Respuesta :
Answer:
The force of attraction between the two particles will become half.
Explanation:
Consider force F between two objects with masses m and m' which are placed r distance apart from each other.
Mass of first object = m
Mass of second object = m'
Distance between the two objects = r
[tex]F=G\frac{m\times m'}{r^2}[/tex]...(1) (Gravitational force)
If the mass of one of two particles is doubled and the distance between them is doubled the force between them be F'.
Mass of first object = m
New mass of second object = M = 2m'
Distance between the two objects = R = 2r
[tex]F'=G\times \frac{m\time M}{R^2}=\frac{m\times 2m'}{4r^2}=G\frac{m\times m'}{2r^2}[/tex]...(2) (Gravitational force)
Dividing (1) from (2):
[tex]\frac{F}{F'}=\frac{G\frac{m\times m'}{r^2}}{G\frac{m\times m'}{2r^2}}[/tex]
[tex]F=2F'[/tex]
[tex]F'=\frac{F'}{2}[/tex]
The force of attraction between the two particles will become half.
When the mass of one of the two particles is doubled and the distance between them is doubled, the force of attraction between the two particles will reduce by half.
The force of attraction between two masses in the universe is given by Newton's law of universal gravitation.
[tex]F = \frac{Gm_1m_2}{R^2}[/tex]
where;
- F is the force of attraction between the two masses
- R is the distance between the two masses
- m₁ and m₂ are the two masses
When the mass of one of the two particles is doubled and the distance between them is doubled, the force of attraction becomes;
[tex]F_2 = \frac{Gm_12m_2}{(2R)^2} \\\\F_2 = \frac{2Gm_1m_2}{4R^2} \\\\F_2 = \frac{2}{4} (\frac{Gm_1m_2}{R^2} )\\\\F_2 = \frac{1}{2} (F)[/tex]
Thus, when the mass of one of the two particles is doubled and the distance between them is doubled, the force of attraction between the two particles will reduce by half.
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