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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The text passage contains a physics problem related to the angular momentum of a planet in an elliptical orbit around the sun, followed by multiple-choice options and a detailed solution.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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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0
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Variation in g
PHYSICS
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user
The text passage contains a physics problem related to the angular momentum of a planet in an elliptical orbit around the sun, followed by multiple-choice options and a detailed solution.

TYPE: SINGLE_QUESTION_WITH_ANSWER