text: Question
  
  # A planet of mass m revolves in elliptical orbit around the sun so that its maximum and minimum distances from the sun are equal to ra and rp respectively. Find the angular momentum of this planet relative to the sun.
  
  A
  L=mGMrpra(rp+ra)
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  B
  L=m2GMrpra(rp+ra)
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  C
  L=M2GMrpra(rp+ra)
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  D
  L=M(rp+ra)Gmrpra
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  Solution
  
  ## The correct option is B L=m√2GMrpra(rp+ra)For a planet moving around the sun in an orbit, angular momentum (L) is constant.L=mvara=mvbrb⇒va=vbrbraBy conserving energy between the two points, farthest and nearest.−GMmrb+12mv2b=−GMmra+12mv2a⇒GM(1ra−1rb)=12(v2a−v2b)Substituting va from momentum equation.⇒GM(1ra−1rb)=12[v2b(r2br2a)−v2b]⇒GM[rb−rararb]=v2b2[(rb−ra)(rb+ra)r2a]⇒v2b=2GMra(ra+rb)rb∴L=mvbrb=m√2GMra(ra+rb)rbrb=m√2GMrarbra+rb
  
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explanation: The document contains a physics question about the angular momentum of a planet in an elliptical orbit around the sun. It also includes multiple-choice options and a detailed solution to the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Question
  
  # A planet of mass m revolves in elliptical orbit around the sun so that its maximum and minimum distances from the sun are equal to ra and rp respectively. Find the angular momentum of this planet relative to the sun.
  
  A
  L=mGMrpra(rp+ra)
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  B
  L=m2GMrpra(rp+ra)
  Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
  C
  L=M2GMrpra(rp+ra)
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  D
  L=M(rp+ra)Gmrpra
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  Open in App
  Solution
  
  ## The correct option is B L=m√2GMrpra(rp+ra)For a planet moving around the sun in an orbit, angular momentum (L) is constant.L=mvara=mvbrb⇒va=vbrbraBy conserving energy between the two points, farthest and nearest.−GMmrb+12mv2b=−GMmra+12mv2a⇒GM(1ra−1rb)=12(v2a−v2b)Substituting va from momentum equation.⇒GM(1ra−1rb)=12[v2b(r2br2a)−v2b]⇒GM[rb−rararb]=v2b2[(rb−ra)(rb+ra)r2a]⇒v2b=2GMra(ra+rb)rb∴L=mvbrb=m√2GMra(ra+rb)rbrb=m√2GMrarbra+rb
  
  Suggest Corrections
  0
  Related Videos
  Variation in g
  PHYSICS
  Watch in App
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a physics question about the angular momentum of a planet in an elliptical orbit around the sun. It also includes multiple-choice options and a detailed solution to the problem.
  
  Label: question-and-answer