{"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":"9a4aef3a-3e42-522f-8eb3-45048145c544","task_key":"olympiad--test--f398c3ad~2d6cff~2d45b1~2da21d~2d5ce963db75aa","task_revision_id":"1","upstream_id":"f398c3ad-6cff-45b1-a21d-5ce963db75aa","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 \\\\)` situated at the coordinates `\\\\( (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 \\\\\\\\), is situated at `\\\\( (x, y) \\\\)`.\\n\\nSuppose \\\\\\\\(x_1\\\\\\\\) and \\\\\\\\(x_2\\\\\\\\) satisfy the condition `\\\\( x_2 - x_1 = R \\\\)`. For convenience, we introduce the dimensionless constants `\\\\( \\\\alpha=\\\\frac{M_{2}}{M_{1}+M_{2}} \\\\)` and `\\\\( \\\\beta=\\\\frac{M_1}{M_1+M_2} \\\\)` (which might be used later in your calculation).\\n\\nFind the equilibrium point for mass \\\\\\\\(m \\\\\\\\) of the form \\\\\\\\((X,Y) = (x,0) \\\\\\\\) satisfying the condition `\\\\( x < 0 \\\\)`, in terms of \\\\\\\\(R, \\\\\\\\alpha \\\\\\\\). Keep only terms that include \\\\\\\\( \\\\\\\\alpha^0 \\\\\\\\), \\\\\\\\( \\\\\\\\alpha^1 \\\\\\\\) as part of the expression.\\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":[]}