First slide

Acceeleration due to gravity on surface of planet

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 $(ρ_{e})$ and moon $(ρ_{m})$ is $(\frac{ρ_{e}}{ρ_{m}}) = \frac{5}{3}$ then radius of moon R_m in terms of R_e will be

Moderate

A

$\frac{5}{18} R_{e}$
B

$\frac{1}{6} R_{e}$
C

$\frac{3}{18} R_{e}$
D

$\frac{1}{2 \sqrt{3}} R_{e}$

Solution

$g = \frac{4}{3} πGρR \Rightarrow g \propto ρR \Rightarrow \frac{g_{e}}{g_{m}}$
$= \frac{ρ_{e}}{ρ_{m}} \times \frac{R_{e}}{R_{m}}$
$\Rightarrow \frac{6}{1} = \frac{5}{3} \times \frac{R_{e}}{R_{m}} \Rightarrow R_{m} = \frac{5}{18} R_{e}$

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