This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 2 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 0.5 m above the lowest point (reference level), so PE = (2 kg)(10 m/s²)(0.5 m) = 10 J. Choice C is correct because it accurately calculates PE = mgh = (2)(10)(0.5) = 10 J with proper substitution. Choice A is wrong because it makes a calculation error: uses wrong formula or arithmetic mistake, like omitting g and calculating just mh = (2)(0.5) = 1 J, when actually PE includes g. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). At the same height h = 2 m, comparing different masses: 2 kg pot has PE = (2)(10)(2) = 40 J, 4 kg pot has PE = (4)(10)(2) = 80 J (exactly double)—gravitational potential energy is directly proportional to mass at constant height: PE ∝ m. Choice C is correct because it properly identifies the proportional relationship: double mass → double PE. Choice D is wrong because it applies wrong relationship: claims doubling mass quadruples PE (confusing with KE-speed squared), when actually PE ∝ m is linear (double m → double PE, not quadruple). Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). To find the increase in gravitational potential energy, calculate PE at each position and find the difference: initially on floor (h = 0 m), PE₁ = (1 kg)(10 m/s²)(0 m) = 0 J; on low shelf (h = 1 m), PE₂ = (1 kg)(10 m/s²)(1 m) = 10 J; therefore, increase in PE = PE₂ - PE₁ = 10 J - 0 J = 10 J. This 10 J increase represents the work you did lifting the book from floor to shelf—you applied an upward force equal to the book's weight (mg = 10 N) through a distance of 1 m, doing work = force × distance = 10 N × 1 m = 10 J, which is now stored as gravitational potential energy. Choice C is correct because it accurately calculates the change in PE as 10 J when moving from 0 m to 1 m height. Choice A (1 J) appears to have omitted g, calculating just m×Δh = 1×1 = 1 J; Choice B (0 J) incorrectly suggests no change in PE despite changing height; Choice D (100 J) makes an arithmetic error, possibly calculating 1×10×10 instead of 1×10×1. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 1 m shelf increases its PE by (1)(10)(1) = 10 J—you did 10 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 10 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 500 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 20 m above the ground (reference level), so PE = (500 kg)(10 m/s²)(20 m) = 100,000 J. This means the roller coaster cart has 100,000 Joules of gravitational potential energy at the top of the hill—if it were to roll down from 20 m height to ground level, this 100,000 J of PE would convert to kinetic energy (in ideal case with no friction, KE at ground would be 100,000 J, giving the cart significant speed). Choice C is correct because it correctly calculates PE = mgh = (500)(10)(20) = 100,000 J with proper substitution. Choice A (10,000 J) appears to have made an arithmetic error, possibly calculating 500×20 = 10,000 without including g; Choice B (50,000 J) might have used wrong height (10 m instead of 20 m) giving 500×10×10 = 50,000; Choice D (1,000 J) severely underestimates, perhaps dividing instead of multiplying or using wrong values. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: a 500 kg roller coaster cart at 20 m height has PE = 100,000 J—this enormous energy was provided by the lift mechanism pulling the cart up the first hill, and as the cart descends, this PE converts to KE making the ride thrilling; water behind a dam at similar heights stores millions of joules as gravitational PE, which converts to flowing water's KE to spin turbines for hydroelectric power.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). For an object at rest, PE depends only on m, g, and h—no speed or other factors, as kinetic energy would involve speed but PE is positional. Choice A is correct because it properly identifies the quantities in PE = mgh: mass, height above reference, and g. Choice B is wrong because it includes speed, which is for kinetic energy (KE = ½mv²), not gravitational PE. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The change in gravitational potential energy is calculated using ΔPE = mgΔh: mass m = 5 kg, g = 10 m/s², change in height Δh = 3 m (from 1 m to 4 m), so ΔPE = (5)(10)(3) = 150 J; alternatively, initial PE = (5)(10)(1) = 50 J, final PE = (5)(10)(4) = 200 J, ΔPE = 200 - 50 = 150 J. Choice C is correct because it accurately calculates ΔPE = mgΔh = (5)(10)(3) = 150 J with proper substitution. Choice D is wrong because it makes a calculation error: uses final PE = 200 J instead of the change ΔPE = 150 J, confusing total PE with the change. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy gained is calculated using ΔPE = mgΔh: mass m = 2 kg, g = 10 m/s², change in height Δh = 3 m (from 0 m to 3 m), so ΔPE = (2)(10)(3) = 60 J. Choice C is correct because it accurately calculates the gain in PE = mgΔh = (2)(10)(3) = 60 J with proper substitution. Choice A is wrong because it makes a calculation error: arithmetic mistake like (2)(10)(0.25) or using wrong height, resulting in 5 J, when actually it's 60 J for 3 m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). With the new reference at the 1 m table, the shelf is now at h = 1 m above the reference, so PE = (1 kg)(10 m/s²)(1 m) = 10 J, compared to original PE = (1)(10)(2) = 20 J using ground as reference—the calculated value changes with reference level, but differences in PE (like changes) remain the same regardless of reference. Choice B is correct because it appropriately applies the formula to the new reference, calculating PE = mgh with h=1 m giving 10 J. Choice A is wrong because it confuses reference point incorrectly: claims PE becomes 0 J just because it's on a shelf, but PE is relative to the chosen reference and is not zero unless h=0. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). To find height, rearrange PE = mgh to h = PE / (mg): with PE = 150 J, m = 3 kg, g = 10 m/s², h = 150 / (3×10) = 150 / 30 = 5 m. This means the object is 5 m above the ground, storing 150 J of PE that could convert to KE if it falls. Choice C is correct because it correctly calculates h = PE / (mg) = 150 / (3×10) = 5 m. Choice D is wrong because it makes a calculation error: perhaps omitting m and calculating 150 / 10 = 15 m, but mass must be included since PE ∝ m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). At the same height h = 1.5 m, comparing different masses: 1 kg object has PE = (1)(10)(1.5) = 15 J, 2 kg object has PE = (2)(10)(1.5) = 30 J, and 5 kg object has PE = (5)(10)(1.5) = 75 J—the 5 kg has the greatest, showing gravitational potential energy is directly proportional to mass at constant height: PE ∝ m. The heavier object has more PE at the same height because it required more work to lift it there (lifting 5 kg through 1.5 m takes more work than lifting 1 kg through same 1.5 m), and it stores that work as gravitational potential energy. Choice C is correct because it properly identifies the proportional relationship: greater mass → greater PE at same height. Choice D is wrong because it misunderstands proportionality: claims all have same PE since same height, but actually PE ∝ m, so different masses have different PE even at same h. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.