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, \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\]You need to login to perform this action.
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