Respuesta :
Answer:
When the gravitational force on the Moon from the Earth = 4.00 Fm, the distance of the Moon from the Earth is 0.5·D
Explanation:
The given information includes;
The distance of the moon from the Earth = 0.25·D
The gravitational force, F, on the Moon from the Earth = 16.00 Fm
When the gravitational force on the Moon from the Earth = 4.00 Fm, the distance of the Moon from the Earth is found as follows;
From Newton's law of gravitation;
[tex]F_{1} = F_{2} =G\dfrac{m_{1}m_{2}}{r^{2}}[/tex]
At r = 0.25·D, F = 16.00 Fm
Therefore;
G×m₁×m₂ = (0.25·D)²×16.00 Fm = D²×Fm = Constant
When, the gravitational force of the Moon from the Earth = 4.00 Fm, we have;
[tex]F = 4.00 \ Fm =\dfrac{D^2 \times Fm}{r_2^{2}}[/tex]
Therefore;
[tex]r_2^{2} =\dfrac{D^2 \times Fm}{4.00 \ Fm} = \dfrac{D^2}{4}[/tex]
[tex]r_2 =\sqrt{\dfrac{D^2}{4}} = \dfrac{D}{2} = 0.5 \cdot D[/tex]
r₂ = 0.5·D
Where;
r₂ = The new distance of the Moon from the Earth
Therefore the distance of the Moon from the Earth when the gravitational force on the Moon from the Earth = 4.00 Fm is r₂ = 0.5·D.
