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AMU Medical AMU Solved Paper-2012

  • question_answer
    Consider a satellite orbiting the earth as shown in the figure below. Let \[{{L}_{a}}\] and \[{{L}_{p}}\] represent the angular momentum of the satellite about the earth when at aphelion and perihelion respectively. Consider the following relations.                
    (i) \[{{L}_{a}}={{L}_{p}}\]             
    (ii) \[{{L}_{a}}=-{{L}_{p}}\]                           
    (iii) \[{{r}_{a}}\times {{L}_{a}}={{r}_{p}}\times {{L}_{p}}\]
    Which of the above relation (s) is/are true?

    A)  (i) only                

    B)  (ii) only

    C)  (iii) only              

    D)  (i) and (iii)

    Correct Answer: A

    Solution :

                     Using the law of conservation of angular momentum. Angular momentum of planet at p                                 = Angular momentum of planet at a i.e.,        \[{{L}_{p}}={{L}_{a}}\] But         \[{{r}_{a}}>{{r}_{p}}\] So,          \[{{r}_{a}}\times {{L}_{a}}\times {{r}_{p}}\times {{L}_{p}}\] Hence, only option (a) is correct.


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