AP Physics 1 Quiz: Gravitational Force

What this quiz covers

This quiz focuses on Gravitational Force, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. It decreases to $\tfrac{1}{4}$ of the original value. (correct answer)
2. It decreases to $\tfrac{1}{2}$ of the original value because only one mass is doubled.
3. It stays the same because the masses do not change.
4. It increases by a factor of 2 because the larger mass is $2m$.

Explanation: This question assesses understanding of the gravitational force law. Gravitational force between two objects is directly proportional to the product of their masses, meaning if the product increases, the force increases accordingly. It is also inversely proportional to the square of the distance between their centers, so doubling the distance reduces the force to one-fourth of its original value. In this scenario, the masses remain unchanged while the distance doubles, leading to a force that is one-fourth of the original due to the inverse-square relationship. A common distractor, choice B, incorrectly assumes that only one mass is doubled and suggests the force halves, but no mass change occurs here. To solve similar problems, always calculate the ratio of the new force to the old by considering changes in mass product and distance squared separately.

Question 2

1. It becomes $9$ times larger (correct answer)
2. It becomes $3$ times larger
3. It becomes $1/9$ as large
4. It is unchanged because the masses are unchanged

Explanation: This question tests understanding of the inverse-square relationship for gravitational force with distance. The gravitational force follows F = Gm₁m₂/r², where force is inversely proportional to the square of separation distance. When distance decreases from 3r to r (a factor of 3 decrease), the force increases by a factor of 3² = 9, because the smaller denominator r² compared to (3r)² = 9r² makes the force 9 times larger. Choice D incorrectly assumes distance changes don't affect gravitational force between objects. Remember that halving the distance quadruples the force, while tripling the distance makes the force one-ninth as strong.

Question 3

1. Unchanged
2. Twice as large
3. One-half as large (correct answer)
4. One-fourth as large

Explanation: This question tests understanding of how gravitational force depends on both mass and distance simultaneously. The gravitational force follows F = Gm₁m₂/r², depending directly on mass product and inversely on distance squared. When the probe's mass doubles (factor of 2 increase) and distance doubles (factor of 4 decrease due to squaring), the net effect is: (2 × 1)/4 = 1/2 of the original force. Choice A incorrectly assumes the mass and distance effects cancel out completely. To analyze combined changes, multiply the mass effect by the reciprocal of the squared distance effect.

Question 4

1. It is $2$ times as large because the distance doubled
2. It is $1/2$ as large because only one object is heavier
3. It is $1/4$ as large (correct answer)
4. It is unchanged because the same two masses interact

Explanation: This question tests understanding of how gravitational force changes with distance between objects. The gravitational force follows the inverse-square law: F = Gm₁m₂/r². When the separation doubles from r to 2r, the force becomes F = Gm₁m₂/(2r)² = Gm₁m₂/4r², which is 1/4 of the original force. Choice A incorrectly suggests force increases with distance, contradicting the fundamental principle that gravitational attraction weakens with separation. To solve distance-change problems, remember that doubling distance always reduces force to one-fourth, regardless of the specific mass values.

Question 5

1. Three times as large
2. Nine times as large (correct answer)
3. One-ninth as large
4. Unchanged because the masses are unchanged

Explanation: This question tests understanding of the inverse-square law for gravitational force with distance. The gravitational force follows F = Gm₁m₂/r², where force is inversely proportional to the square of separation. When distance decreases from r to r/3, the denominator becomes (r/3)² = r²/9, making the force 9 times larger (since dividing by a smaller denominator yields a larger result). Choice C incorrectly inverts the relationship, suggesting force decreases when objects get closer. Remember that reducing distance by a factor increases force by that factor squared.

Question 6

1. Half as large
2. Twice as large
3. Four times as large (correct answer)
4. Unchanged because $M$ is much larger than $m$

Explanation: This question tests understanding of the inverse-square relationship between gravitational force and distance. The gravitational force follows F = Gm₁m₂/r², where force is inversely proportional to distance squared. When separation is halved from r to r/2, the denominator becomes (r/2)² = r²/4, making the force 4 times larger (since dividing by a smaller number gives a larger result). Choice D incorrectly suggests that the mass ratio affects how distance changes influence force, but the inverse-square law applies regardless of mass values. To handle distance reductions, remember that halving distance quadruples force.

Question 7

1. It doubles, because each sphere's weight doubles.
2. It stays the same, because $r$ is unchanged.
3. It quadruples, because the product of the masses becomes $4m^2$. (correct answer)
4. It halves, because the masses are larger and pull less strongly per kilogram.

Explanation: This question tests comprehension of gravitational force dependence on mass. Gravitational force increases directly with the product of the masses, so doubling each mass quadruples the product and thus the force. The inverse-square relationship with distance means unchanged distance keeps that factor constant. Replacing both spheres with twice the mass at the same separation results in a force four times larger. Distractor B incorrectly claims the force stays the same because distance is unchanged, ignoring the mass increase's effect on the product. When approaching similar questions, identify unchanged variables like distance and focus on scaling the mass product to predict force changes.

Question 8

1. It becomes $\tfrac{1}{4}$ as large.
2. It becomes $2$ times as large.
3. It becomes $4$ times as large. (correct answer)
4. It stays the same because the masses did not change.

Explanation: This question tests understanding of gravitational force and the inverse-square law for distance. The gravitational force follows F = Gm₁m₂/r², where force is inversely proportional to the square of the separation distance. When the separation decreases from r to r/2 (halves), the denominator becomes (r/2)² = r²/4. Since we're dividing by a smaller number (r²/4 instead of r²), the force becomes 4 times larger. Choice A incorrectly applies the inverse relationship, suggesting the force decreases when objects get closer. Remember that decreasing distance increases gravitational force, and halving the distance makes the force four times stronger.

Question 9

1. It doubles because the smaller craft has less weight.
2. It becomes half as large. (correct answer)
3. It becomes one-fourth as large.
4. It stays the same because distance is unchanged.

Explanation: This question tests understanding of how gravitational force depends on the masses of interacting objects. The gravitational force is proportional to the product of the two masses: F = Gm₁m₂/r². Initially, the force is F₁ = Gm(4m)/r² = 4Gm²/r². When the 4m spacecraft is replaced with a 2m spacecraft, the new force becomes F₂ = Gm(2m)/r² = 2Gm²/r². Comparing these, F₂ = F₁/2, so the force becomes half as large. Choice A incorrectly suggests the force doubles, perhaps confusing the effect of reducing mass with some other concept. To solve mass-change problems, calculate the ratio of the new mass product to the original mass product.

Question 10

1. It becomes four times as large.
2. It becomes half as large because only mass matters.
3. It becomes one-fourth as large. (correct answer)
4. It stays the same because gravity is independent of distance.

Explanation: This question assesses understanding of the gravitational force between two masses as described by Newton's law of universal gravitation. The gravitational force is directly proportional to the product of the two masses involved, meaning that increasing either mass increases the force linearly with that change. Simultaneously, the force is inversely proportional to the square of the distance between the centers of the masses, so doubling the distance reduces the force to one-fourth of its original value. This inverse-square relationship arises because gravity spreads out in all directions, diluting its strength with the square of the distance. A common distractor, like choice D, incorrectly assumes that gravitational force is independent of distance, which might stem from confusing it with constant gravitational fields near Earth's surface. To solve similar problems, always identify the factors changed and apply the proportionality: multiply by the mass ratio and divide by the square of the distance ratio.

Question 11

1. $1/3$
2. $1/6$
3. $1/9$ (correct answer)
4. 1, because the same two masses interact

Explanation: This question tests understanding of how gravitational force depends on distance between objects. The gravitational force follows F = Gm₁m₂/r², inversely proportional to distance squared. When separation increases from r to 3r, the force becomes proportional to 1/(3r)² = 1/9r², making it 1/9 of the original force. Choice D incorrectly assumes that having the same masses in both situations means the force doesn't change, ignoring the critical role of distance. To find force ratios, divide the original distance squared by the new distance squared.

Question 12

1. Three times as large
2. Nine times as large (correct answer)
3. One-third as large because the masses are larger
4. Unchanged because distance is unchanged

Explanation: This question tests understanding of how gravitational force scales with mass changes. The gravitational force is proportional to the product of both masses: F = Gm₁m₂/r². In case A, the mass product is m × m = m². In case B, both masses triple, so the mass product becomes 3m × 3m = 9m², which is 9 times the original. Choice C incorrectly assumes larger masses somehow reduce the force, contradicting the direct proportionality relationship. When both masses change by the same factor, multiply that factor by itself to find the force change.

Question 13

1. Half as large because only one mass changed
2. Unchanged because distance is unchanged
3. Twice as large (correct answer)
4. Four times as large

Explanation: This question tests understanding of how gravitational force depends on the masses of interacting objects. The gravitational force is directly proportional to the product of both masses: F = Gm₁m₂/r². Initially, the force is proportional to (2m)(m) = 2m². When asteroid X's mass doubles from 2m to 4m, the new force is proportional to (4m)(m) = 4m², which is twice the original force. Choice A incorrectly assumes the force change depends on how many masses change rather than the actual mass values. When solving gravitational problems, remember that doubling either mass doubles the force, regardless of which mass changes.

Question 14

1. It becomes $4$ times as large.
2. It becomes $2$ times as large.
3. It becomes $\tfrac{1}{2}$ as large.
4. It becomes $\tfrac{1}{4}$ as large. (correct answer)

Explanation: This question tests understanding of how gravitational force depends on distance between objects. The gravitational force between two objects follows Newton's law of universal gravitation: F = Gm₁m₂/r², where the force is inversely proportional to the square of the distance between their centers. When the separation increases from r to 2r (doubles), the distance term in the denominator becomes (2r)² = 4r². Since the force is inversely proportional to r², the new force becomes F/4, or one-fourth as large. Choice A incorrectly suggests the force increases, which would violate the inverse relationship between force and distance. To solve problems like this, remember that doubling the distance makes the force four times weaker due to the inverse-square law.

Question 15

1. It doubles because each mass is doubled.
2. It quadruples. (correct answer)
3. It stays the same because distance is unchanged.
4. It becomes $\tfrac{1}{4}$ as large because doubling mass reduces acceleration.

Explanation: This problem tests understanding of how gravitational force depends on both masses. The gravitational force is F = Gm₁m₂/r², where force is proportional to the product of the masses. Initially, with masses 2M and 3M, the force is F = G(2M)(3M)/r² = 6GM²/r². When both masses are doubled to 4M and 6M, the new force becomes F' = G(4M)(6M)/r² = 24GM²/r² = 4F. Doubling both masses makes their product four times larger (2×2 = 4), so the force quadruples. Choice A incorrectly suggests the force only doubles, failing to account for both masses changing. To solve problems with multiple mass changes, calculate how the product m₁m₂ changes to find the force change factor.

Question 16

1. $2F$, because the larger mass is $4m$.
2. $F$, because the masses do not change.
3. $\tfrac{1}{2}F$, because the distance doubles.
4. $\tfrac{1}{4}F$, because force varies as $\tfrac{1}{r^2}$. (correct answer)

Explanation: This question examines the impact of distance on gravitational force. The force is proportional to the product of masses, which remains constant here. It decreases with the square of increasing distance, so doubling the separation reduces the force to one-fourth. With masses unchanged and distance doubled, the new force is one-fourth of the original. Distractor C suggests it halves because distance doubles, but this overlooks the squared nature of the inverse relationship. For transferable skill, remember to apply the inverse-square law by squaring the distance ratio when predicting force variations.

Question 17

1. It becomes five times as large. (correct answer)
2. It becomes 25 times as large.
3. It stays the same because P's mass is unchanged.
4. It decreases because heavier objects have less acceleration.

Explanation: This question assesses understanding of the gravitational force between two masses as described by Newton's law of universal gravitation. The gravitational force is directly proportional to the product of the masses, so replacing one mass with five times its value multiplies the force by five. The inverse-square dependence on distance is irrelevant here since distance remains unchanged. This qualitative view highlights how gravitational attraction scales linearly with mass when other factors are fixed. Choice C, a distractor, claims it stays the same because one mass is unchanged, ignoring the product nature of the force law. A transferable strategy is to focus on the changed variables and apply F_new = F_old × (new mass product / old mass product) × (old r / new r)^2.

Question 18

1. Pair 2 has greater force because one mass is larger.
2. Pair 1 has greater force because the masses are equal.
3. The forces are equal because the mass products are the same. (correct answer)
4. Pair 2 has smaller force because the smaller object weighs less.

Explanation: This question examines how different mass combinations affect gravitational force. The force is proportional to the product of masses, so equal products yield equal forces regardless of individual values. Distance is the same, keeping the inverse-square factor identical. Both pairs have the same mass product of m^2, resulting in equal forces. Distractor A claims pair 2 has greater force due to one larger mass, but the product is what matters, not individual sizes. A transferable approach is to always compute m1 m2 for each pair and compare products when distances are equal.

Question 19

1. The same because the distance is the same
2. Twice as large (correct answer)
3. Four times as large
4. Half as large because only one mass increased

Explanation: This question tests understanding of how gravitational force depends on the masses of interacting objects. The gravitational force is proportional to the product of both masses: F = Gm₁m₂/r². In setup 1, the mass product is m × m = m². In setup 2, the mass product is 2m × m = 2m², which is twice as large. Choice D incorrectly assumes that only simultaneous changes to both masses affect the force, but changing either mass changes the product. When analyzing mass changes, multiply the masses together and compare the products to find the force ratio.

Question 20

1. It becomes $\tfrac{4}{9}$ as large. (correct answer)
2. It becomes $\tfrac{2}{3}$ as large.
3. It becomes $\tfrac{3}{2}$ as large because distance increased.
4. It stays the same because the masses did not change.

Explanation: This question tests understanding of how gravitational force changes with distance. The gravitational force follows F = Gm₁m₂/r², inversely proportional to the square of separation. Initially, F = Gm(3m)/r² = 3Gm²/r². When distance changes from r to 3r/2, the new force is F_new = 3Gm²/(3r/2)² = 3Gm²/(9r²/4) = 3Gm²·4/9r² = 12Gm²/9r² = 4Gm²/3r². Comparing to the original, F_new = (4/3)·(Gm²/r²) = (4/9)·(3Gm²/r²) = (4/9)F. Choice C incorrectly suggests force increases with distance, violating the inverse relationship. To find the new force, divide by the square of the distance ratio: (3/2)² = 9/4.