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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Acceleration Due to Gravity

  • 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 \[{{g}_{2}}\] respectively, then           [AIIMS 1985]

    A)             \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\]         

    B)             \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\]

    C)             \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{R_{1}^{2}}{R_{2}^{2}}\]     

    D)             \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{R_{1}^{3}}{R_{2}^{3}}\]

    Correct Answer: A

    Solution :

                    \[g=\frac{4}{3}\pi \rho GR\]. If \[\rho \] = constant then \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\]


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