Question

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}}, $ then :

• 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}}} $

Answer 1

Answer: (D)

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}}} $