Question

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

• 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. $g _ { 1 } : g _ { 2 } = R _ { 1 } \rho _ { 1 } : R _ { 2 } \rho _ { 2 }$

Answer 1

Answer: (D)

$g _ { 1 } : g _ { 2 } = R _ { 1 } \rho _ { 1 } : R _ { 2 } \rho _ { 2 }$

Answer 2

$g = \frac { 4 } { 3 } \pi \rho G R$ $\therefore$ $\frac { g _ { 1 } } { g _ { 2 } } = \frac { R _ { 1 } \rho _ { 1 } } { R _ { 2 } \rho _ { 2 } }$