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CMC Medical CMC-Medical VELLORE Solved Paper-2009

  • question_answer
    Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of escape velocity \[\frac{{{V}_{A}}}{{{V}_{B}}}\]is

    A)  2                                            

    B)  \[\sqrt{2}\]

    C)  \[\frac{1}{\sqrt{2}}\]                                    

    D)  \[\frac{1}{2}\]

    Correct Answer: A

    Solution :

                    Escape velocity is given by \[{{v}_{e}}=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G}{R}\times \frac{4}{3}\pi {{R}^{3}}\rho }\] \[\Rightarrow \]               \[{{v}_{e}}=R\sqrt{\frac{8}{3}\pi G\rho }\] \[\therefore \]  \[\frac{{{v}_{A}}}{{{v}_{B}}}=\frac{{{R}_{A}}}{{{R}_{B}}}=2\]


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