Answer:
Explanation:
In Newton's law of universal gravitation
F = Gm₁m₂/r²
Where G is a gravitational constant = 6.674e-11m³/kgs²
m₁ and m₂ are the masses of the two bodies or objects in question, in kilogram (kg)
r is the distance in meters between them
From the question, the rock is placed halfway between the planets
So, it's distance from planet A is 8R/2 = 4R
And it's distance from planet B is also 8R/2 = 4R
Using F = Gm₁m₂/r²
To Planet A
r = 4R,
m₁ = mass of Rock = m
m₂ = mass of planet A = 3M
So Fa = G mm₂/r² = Gm(3M) / (4R)²
To Planet B,
r = 4R,
m₁ = mass of Rock = m
m₂ = mass of planet B = 4M
Fb = G mm₂/r² = Gm(4M) / (4R)²
Comparing both forces together, we realise that Planet B has the largest force,
so take we F = Fb – Fa
F = Fb – Fa = Gm(4M) / (4R)² – Gm(3M) / (4R)²
F = GmM/16R²)(4–3)
F = GmM/16R²
Note that Force = Mass * Acceleration
So, F = ma
So, ma = GmM/16R² ------- Divide through by m
a = GM/16R²
From the question
M = 7.3×10^23kg
R = 5.8×10^6 m
So, a = (6.674 * 10^-11 * 7.3×10^23)/16(5.8×10^6)²
a = (48.7202 * 10^12)/16(33.64 * 10^12)
a = (48.7202 * 10^12)/(538.4 * 10^12)
a = 48.7202/538.4
a = 0.090517612960760
a = 0.091m/s² ----------Approximated
