JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Self Evaluation Test - Gravitation

  • question_answer
    The acceleration due to gravity on the surface of the moon is 1/6 that on the surface of earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities on earth and moon will be

    A) \[\frac{\sqrt{6}}{2}\]

    B) \[\sqrt{24}\]

    C) 3

    D) \[\frac{\sqrt{3}}{2}\]

    Correct Answer: B

    Solution :

    [b] \[{{v}_{e}}=\sqrt{2{{g}_{e}}{{R}_{e}}};={{v}_{m}}=\sqrt{2{{g}_{m}}{{R}_{m}}}\] \[\frac{{{v}_{e}}}{{{v}_{m}}}=\sqrt{\frac{{{g}_{e}}}{{{g}_{m}}}\frac{{{\operatorname{R}}_{e}}}{{{R}_{m}}}}=\sqrt{\frac{{{g}_{e}}}{{{g}_{e}}/6}\frac{{{\operatorname{R}}_{e}}}{{{\operatorname{R}}_{e}}/4}}=\sqrt{24}\]


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