Respuesta :
Answer:
The magnitude of the new gravitational force becomes 32 times of the original force.
Explanation:
Two objects, with masses m₁ and m₂, are originally a distance r apart. the gravitational force between them is given by :
[tex]F=\dfrac{Gm_1m_2}{r^2}[/tex]
If the second object has its mass changed to 2m₂ and the distance is changed to r/4, such that,
[tex]m_2'=2m_2[/tex] and [tex]r'=\dfrac{r}{4}[/tex]
The new gravitational force is given by :
[tex]F'=G\dfrac{m_1m'_2}{r'^2}[/tex]
[tex]F'=G\dfrac{m_1(2m_2)}{(r/4)^2}[/tex]
[tex]F'=32\times G\dfrac{m_1m_2}{r^2}[/tex]
[tex]F'=32F[/tex]
So, the magnitude of the new gravitational force becomes 32 times of the original force. Hence, the correct option is (B) "32F".
The gravitational force will increase 32 times , if mass of m2 is increase 2 times and distance between them is decreased by 4 times.
Newton's law of universal gravitation,
[tex]\bold {F=G{\dfrac{m_1m_2}{r^2}}}[/tex]
Where,
F = force
G = gravitational constant
m1 = mass of object 1
m2 = mass of object 2 = 2 x m2
r = distance between centers of the masses = r/4
So, new gravitational force,
[tex]\bold {F'=G{\dfrac{m_1(2m_2)}{(r/4)^2}}}\\\\\bold {F'= 32 \times G{\dfrac{m_1m_2}{r^2}}}\\\\\bold {F'= 32 F}[/tex]
Therefore, the gravitational force will increase 32 times , if mass of m2 is increase 2 times and distance between them is decreased by 4 times.
To know more about gravitational force,
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