vec{g}=-g\\\\hat{z} \\\\)`. Assume that the angular velocity remains constant during the subsequent motion of the cylinder. Ignore dissipative forces and the buoyancy force, but consider the Magnus force \\\\\\\\( \\\\\\\\vec{F}=S(\\\\\\\\vec{v}\\\\\\\\times\\\\\\\\vec{\\\\\\\\omega}) \\\\\\\\), where \\\\\\\\( S=2\\\\\\\\pi R^2L\\\\\\\\rho \\\\\\\\) and \\\\\\\\( \\\\\\\\vec{v} \\\\\\\\) is the velocity of the center of mass. Solve for the trajectory function `\\\\(x(z)\\\\)` as a function of \\\\\\\\( z \\\\\\\\), \\\\\\\\( \\\\\\\\omega \\\\\\\\), \\\\\\\\( g \\\\\\\\), and the constant \\\\\\\\( k = \\\\\\\\frac{S}{m} \\\\\\\\).\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"physics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}