Question # The acceleration due to gravity on the moon is only one-sixth that of earth. If the earth and moon are assumed to have the same density, the ratio of the radii of earth and moon will be

# The acceleration due to gravity on the moon is only one-sixth that of earth. If the earth and moon are assumed to have the same density, the ratio of the radii of earth and moon will be

(A) 6

(B) ( 6^{1 / 3} )

(C) ( 6^{2 / 3} )

(D) ( 6^{2} )

Solution

( g=frac{G M}{R^{2}} quad 6=frac{R_{e}}{R_{m}} quad frac{R_{e}}{R_{m}}=6 )

( frac{partial_{e}}{partial_{m}}=frac{M_{e} R_{m}^{2}}{M_{m} R_{c}^{2}} )

( 6=frac{V_{e} R_{m}^{2}}{V_{m} R_{e}^{2}} )