Respuesta :
Answer:
Explanation:
The force due to gravitation is equal to zero for each of the masses.
M1= 181kg
M2= 712kg
m = 72.6kg
The distance between M1 and M2 is said to be fixed , therefore no value should be given I.e it's a constant.
From the formula for gravitational force we have that
F = GMm/r^2
GmM1/(d-r)^2. = GmM2/r^2
where r is the distance between the 72.6 kg and 712kg
d is the distance between M1 and M2
Solving mathematically
r(√M1+√M2) = d√M2
r = d√M2/√M1 + √M2
d×26.68/ 13.45+26.68
d×26.68/40.13
r = 0.665d
The distance between the object of mass 712kg and the object of mass 181 kg is 0.664 d.
The object placed at the midway will experience zero force.
How do you calculate the distance between the objects?
Given that two objects have masses of 181 kg and 712 kg represented by m1 and m2. The objects are at a fixed distance d apart from each other. There is another object, placed in the midway of both objects, has a mass m of 72.6 kg.
Let us consider that the gravitational force will equal zero for both the objects having the mass of m1 and m2. Hence
[tex]\dfrac{Gm_1m}{(d-r)^2} = \dfrac {Gm_2m}{r^2}[/tex]
Where r is the distance between the object of mass m1 and the object placed at the midway. D is the total distance between the object of mass m1 and the object of mass m2.
By simplifying the above equation, we get,
[tex]m_1r^2 = m_2(d-r)^2[/tex]
[tex]\sqrt{m_1} r = \sqrt{m_2} (d-r)[/tex]
[tex]r (\sqrt{m_1} +\sqrt{m_2} ) = d\sqrt{m_2}[/tex]
[tex]r = \dfrac {d\sqrt{m_2}} {\sqrt{m_1}+ \sqrt{m_2} }[/tex]
Substituting the values of m1 and m2,
[tex]r = \dfrac {d\times \sqrt{712} }{\sqrt{181} + \sqrt{712} }[/tex]
[tex]r = 0.664 d[/tex]
Hence the distance between the object of mass 712kg and the object of mass 181 kg is 0.664 d. The object placed at the midway will experience zero force.
To know more about the force, follow the link given below.
https://brainly.com/question/26115859.
