Gravitation Question 334
Question: The radii of two planets are respectively $ R _{1} $ and $ R _{2}$ their densities are respectively $ {{\rho } _{1}} and {{\rho } _{2}} $ . The ratio of the accelerations due to gravity at their surfaces is
Options:
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}R _{2}:R _{2}{{\rho } _{1}}$
D) $ g _{1}:g _{2}=R _{1}{{\rho } _{1}}:R _{2}{{\rho } _{2}}$
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Answer:
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}}}$
