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Sagot :
The gravitational force varies directly with mass of the objects and
inversely with the square of the distance between them, therefore,
doubling the mass doubles the gravitational force while halving the
distance between the masses quadruples the gravitational force. The
option that create the greatest increase in the gravitational force is;
Halving the distance between the masses.
Reasons:
The known parameters are;
m₁ = 200 kg
m₂ = 400 kg
The distance between the centers of the masses = 8 meters
Required:
Change in variable that produces the greatest increase in the gravitational
force.
Solution;
The equation for the gravitational force is [tex]F = \mathbf{G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}}[/tex]
The gravitational force between the masses is therefore;
[tex]F =6.67408 \times 10^{-11} \times \dfrac{200 \times 400}{8^{2}} = 8.3426 \times 10^{-8}[/tex]
F = 8.3426 × 10⁻⁸ N
Doubling the mass of m₂ gives;
[tex]F_{2 \cdot m } = G \cdot \dfrac{m_{1} \cdot 2 \times m_{2}}{r^{2}} = \mathbf{2 \times G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}}[/tex]
Doubling the mass of m₂, doubles the gravitational force.
[tex]F_{2 \cdot m }[/tex] = 2 × F = 2 × 8.3426 × 10⁻⁸ N = 1.66852 × 10⁻⁷ N
Halving the distance between the masses gives;
[tex]F_{\frac{r}{2} } =G \cdot \dfrac{m_{1} \cdot m_{2}}{\left(\dfrac{r}{2} \right) ^{2}} = 4 \times G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}[/tex]
[tex]F_{\frac{r}{2} }[/tex] = 4 × F = 4 × 8.3426 × 10⁻⁸ N = 3.33704 × 10⁻⁷ N
Therefore, halving the distance between the masses quadruples (multiplies
by 4) the gravitational force between the masses.
Halving the distance between the masses creates the greatest
increase in the gravitational force because the gravitational force varies
with inverse of the square of the distance between the masses, and,
halving the distance between the masses has the effect of quadrupling the
gravitational force.
Learn more here:
https://brainly.com/question/21305452
Answer:
The gravitational force varies directly with mass of the objects and
inversely with the square of the distance between them, therefore,
doubling the mass doubles the gravitational force while halving the
distance between the masses quadruples the gravitational force. The
option that crate the greatest increase in the gravitational force is halving
the distance between the masses.
Step-by-step explanation:
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