{"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":"ebc1d55e-43f6-5c5c-89bc-2d5b5137ea86","task_key":"olympiad--test--bc8a05ac~2d9db5~2d47b4~2d8618~2d84aa4a46466a","task_revision_id":"1","upstream_id":"bc8a05ac-9db5-47b4-8618-84aa4a46466a","short_description":"Consider a particle of mass `\\( m \\)`, that is constrained to move on a…","config":"olympiad","split":"test","body":"{\"problem\":\"Consider a particle of mass `\\\\( m \\\\)`, that is constrained to move on a spherical shell with radius `\\\\( R \\\\)`. The spherical shell is rotating with angular velocity `\\\\( \\\\omega \\\\)`.  Initially this particle is at the equator and is initially projected northward perpendicular to the equator (in the rotating reference frame of the sphere) at a surface relative velocity of `\\\\( v \\\\)`. Ignore any resistive forces. Denote the greatest latitude of the particle as `\\\\( \\\\theta_{max} \\\\)`. Assume `\\\\( \\\\theta_{max} \\\\ll 1 \\\\)` so that the small angle approximations `\\\\( \\\\sin(\\\\theta) = \\\\theta \\\\)` and `\\\\( \\\\cos(\\\\theta) = 1 \\\\)` can be used. Denote the latitude of the particle at time `\\\\( t \\\\)` as `\\\\( \\\\theta(t) \\\\)`. Find the time period `\\\\( T \\\\)` of `\\\\( \\\\theta(t) \\\\)`.\\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":[]}