Question

Two planets of radii r₁ and r₂ are made from the same material. The ratio of the acceleration due to gravity g₁/g₂ at the surfaces of the two planets is
(a) r₁/r₂
(b) r₂/r₁
(c) (r₁/r₂)²
(d) (r₂/r₁)²

Answer 1

Answer:

A) r1/r2

Explanation:

Acceleration due to gravity - (g)  

Force extended by earth on a body is gravity

g = GM/R²

g = 4/3πpGR

Where g is the gravity, p is the density of earth  and R is Radius of earth

Thus,

Mass of the planets: M1 = density × volume = d×(4/3πr³)  

M2 = d×(4/3πr2³)  

Now, g1 = 4(G×dπr1³)/(3r²) = 4/3×G×d×r1  

And g2 = 4(G×dπr2³)/(3r2²) = 4/3×G×d×r2  

Now the ratio of acceleration due to gravity  is -

= g1/g2 = 4/3×G×d×r1/4/3*G*d*r2

= r1/r2