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 (ρ_e / ρ_m) = 5/3 then radius of moon R_e in terms of R_e will be ________ 

(A) (5 / 18)R_e 

(B) (1/6) R_e 

(C) (3 / 16)R_e 

(D) [1 / (2√3)]R_e

Answer 1

Correct option: (A) (5 / 18)R_e

Explanation:

g = (GM / R²)

= (G/R²) × (4/3)πR³ρ

g = (4/3)πRρG

g ∝ Rρ

given (ρ_e / ρ_m) = (5/3) and g_m = (g_e / 6)

(g_e / g_m) = (R_e / R_m) × (ρ_e / ρ_m)

6 = (5/3) × (R_e / R_m)

hence

(R_e / R_m) = (18 / 5)

R_m = (5 / 18)R_e