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

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     The radii of two planets are respectively \[{{R}_{1}}\] and \[{{R}_{2}}\] and their densities are respectively \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\]. The ratio of the accelerations due to gravity at their surfaces is [MP PET 1994]

    A)             \[{{g}_{1}}:{{g}_{2}}=\frac{{{\rho }_{1}}}{R_{1}^{2}}:\frac{{{\rho }_{2}}}{R_{2}^{2}}\]           

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

    C)             \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{\rho }_{2}}:{{R}_{2}}{{\rho }_{1}}\]  

    D)             \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{\rho }_{1}}:{{R}_{2}}{{\rho }_{2}}\]

    Correct Answer: D

    Solution :

                    \[g=\frac{4}{3}\pi \rho GR\]\[\therefore \]\[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{R}_{1}}{{\rho }_{1}}}{{{R}_{2}}{{\rho }_{2}}}\]


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