{"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":"9dcd8187-b6bf-5620-8463-d52fd511f20f","task_key":"olympiad--test--cb11faa6~2de12a~2d4621~2d9fa7~2df6f4b11a9300","task_revision_id":"1","upstream_id":"cb11faa6-e12a-4621-9fa7-f6f4b11a9300","short_description":"Consider the following system situated in a rotating 2D cartesian coordinate…","config":"olympiad","split":"test","body":"{\"problem\":\"Consider the following system situated in a rotating 2D cartesian coordinate system. The system rotates with an angular velocity `\\\\( {\\\\vec \\\\Omega}=\\\\Omega \\\\hat z \\\\)` about the z-axis. There are two point masses `\\\\( M_1 \\\\)` and `\\\\( M_2 \\\\)` fixed in the rotating frame at `\\\\( (x_1, 0) \\\\)` and `\\\\( (x_2, 0) \\\\)`, respectively. The center of mass of `\\\\( M_1 \\\\)` and `\\\\( M_2 \\\\)`, `\\\\( O \\\\)`, happens to coincide with the origin of the coordinate system. Now, we introduce a third point mass \\\\\\\\( m \\\\\\\\), situated at `\\\\( (x, y) \\\\)`.\\n\\nSuppose \\\\\\\\(x_1\\\\\\\\) and \\\\\\\\(x_2\\\\\\\\) satisfy the condition `\\\\( x_2 - x_1 = R \\\\)`.\\n\\nFind the equilibrium point for mass \\\\\\\\(m \\\\\\\\) of the form \\\\\\\\((X,Y) = (x,y) \\\\\\\\) satisfying the condition `\\\\( y > 0 \\\\)`, in terms of \\\\\\\\(M_1, M_2, R \\\\\\\\).\\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":[]}