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Answer :
To find the force of gravitational attraction between two spheres, we use Newton's law of universal gravitation. The formula is:
[tex]\[ F = G \times \frac{{m_1 \times m_2}}{{d^2}} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the two objects,
- [tex]\( G \)[/tex] is the gravitational constant, approximately [tex]\( 6.67430 \times 10^{-11} \, \text{m}^3\, \text{kg}^{-1}\, \text{s}^{-2} \)[/tex],
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects,
- [tex]\( d \)[/tex] is the distance between the centers of the two masses.
For this problem:
- [tex]\( m_1 = 10.1 \, \text{kg} \)[/tex],
- [tex]\( m_2 = 45.4 \, \text{kg} \)[/tex],
- [tex]\( d = 38.5 \, \text{m} \)[/tex].
Plug these values into the formula:
[tex]\[ F = 6.67430 \times 10^{-11} \times \frac{{10.1 \times 45.4}}{{(38.5)^2}} \][/tex]
After performing the calculation, the force of gravitational attraction between the two spheres is approximately:
[tex]\[ 2.064721553044358 \times 10^{-11} \, \text{N} \][/tex]
This value indicates the force in newtons.
[tex]\[ F = G \times \frac{{m_1 \times m_2}}{{d^2}} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the two objects,
- [tex]\( G \)[/tex] is the gravitational constant, approximately [tex]\( 6.67430 \times 10^{-11} \, \text{m}^3\, \text{kg}^{-1}\, \text{s}^{-2} \)[/tex],
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects,
- [tex]\( d \)[/tex] is the distance between the centers of the two masses.
For this problem:
- [tex]\( m_1 = 10.1 \, \text{kg} \)[/tex],
- [tex]\( m_2 = 45.4 \, \text{kg} \)[/tex],
- [tex]\( d = 38.5 \, \text{m} \)[/tex].
Plug these values into the formula:
[tex]\[ F = 6.67430 \times 10^{-11} \times \frac{{10.1 \times 45.4}}{{(38.5)^2}} \][/tex]
After performing the calculation, the force of gravitational attraction between the two spheres is approximately:
[tex]\[ 2.064721553044358 \times 10^{-11} \, \text{N} \][/tex]
This value indicates the force in newtons.
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