Answer :
The distance of 39.3 kg mass from 536 kg mass will be .0567d to have zero force of attraction.
What is Gravitational Force ?
The force of attraction between any two bodies is inversely proportional to the square of the distance between them and directly proportional to the product of their masses.
If the cannon is fired after being filled with gunpowder, the following situations could occur.
- The gun will fall to Earth in a projectile motion if its speed is low.
- The cannonball will continue to circle the Earth in a constant orbit if, at that precise height, its speed is equal to the orbital speed.
- The cannonball maintains an elliptical orbit around the Earth if its speed is more than the orbital velocity but insufficient to escape from it, that is, lower than the Earth's escape velocity.
- The projectile departs the Earth on a parabolic or hyperbolic trajectory if the speed is equal to escape velocity or greater.
The masses are
m₁ = 313 kg
m₂ = 536 kg
m = 39.3 kg
So as per sum if the distance between m₁ and m₂ is d and distance between m and m₂ is s then
The gravitational force between m₁ and m is equal to gravitational force between m and m₂.
[tex]\frac{G*m\x_{1} *m }{(d-s)\x^{2} } =\frac{G*m\x_{2} *m }{s\x^{2} }[/tex]
⇒ m₁* s² = m₂ * (d-s)²
⇒313s² = 536d² - 1072ds + 536s²
⇒223s² + 536d² - 1072ds = 0
⇒ s = 0.567d
The distance of 39.3 kg mass from 536 kg mass will be .0567d to have zero force of attraction.
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