Answer:
PART A
g(R) = ;
PART B
g(R) = g(Rp) × .
Explanation:
Given density of planet = rho.
The planet's radius = Rp.
An object is located a distance R from the center of the planet,
where R< Rp.
The gravitational fore between two point masses m₁ and m₂ is,
F = ; G= universal gravitational constant
r = distance between the masses.
for mass m₂ , F= m₂ g; where g = acceleration due to gravity;
so, g = = ;
From figure, only inside part of the planet exerts force and which can be treated as a point mass.
so, g =
where = mass of the planet with radius R.
⇒ = rho × ×R³
⇒ g(R) = → PART A
PART B
At the surface g(Rp) =
⇒ g(R) = g(Rp) ×