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BVP Medical BVP Medical Solved Paper-2002

  • question_answer
    Two planets have the same average density but their radii are \[{{R}_{1}}\]and \[{{R}_{2}}.\] If acceleration due to gravity on these planets be \[{{g}_{1}}\] and \[{{g}_{2}},\] then :

    A) \[\frac{g1}{g2}=\frac{R_{1}^{3}}{R_{2}^{3}}\]                    

    B) \[\frac{g1}{g2}=\frac{R_{1}^{2}}{R_{2}^{2}}\]

    C) \[\frac{g1}{g2}=\frac{{{R}_{2}}}{{{R}_{1}}}\]                        

    D) \[\frac{g1}{g2}=\frac{{{R}_{1}}}{{{R}_{2}}}\]

    Correct Answer: D

    Solution :

                    Acceleration due to gravity \[g=\frac{GM}{{{R}^{2}}}\] \[=\frac{GVd}{{{R}^{2}}}=G\frac{\frac{4}{3}\pi {{R}^{3}}d}{{{R}^{2}}}\] \[8=\frac{4}{3}\pi GdR\]           ...(1) Both the planet have same average density . Hence,  \[g\propto R\] Therefore,    \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\]


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