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 ρe and moon ρm is (ρe / ρm) = 5/3 then radius of moon Re in terms of Re will be ____

(A) (5 / 18)Re

(B) (1/6) Re

(C) (3 / 16)Re

(D) [1 / (2√3)]Re

Answer 1

Correct option: (A) (5 / 18)Re

Explanation:

g = (GM / R2)

= (G/R2) × (4/3)πR3ρ

g = (4/3)πRρG

g ∝ Rρ

given (ρe / ρm) = (5/3) and gm = (ge / 6)

(ge / gm) = (Re / Rm) × (ρe / ρm)

6 = (5/3) × (Re / Rm)

hence

(Re / Rm) = (18 / 5)

Rm = (5 / 18)Re