Question

Two planets if radii in the ratio 2 : 3 are made from the material of density in the ratio 3 : 2. Then the ratio of acceleration due to gravity g1/g2 , at the surface of the two planets will be -----?

Answer 1

hello,
we know that g=Gm/r²
g is acceleration due to gravity
G is gravitational constant
for 1st planet let the radius be r₁,mass be m₁,density be d₂,acceleration due to gravity be g₁
V=4/3πr³
V₁=4/3πr₁³
we know that d=m/V
m=Vd
m₁=V₁d₁
m₁=4/3πr₁³d₁
g₁=Gm₁/r₁²
g₁=G4/3πr₁³d₁/r₁²
g₁=G4/3πr₁d₁

2nd planet-let the mass be m₂,g be g₂,V be V₂,d be d₂,r be r₂
V₂=4/3πr₂³
m₂=V₂d₂
m₂=4/3πr₂³d₂
g₂=Gm₂/r₂²
g₂=G4/3πr₂³d₂/r₂²
g₂=G4/3πr₂d₂

now,g₁/g₂
(4/3πr₁d₁)/(4/3πr₂d₂)
=r₁d₁/r₂d₂
but r₁/r₂=2/3 and d₁/d₂=3/2
2×3/2×3
=1
hence g₁/g₂=1 which means g₁=g₂
hope this helps u,if u like please mark it as brainliest

Answer 2

g1=4/3πρGR..........i

g'2=4/3πρGR.........ii
radius of g1=2x
radius of g2=3x
density of g1 planet=3y
density of g2 planet =2y



divide eq i by eq  ii

g1/g2'=ρR/ρR
     =2x×3y/2x×3y
     =1
    so therefore  g1=g2...answer.

I hope its help you.