Question

R and r are the radii of the earth and moon respectively. $\rho _ { e }$ and $\rho _ { m }$ are the densities of earth and moon respectively. The ratio of the accelerations due to gravity on the surfaces of earth and moon is

• A. $\frac { R } { r } \frac { \rho _ { e } } { \rho _ { m } }$
• B. $\frac { r } { R } \frac { \rho _ { e } } { \rho _ { m } }$
• C. $\frac { r } { R } \frac { \rho _ { m } } { \rho _ { e } }$
• D. $\frac { R } { r } \frac { \rho _ { e } } { \rho _ { m } }$

Answer 1

Answer: (A)

$\frac { R } { r } \frac { \rho _ { e } } { \rho _ { m } }$

Answer 2

$g = \frac { 4 } { 3 } \pi \rho G R$ ∴$g \propto r \rho$∴ $\frac { g _ { e } } { g _ { m } } = \frac { R } { r } \times \frac { \rho _ { e } } { \rho _ { m } }$