Question

The strength of the gravitational force between two objects depends on two factors: mass and distance.suppose that two objects attract each other with gravitational force of 16 units.If the distance between the two objects is doubled,then what is the new force of attraction between the two objects?

Answer 1

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:  

$\rm F=G.\dfrac{m_1.m_2}{r^2}$

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 :

$\tt F\approx \dfrac{1}{r^2}$

Suppose that, gravitational force 16 units.

$\tt F_1=\dfrac{1}{r_1^2}\\\\16=\dfrac{1}{r_1^2}\rightarrow r_1^2=\dfrac{1}{16}$

If the distance between the two objects is doubled, then what the new force :

$\tt r_2=2r_1\\\\F_2=\dfrac{1}{(2r_1)^2}=\dfrac{1}{4r_1^2}\\\\F_2=\dfrac{1}{4\times \dfrac{1}{16} }\\\\F_2=4~units$