test","extracted_subject":"PHYSICS","extracted_chapter":"WORK ENERGY POWER","extracted_topic":"COLLISIONS ","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_941.png?top_left_x=532&top_left_y=408&width=532&height=646&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23ca370136192204c1af4","slug":"a-ball-falls-from-a-height-hsub0sub-there-are-n-co","content":"A ball falls from a height h₀. There are n collisions with the earth. If the velocity of rebound after n collisions is v_n and the ball rises to a height h_n, then coefficient of restitution e is given by :","options":[{"_id":"68a407f47f15af4716c92837","text":"\$e^{n} = \\sqrt{\\frac{h_{n}}{h_{0}}}\$","sequence":0,"isCorrect":true},{"_id":"68a407f47f15af4716c92838","text":"\$e^{n} = \\sqrt{\\frac{h_{0}}{h_{n}}}\$","sequence":1,"isCorrect":false},{"_id":"68a407f47f15af4716c92839","text":"\$ne = \\sqrt{\\frac{h_{n}}{h_{0}}}\$","sequence":2,"isCorrect":false},{"_id":"68a407f47f15af4716c9283a","text":"\$\\sqrt{n}e = \\sqrt{\\frac{h_{n}}{h_{0}}}\$","sequence":3,"isCorrect":false}],"correct_answer":"$$e^{n} = \\sqrt{\\frac{h_{n}}{h_{0}}}$","explanation":"h_n = e²ⁿh₀ or eⁿ = \$\\sqrt{\\frac{h_{n}}{h_{0}}}\$","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:41:55.734Z","__v":0,"vector_store_id":"3e73d359-05ff-45b9-969b-d9952cb500a0","updated_at":"2024-08-30T21:41:55.734Z","isStarred":false},"params":{"questionSlug":"a-ball-falls-from-a-height-hsub0sub-there-are-n-co"}}]}]]

Question: A ball falls from a height h<sub>0</sub>. There are n collisions with the earth. If the velocity of ...

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