This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This pattern holds because weight is calculated as W = mg (mass × gravitational field strength), and with g = 10 m/s² constant on Earth's surface, weight must be proportional to mass: W = 10m means a 1.5 kg book has weight = 1.5 kg × 10 m/s² = 15 N. Choice C is correct because it accurately calculates the book's weight using the proportional relationship: 1.5 kg × 10 m/s² = 15 N. Choice A (1.5 N) makes calculation error by not multiplying mass by g; Choice B (10 N) incorrectly uses 1 kg instead of 1.5 kg given in problem; Choice D (150 N) makes decimal error suggesting 15 kg was used instead of 1.5 kg. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that increasing either mass increases the gravitational force between two objects: when the changing object's mass doubles from 1 kg to 2 kg (keeping the other object's mass constant), the force doubles from 2 N to 4 N; when mass doubles again from 2 kg to 4 kg, force doubles from 4 N to 8 N—this demonstrates that gravitational force depends on both masses, and the relationship is proportional for each mass individually. Choice A is correct because it accurately identifies the proportional relationship: double the mass → double the gravitational force. Choice B reverses the relationship, claiming force decreases as mass increases when the data clearly show force increasing with mass: 1 kg → 2 N, 2 kg → 4 N, 4 kg → 8 N (all increasing together); Choice C claims mass doesn't affect gravitational force, when the entire dataset demonstrates that mass is the primary factor determining force; Choice D makes an incorrect calculation, claiming quadrupling mass (from 1 to 4 kg) increases force by only 2 N when actually it increases from 2 N to 8 N (increase of 6 N). Understanding gravitational force's dependence on mass: (1) gravitational force between two objects depends on both their masses, following F = Gm₁m₂/r² where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between them, (2) keeping one mass and distance constant makes force proportional to the other mass: F ∝ m, (3) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: satellite engineers use this principle to calculate orbital mechanics—doubling a satellite's mass doubles the gravitational force on it, but doesn't change its orbit because acceleration (a = F/m) stays constant when both force and mass double.

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 2 kg book weighs 20 N on Earth while a 1 kg book weighs 10 N (twice the mass, twice the weight). Additionally, more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth; for the Moon (less massive), g=1.6 m/s², so a 70 kg person weighs 70 × 1.6 ≈ 112 N. Choice A is correct because it properly explains that lower planet mass (Moon) leads to weaker gravity, resulting in lower weight (112 N vs 700 N on Earth). Choice C is wrong because it claims the weight stays about 700 N, when the lower g on Moon means much less weight (about 1/6). Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The data clearly demonstrate proportionality: an object with mass 3 kg has weight 30 N on Earth (3 × 10 = 30), and when mass doubles to 6 kg, weight must double to 60 N (6 × 10 = 60)—each time mass doubles, weight doubles, showing the linear proportional relationship. Choice C is correct because it accurately identifies the proportional relationship: doubling mass from 3 kg to 6 kg doubles the weight from 30 N to 60 N. Choice A (15 N) makes prediction violating proportionality: claims doubling mass halves the force, when the pattern shows exact doubling; Choice B (30 N) claims mass doesn't affect gravitational force, when the entire principle demonstrates that mass is the primary factor determining weight; Choice D (90 N) suggests tripling when actually proportional: as mass doubles, force also doubles (not triples). Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 2 kg book weighs 20 N on Earth while a 1 kg book weighs 10 N (twice the mass, twice the weight). The data clearly demonstrate proportionality: an object with mass 3 kg has weight 30 N on Earth, and when doubled to 6 kg, the weight should double to 60 N, following the pattern where each time mass doubles, weight doubles, showing the linear proportional relationship. Choice C is correct because it accurately identifies the proportional relationship: more mass → more gravitational force / correctly predicts that doubling mass doubles weight. Choice B is wrong because it suggests weight stays at 30 N or doesn't fully double, when the pattern shows exact doubling: doubling from 3 kg to 6 kg should go from 30 N to 60 N. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This pattern holds because weight is calculated as W = mg (mass × gravitational field strength), and with g = 10 m/s² constant on Earth's surface, weight must be proportional to mass: a 4 kg object has weight = 4 kg × 10 m/s² = 40 N while a 2 kg object has weight = 2 kg × 10 m/s² = 20 N (twice the mass, twice the weight). Choice A is correct because it accurately identifies that Student 1 is correct: more mass → more gravitational force, as the 4 kg object experiences 40 N of gravitational force while the 2 kg object experiences only 20 N. Choice B claims Student 2 is correct and that mass doesn't affect gravitational force, when the entire principle demonstrates that mass is the primary factor determining weight (gravitational force on object); Choice C suggests both are correct when they make contradictory claims; Choice D makes unit error claiming weight is measured in kilograms when weight (force) is measured in newtons while mass is measured in kilograms. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 2 kg book weighs 20 N on Earth while a 1 kg book weighs 10 N (twice the mass, twice the weight). The simulation results show that increasing either mass increases the gravitational force between two objects: in Case 1 (m1=2 kg, m2=3 kg), force proportional to 2×3=6; in Case 2 (m1=4 kg, m2=3 kg), proportional to 4×3=12, so force doubles when m1 doubles—this demonstrates that gravitational force depends on both masses (each contributes), and the relationship is proportional for each mass individually (both contribute multiplicatively to total force). Choice C is correct because it correctly predicts that doubling one mass doubles the gravitational force. Choice A is wrong because it claims the force halves, when actually doubling m1 doubles the force (from proportional to 6 to 12). Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 2 kg book weighs 20 N on Earth while a 1 kg book weighs 10 N (twice the mass, twice the weight). The data clearly demonstrate proportionality: an apple with mass 0.1 kg has weight 1 N on Earth (0.1 × 10), while a textbook with 1 kg has weight 10 N (1 × 10), showing the linear proportional relationship. Choice B is correct because it accurately identifies the proportional relationship: more mass → more gravitational force, so textbook weighs more. Choice D is wrong because it reverses the relationship, claiming less mass means more weight, when actually more mass means more weight. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. Additionally, more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth. Comparing planets with different masses shows that more massive planets have stronger surface gravity: Mars (lower mass than Earth) has weaker gravity (g = 3.7 m/s², so 1 kg object weighs only 3.7 N), Earth (medium mass) has moderate gravity (g = 10 m/s², so 1 kg weighs 10 N), and Jupiter (much more massive than Earth) has very strong gravity (g = 25 m/s², so 1 kg weighs 25 N)—the planet's mass determines its gravitational field strength, which determines how much objects weigh on that planet. Choice A is correct because it properly explains that massive planets have stronger gravity because their large mass creates stronger gravitational fields. Choice C is wrong because it claims less massive planets have stronger gravity, but the data show Mars (less massive) has weaker gravity than Earth or Jupiter. Understanding this helps explain why astronauts on Mars could jump higher due to weaker gravity pulling them down.

This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. Additionally, more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth. For planetary mass variation: the Moon has lower mass than Earth, so weaker gravity (g = 1.6 N/kg vs 10 N/kg), meaning a 70 kg person weighs 70 × 1.6 = 112 N on Moon and 70 × 10 = 700 N on Earth. Choice B is correct because it correctly predicts weights using W = mg for each location. Choice A is wrong because it reverses the values, claiming Earth 112 N and Moon 700 N, when weaker Moon gravity should give lower weight. Practical implications: this explains why Apollo astronauts bounded easily on the Moon—their weight was about 1/6 of Earth's, making movement feel lighter despite unchanged mass.