Question

Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities of earth $\left( \rho _ { m } \right)$ and moon $R _ { m }$ in terms of $R _ { e }$ will be

• A. $\frac { 5 } { 18 } R _ { e }$
• B. $\frac { 1 } { 6 } R _ { e }$
• C. $\frac { 3 } { 18 } R _ { e }$
• D. $\frac { 1 } { 2 \sqrt { 3 } } R _ { e }$

Answer 1

Answer: (A)

$\frac { 5 } { 18 } R _ { e }$

Answer 2

Acceleration due to gravity $g = \frac { 4 } { 3 } \pi \rho G R$ $\therefore g \propto \rho R$ or $\frac { g _ { m } } { g _ { e } } = \frac { \rho _ { m } } { \rho _ { e } } \cdot \frac { R _ { m } } { R _ { e } }$ [As $\frac { g _ { m } } { g _ { e } } = \frac { 1 } { 6 }$ and $\frac { \rho _ { e } } { \rho _ { m } } = \frac { 5 } { 3 }$ (given)]

$\therefore$ $\therefore$ $R _ { m } = \frac { 5 } { 18 } R _ { e }$