The new force of attraction between the two objects = 4 units
Further explanation
Gravity is a force that arises because of the attraction between objects with mass.
The magnitude of this attraction is proportional to the mass of the object.
The greater the mass of the object, the greater the gravitational force
Relationships can both be stated in
Newton's Gravity Law:
[tex]\rm F=G.\dfrac{m_1.m_2}{r^2}[/tex]
with F = gravitational force, 6.67 × 10⁻¹¹
G = gravitational constant,
m1, m2 = mass of object,
r = distance between two objects.
Because m₁,m₂ and G constant, then :
[tex]\tt F\approx \dfrac{1}{r^2}[/tex]
Suppose that, gravitational force 16 units.
[tex]\tt F_1=\dfrac{1}{r_1^2}\\\\16=\dfrac{1}{r_1^2}\rightarrow r_1^2=\dfrac{1}{16}[/tex]
If the distance between the two objects is doubled, then what the new force :
[tex]\tt r_2=2r_1\\\\F_2=\dfrac{1}{(2r_1)^2}=\dfrac{1}{4r_1^2}\\\\F_2=\dfrac{1}{4\times \dfrac{1}{16} }\\\\F_2=4~units[/tex]
