Gravitational force increases as the mass increases and decreases as the distance between the bodies is increased.
- The correct option is; The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.
Reasons:
The given parameters are;
The moons of the planet = Moon A and Moon B
Mass of Moon A = 2·M
Mass of moon B = M
The distance between Moon B and the planet = 2 × The distance between Moon A and the planet
Required:
Comparison (compare) of the force exerted from the planet on Moon A and Moon B.
Solution:
The force, F, exerted from the planet is the gravitational force which is given by Newton's Law of Gravitation as follows;
- [tex]\displaystyle F = \mathbf{G \cdot \frac{M_{planet} \times M}{R^2}}[/tex]
Where;
G = Universal gravitational constant
[tex]M_{planet}[/tex] = Mass of the planet
M = Mass of the Moon
R = The distance from the planet to the Moon
For Moon A, we have;
Mass = 2·M
Distance = R
Which gives;
[tex]\displaystyle F_A = G \cdot \frac{M_{planet} \times 2\cdot M}{R^2} = 2\cdotG \cdot \frac{M_{planet} \times M}{R^2} = \mathbf{2 \cdot F}[/tex]
With Moon B, we have;
Mass = M
Distance = 2·R
Therefore;
[tex]\displaystyle F_B = G \cdot \frac{M_{planet} \times M}{(2 \cdot R)^2} = G \cdot \frac{M_{planet} \times M}{4 \cdot R^2} = \frac{1}{4} \cdot G \cdot \frac{M_{planet} \times M}{R^2} = \mathbf{\frac{1}{4} \cdot F}[/tex]
Which gives;
[tex]\displaystyle \frac{F_A}{F_B} = \frac{2 \cdot F}{\frac{1}{4} \cdot F } =2 \times \frac{4}{1} = \mathbf{8}[/tex]
[tex]\displaystyle \frac{F_A}{F_B} = 8[/tex]
[tex]F_A = \mathbf{8 \times F_B}[/tex]
The force from the planet on Moon A, [tex]F_A[/tex], is 8 times the force from the planet on Moon B.
Therefore, whereby option B is;
- The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.
The correct option is option B
Learn more about Newton's Law of gravitation here:
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