Class 9 Science NCERT Notes – Chapter 9: Gravitation (PDF, MindMap, Q&A, Quizzes)

Chapter 9 (Physics): Gravitation – Class 9 NCERT Science Detailed Study Notes.

1. Introduction to Gravitation

• Fundamental Concept: A force is required to alter the speed or the direction of motion of any object.
• Newton’s Insight: Isaac Newton proposed that a single, universal force is responsible for phenomena such as an apple falling to the Earth, the Moon orbiting the Earth, and the planets orbiting the Sun. This force is known as the gravitational force.
• Circular Motion and Centripetal Force:
  • An object moving in a circular path, like a stone being whirled on a string, is constantly changing its direction. This change in direction implies a change in velocity, which means the object is accelerating.
  • The force causing this acceleration is directed towards the center of the circular path. This is called centripetal force (meaning “centre-seeking”).
  • If the centripetal force is removed (e.g., the string is released), the object will fly off in a straight line that is a tangent to the circular path at that point.
  • The Moon’s orbit around the Earth is maintained by a centripetal force provided by the Earth’s gravitational attraction. Without this force, the Moon would move in a straight line.

2. Universal Law of Gravitation

• The Law: Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• Mathematical Formulation: The force (F) between two objects of masses M and m, separated by a distance d, is given by the equation:
  • F ∝ M × m (Force is directly proportional to the product of the masses).
  • F ∝ 1 / d² (Force is inversely proportional to the square of the distance). This is known as the inverse-square rule. For example, if the distance is doubled, the force becomes one-fourth as strong.
• Universal Gravitational Constant (G):
  • G is the constant of proportionality in the equation.
  • Its value was determined by Henry Cavendish.
  • The accepted value is G = 6.673 × 10⁻¹¹ N m² kg⁻².
  • The SI unit of G is N m² kg⁻².
• Universality: The law is termed “universal” because it applies to all bodies, regardless of their size or location, whether they are celestial (like planets) or terrestrial (on Earth).
• Third Law of Motion: While the Earth attracts an apple, the apple also attracts the Earth with an equal and opposite force. However, due to the Earth’s immense mass, its resulting acceleration is negligibly small.
• Importance of the Law: The Universal Law of Gravitation successfully explains several key phenomena:
  1. The force that binds us to the Earth.
  2. The motion of the Moon around the Earth.
  3. The motion of planets around the Sun.
  4. The formation of tides due to the gravitational pull of the Moon and the Sun.

3. Free Fall and Acceleration Due to Gravity (g)

• Free Fall: When an object falls towards the Earth under the influence of the gravitational force alone, it is said to be in free fall. During free fall, there is a change in the magnitude of the object’s velocity, meaning it accelerates.
• Acceleration Due to Gravity (g): This is the acceleration produced in a freely falling body due to the Earth’s gravitational force.
  • The SI unit for g is m s⁻².
  • The magnitude of the gravitational force (F) on an object of mass m is given by F = mg.
• Calculating the Value of g:
  • By equating the two expressions for gravitational force (F = mg and F = G(Mm/R²)), we get the formula for g on the Earth’s surface:
  • Using the values: G = 6.7 × 10⁻¹¹ N m² kg⁻², M = 6 × 10²⁴ kg, and R = 6.4 × 10⁶ m, the value of g is calculated to be 9.8 m s⁻².
• Variation in g:
  • The Earth is not a perfect sphere; it is flattened at the poles and bulges at the equator.
  • Since the radius is greater at the equator than at the poles, the value of g is greater at the poles and less at the equator.
  • The force of gravity also decreases with altitude.
• Motion under Gravity:
  • The acceleration g is independent of the mass of the falling object. Therefore, in the absence of air resistance, all objects (hollow or solid, big or small) fall at the same rate.
  • The standard equations for uniformly accelerated motion can be used for objects in free fall by replacing acceleration a with g:
    • v = u + gt
    • s = ut + ½gt²
    • v² = u² + 2gs

4. Mass and Weight

Feature	Mass (m)	Weight (W)
Definition	The measure of an object’s inertia.	The force with which an object is attracted towards the Earth.
Formula	Inherent property of matter.	W = m × g
Constancy	Constant everywhere (Earth, Moon, space).	Varies depending on the location because g varies.
SI Unit	Kilogram (kg)	Newton (N)
Nature	Scalar quantity (magnitude only).	Vector quantity (magnitude and direction – vertically downwards).

5. Weight on the Moon

• The Moon has less mass and a smaller radius than the Earth.
• Consequently, the Moon exerts a lesser gravitational force on objects.
• Through calculations using the universal law of gravitation and the respective masses and radii of the Earth and Moon, it is determined that the weight of an object on the Moon is approximately 1/6th of its weight on the Earth.

6. Thrust and Pressure

• Thrust: The force acting on an object perpendicular to the surface.
• Pressure: The thrust per unit area.
• SI Unit: The SI unit of pressure is N/m², which is also called a Pascal (Pa) in honor of Blaise Pascal.
• Principle: The same force (thrust) exerts a larger pressure when applied over a smaller area and a smaller pressure when applied over a larger area. This explains why nails have pointed tips, knives have sharp edges, and building foundations are wide.
• Pressure in Fluids: All liquids and gases are fluids. Fluids exert pressure on the base and walls of the container they are in. Pressure in a confined fluid is transmitted equally in all directions.

7. Buoyancy and Archimedes’ Principle

• Buoyancy (Upthrust): The upward force exerted by a fluid on an object that is partially or fully immersed in it. This force makes objects feel lighter in a fluid. The magnitude of the buoyant force depends on the density of the fluid.
• Floating and Sinking: The fate of an object placed in a fluid depends on the comparison between its weight and the buoyant force acting on it. This is directly related to density.
  • Density: The mass of a substance per unit volume.
  • An object with a density less than the fluid’s density will float.
  • An object with a density greater than the fluid’s density will sink.
• Archimedes’ Principle:
  • Statement: When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.
  • Applications: This principle is crucial in designing ships and submarines, and is the basis for instruments like lactometers (to check milk purity) and hydrometers (to determine liquid densities).

*****************************************************************************************

Q&A Section

Part A: Short-Answer Questions

Instructions: Answer each question in 2-3 sentences.

1. What is the fundamental insight Isaac Newton had about the force that causes an apple to fall and the moon to orbit the Earth?
2. Define centripetal force and explain its role in circular motion.
3. What would happen to the Moon if the Earth’s gravitational force suddenly disappeared?
4. State the Universal Law of Gravitation in words.
5. Write the mathematical formula for the Universal Law of Gravitation, defining each variable.
6. What is the significance of the universal gravitational constant, G, and who first determined its value?
7. Explain the “inverse-square” relationship in the context of gravitational force.
8. According to Newton’s third law, an apple attracts the Earth. Why don’t we see the Earth move towards the apple?
9. List three phenomena that the Universal Law of Gravitation successfully explains.
10. What is the definition of “free fall”?
11. What do we call the acceleration experienced by an object in free fall, and what is its standard value near the Earth’s surface?
12. How does the value of g (acceleration due to gravity) change between the Earth’s poles and the equator? Explain why.
13. Why do a stone and a sheet of paper fall at different rates in air but at the same rate in a vacuum?
14. What is the fundamental difference between the mass of an object and its weight?
15. If an object has a mass of 20 kg, what is its weight on Earth? (Use g = 9.8 m s⁻²)
16. Why is an object’s weight on the Moon significantly less than its weight on Earth?
17. Define thrust and pressure, and state the relationship between them.
18. Provide a real-world example of how manipulating area can change the effect of pressure for a given force.
19. What is buoyancy? In which direction does the buoyant force act?
20. Explain the relationship between an object’s density and a fluid’s density in determining whether the object will float or sink.
21. State Archimedes’ Principle.
22. What real-world technology is designed using Archimedes’ Principle?
23. Why does it feel difficult to push an empty, sealed plastic bottle deeper into water?
24. If a stone is thrown vertically upwards, what is the value of its acceleration when it reaches its highest point?
25. What is the SI unit for pressure, and after whom is it named?

Part B: Multiple-Choice Questions

Instructions: Choose the single best answer for each question.

1. The force that keeps the planets in orbit around the Sun is…
   • a) Centrifugal force b) Frictional force c) Gravitational force d) Magnetic force
2. According to the Universal Law of Gravitation, if the distance between two objects is doubled, the gravitational force between them becomes…
   • a) Double b) Half c) Four times stronger d) One-quarter as strong
3. The value of the universal gravitational constant, G, is approximately…
   • a) 9.8 m s⁻² b) 6.673 × 10⁻¹¹ N m² kg⁻² c) 6.0 × 10²⁴ kg d) 3.0 × 10⁸ m/s
4. Mass is a measure of an object’s…
   • a) Weight b) Volume c) Inertia d) Gravitational pull
5. The weight of an object is calculated using the formula…
   • a) W = m / g b) W = g / m c) W = m × g d) W = m × a²
6. An object’s weight on the moon is what fraction of its weight on the Earth?
   • a) 1/2 b) 1/4 c) 1/6 d) 1/8
7. The SI unit of weight is the…
   • a) Kilogram (kg) b) Pascal (Pa) c) Joule (J) d) Newton (N)
8. The force acting perpendicular to a surface is called…
   • a) Pressure b) Thrust c) Buoyancy d) Inertia
9. The SI unit of pressure is the…
   • a) Newton (N) b) Watt (W) c) Pascal (Pa) d) Kilogram (kg)
10. An object will float in a liquid if…
    • a) Its density is greater than the liquid’s density. b) Its density is less than the liquid’s density. c) Its mass is less than the liquid’s mass. d) Its volume is equal to the liquid’s volume.
11. Archimedes’ Principle states that the buoyant force is equal to the…
    • a) Weight of the object in air. b) Volume of the fluid displaced. c) Weight of the fluid displaced. d) Mass of the object.
12. The acceleration due to gravity, g, is…
    • a) Greater at the equator than at the poles. b) Greater at the poles than at the equator. c) The same everywhere on Earth’s surface. d) Dependent on the object’s mass.
13. In the absence of air resistance, a heavy object and a light object dropped from the same height will…
    • a) Fall at the same rate. b) The heavy object will fall faster. c) The light object will fall faster. d) The rate depends on their shape.
14. The term for all liquids and gases is…
    • a) Densities b) Fluids c) Pressures d) Buoyants
15. If the mass of one of two interacting objects is doubled, the gravitational force between them…
    • a) Is halved b) Is doubled c) Is quadrupled d) Remains the same
16. The path an object would take if centripetal force were removed is a…
    • a) Circle in the opposite direction b) Straight line towards the center c) Straight line tangent to the circle d) Spiral path outwards
17. Which of the following is an application of Archimedes’ Principle?
    • a) The design of an airplane’s wings b) The function of a hydraulic press c) The design of submarines d) The operation of a simple lever
18. A block of wood with dimensions 20cm x 10cm exerts the greatest pressure on a table when it rests on its…
    • a) 20cm x 10cm face b) The pressure is the same for all faces c) There is not enough information d) The face with the smallest area
19. An object has a mass of 60 kg on Earth. Its mass on the Moon will be…
    • a) 10 kg b) 60 kg c) 360 kg d) 0 kg
20. The force of gravitation is described as a weak force unless…
    • a) The objects are very close b) The objects are moving very fast c) Large masses are involved d) The objects are electrically charged

*****************************************************************************************

Answer Keys

Answer Key for Short-Answer Questions

1. Newton understood that the same force, which he called gravitational force, is responsible for both the motion of celestial bodies like the Moon and the falling of objects on Earth. This unified the laws of physics in the heavens and on Earth.
2. Centripetal force is a “centre-seeking” force that causes an object to accelerate towards the center of a circular path. In circular motion, this force is responsible for constantly changing the object’s direction, keeping it from moving off in a straight line.
3. If the Earth’s gravitational force disappeared, the centripetal force acting on the Moon would be gone. The Moon would then continue moving in a straight line, tangent to its orbit at that exact moment.
4. The Universal Law of Gravitation states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
5. The formula is F = G (M × m) / d². Here, F is the gravitational force, M and m are the masses of the two objects, d is the distance between their centers, and G is the universal gravitational constant.
6. G is the constant of proportionality that relates the masses and distance of objects to the gravitational force between them. Its value was first found by Henry Cavendish using a sensitive balance.
7. The “inverse-square” relationship means that the force is inversely proportional to the square of the distance. For example, if you double the distance (factor of 2), the force becomes 1/(2²) or 1/4 of its original strength.
8. The Earth has an immensely larger mass compared to the apple. According to Newton’s second law (F=ma), for a given force, acceleration is inversely proportional to mass. Therefore, the Earth’s acceleration is so infinitesimally small that it is completely unnoticeable.
9. The Universal Law of Gravitation explains: (i) the force that binds us to the Earth, (ii) the motion of the Moon around the Earth, and (iii) the motion of planets around the Sun (and tides).
10. “Free fall” is the motion of an object when it is falling towards the Earth under the influence of the Earth’s gravitational force alone, with no other forces like air resistance acting on it.
11. The acceleration is called the acceleration due to gravity, denoted by g. Its standard value near the Earth’s surface is 9.8 m s⁻².
12. The value of g is greater at the poles than at the equator. This is because the Earth is not a perfect sphere; its radius is larger at the equator. Since g is inversely proportional to the square of the radius, a smaller radius at the poles results in a larger value for g.
13. They fall at different rates in air because of air resistance. The sheet of paper has a large surface area and experiences more resistance than the compact stone. In a vacuum, there is no air resistance, so both objects fall at the same rate of acceleration (g) regardless of their mass or shape.
14. Mass is the measure of an object’s inertia and is constant regardless of location. Weight is the force of gravity acting on that mass (W = mg) and changes depending on the local value of g.
15. Using the formula W = m × g, the weight is 20 kg × 9.8 m s⁻² = 196 N.
16. An object’s weight on the Moon is less because the Moon has significantly less mass and a smaller radius than the Earth. This results in a much weaker gravitational field and a smaller value for g on the Moon’s surface.
17. Thrust is the force acting perpendicular to a surface. Pressure is defined as the thrust per unit area (Pressure = Thrust / Area).
18. A knife has a very sharp edge, which is a very small surface area. This allows a small applied force (thrust) to generate a very high pressure, enabling it to cut easily.
19. Buoyancy is the upward force exerted by a fluid on an object immersed in it. The buoyant force always acts in the upward direction, opposing the force of gravity.
20. If an object’s density is less than the density of the fluid it is placed in, it will float. If the object’s density is greater than the fluid’s density, it will sink.
21. Archimedes’ Principle states that when a body is immersed fully or partially in a fluid, it experiences an upward force (buoyancy) that is equal to the weight of the fluid it displaces.
22. Archimedes’ Principle is used in the design of ships and submarines. A ship floats because the weight of the water it displaces creates a buoyant force equal to the ship’s total weight.
23. Water exerts an upward buoyant force on the bottle. To push it deeper, one must apply a downward force that overcomes this increasing upthrust. The deeper the bottle is pushed, the more water it displaces and the greater the buoyant force becomes.
24. The acceleration is constant throughout its motion, even at the highest point where its velocity is momentarily zero. The acceleration is always g (9.8 m s⁻²), directed downwards.
25. The SI unit for pressure is the Pascal (Pa), named in honor of the scientist Blaise Pascal.

Answer Key for Multiple-Choice Questions

1. c) Gravitational force
2. d) One-quarter as strong
3. b) 6.673 × 10⁻¹¹ N m² kg⁻²
4. c) Inertia
5. c) W = m × g
6. c) 1/6
7. d) Newton (N)
8. b) Thrust
9. c) Pascal (Pa)
10. b) Its density is less than the liquid’s density.
11. c) Weight of the fluid displaced.
12. b) Greater at the poles than at the equator.
13. a) Fall at the same rate.
14. b) Fluids
15. b) Is doubled
16. c) Straight line tangent to the circle
17. c) The design of submarines
18. d) The face with the smallest area
19. b) 60 kg
20. c) Large masses are involved

*****************************************************************************************

Essay Questions and Answers

1. Explain in detail the Universal Law of Gravitation, including its mathematical representation. Discuss why this law is considered “universal” and provide an example of its application.
   • Answer: The Universal Law of Gravitation, formulated by Isaac Newton, states that every particle of matter in the universe attracts every other particle with a force. This force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers. The mathematical formula for this law is F = G (M × m) / d², where F is the gravitational force, M and m are the masses of the two objects, d is the distance between them, and G is the universal gravitational constant (6.673 × 10⁻¹¹ N m² kg⁻²). The law is considered “universal” because it applies to all objects in the cosmos, regardless of their size, composition, or location. It governs the motion of celestial bodies like planets, moons, and stars, as well as terrestrial objects like a falling apple. An example of its application is calculating the force between the Earth and the Moon, which is the centripetal force that keeps the Moon in orbit. This calculation requires the masses of the Earth and Moon, the distance between them, and the value of G.
2. Differentiate clearly between mass and weight. Explain why an astronaut’s mass is constant, but their weight changes when they travel from Earth to the Moon.
   • Answer: Mass and weight are distinct physical quantities. Mass is the measure of an object’s inertia, or the amount of matter it contains. It is an intrinsic property of an object and is constant everywhere. Its SI unit is the kilogram (kg). Weight, on the other hand, is the force of gravity acting on an object’s mass. It is calculated as the product of mass and the acceleration due to gravity (W = mg). Since weight is a force, its SI unit is the Newton (N). An astronaut’s mass (the amount of matter in their body) remains the same whether they are on Earth or the Moon. However, their weight changes because the acceleration due to gravity g is different in the two locations. The Moon has much less mass than the Earth, resulting in a weaker gravitational pull and a value of g that is about 1/6th of that on Earth. Therefore, the astronaut’s weight on the Moon is only 1/6th of their weight on Earth.
3. Describe the concept of “free fall” and the role of acceleration due to gravity (g). Explain why a crumpled ball of paper falls faster than a flat sheet of paper, and how this would change in a vacuum.
   • Answer: Free fall is the state of an object falling solely under the influence of gravity, with no other forces like air resistance acting upon it. During free fall, an object experiences a constant downward acceleration known as the acceleration due to gravity, or g, which is approximately 9.8 m s⁻² near the Earth’s surface. A key aspect of this acceleration is that it is independent of the falling object’s mass. In the presence of air, a crumpled ball of paper falls faster than a flat sheet because of air resistance. The flat sheet has a much larger surface area, so it experiences a greater upward force from the air, which opposes its downward motion and slows its fall. The crumpled ball is more streamlined and experiences less air resistance. In a vacuum, where there is no air, both the crumpled ball and the flat sheet would fall at the same rate and hit the ground simultaneously, as the only force acting on them would be gravity, and their acceleration (g) would be identical regardless of mass or shape.
4. Explain the concepts of thrust and pressure. Using the example of a person standing on loose sand versus lying down, illustrate how the same force can produce different effects.
   • Answer: Thrust is the force that acts on a surface in a direction perpendicular to that surface. Pressure is defined as the thrust applied per unit area. The relationship is given by the formula: Pressure = Thrust / Area. This formula shows that for a constant thrust, pressure is inversely proportional to the area over which the thrust is applied. A smaller area results in a larger pressure, and a larger area results in a smaller pressure. A person standing on loose sand provides a clear illustration of this principle. The force exerted on the sand is the person’s weight (which acts as the thrust). When standing, this entire thrust is concentrated on the small area of their feet, creating high pressure and causing their feet to sink deep into the sand. When the same person lies down, their weight is distributed over the much larger contact area of their entire body. This larger area results in a much lower pressure, which is why their body does not sink deeply into the sand.
5. What is Archimedes’ Principle? Describe an activity to demonstrate it and explain its application in determining why some objects float while others sink.
   • Answer: Archimedes’ Principle states that an object fully or partially immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object. An activity to demonstrate this involves suspending a stone from a spring balance to note its weight in air. Then, the stone is gradually lowered into a container of water while still attached to the balance. It will be observed that the reading on the spring balance decreases, indicating an upward force is acting on the stone. This upward force is the buoyant force, and according to the principle, it is equal to the weight of the water the stone has pushed aside. This principle explains floating and sinking. An object sinks if its weight is greater than the buoyant force. An object floats if its weight is less than or equal to the buoyant force. This is related to density: an object with a density greater than the fluid will sink because its weight is greater than the weight of the fluid it displaces (the buoyant force). Conversely, an object with a density less than the fluid will float.
6. Derive the formula for calculating the acceleration due to gravity, g, on the surface of the Earth. Explain why g is greater at the poles than at the equator.
   • Answer: The derivation for g combines Newton’s Second Law of Motion and the Universal Law of Gravitation. According to the Second Law, the force on a falling object of mass m is F = mg. According to the Universal Law of Gravitation, the force between the Earth (mass M) and the object (mass m) on its surface (radius R) is F = G(Mm/R²). By equating these two expressions for the same force, we get: mg = G(Mm/R²) We can cancel the object’s mass m from both sides, which shows that the acceleration is independent of the object’s mass: g = GM/R² This is the formula for g. The value of g is greater at the poles than at the equator because the Earth is not a perfect sphere; it is an oblate spheroid, slightly flattened at the poles and bulging at the equator. This means the Earth’s radius (R) is smaller at the poles than at the equator. Since g is inversely proportional to the square of the radius (R²), the smaller radius at the poles results in a larger value for g.
7. Discuss the importance of the Universal Law of Gravitation by explaining four distinct phenomena it successfully describes.
   • Answer: The Universal Law of Gravitation is immensely important as it provides a unified framework for understanding the cosmos. Four key phenomena it explains are:
     1. The force that binds us to the Earth: The law explains why we, and all other objects, are held on the surface of the planet. It is the mutual gravitational attraction between the Earth’s mass and our own mass that we perceive as weight.
     2. The motion of the Moon around the Earth: The law describes the force that acts as the centripetal force keeping the Moon in a stable orbit. It prevents the Moon from flying off into space in a straight line.
     3. The motion of planets around the Sun: In the same way it explains the Moon’s orbit, the law explains why all planets in our solar system orbit the Sun. The Sun’s immense mass creates a powerful gravitational field that dictates the orbital paths of the planets.
     4. The tides: The law explains that the rise and fall of sea levels are primarily caused by the differential gravitational forces exerted by the Moon and the Sun on different parts of the Earth. This gravitational pull creates tidal bulges in the oceans.
8. Compare and contrast the forces involved when an iron nail and a piece of cork of equal mass are placed on the surface of water. Explain why their outcomes are different.
   • Answer: When an iron nail and a piece of cork of equal mass are placed on water, both are subjected to two main vertical forces: the downward force of gravity (their weight) and the upward buoyant force from the water. Since they have equal mass, their weight (W=mg) is identical. The difference in outcome arises from the difference in their volumes and, consequently, their densities. The iron nail has a very small volume for its mass, making it very dense—much denser than water. The buoyant force acting on it (equal to the weight of the small volume of water it displaces) is far less than its weight, so the net force is downwards, and it sinks. The cork, however, has a large volume for the same mass, making its density less than that of water. When placed on the water, it displaces a volume of water whose weight is greater than the cork’s own weight. This results in a buoyant force that is greater than the cork’s weight, causing a net upward force that pushes it to the surface, where it floats.
9. An object is thrown vertically upwards. Describe its velocity and acceleration at the very peak of its trajectory and throughout its entire journey (up and down).
   • Answer: When an object is thrown vertically upwards, its motion is governed by gravity. On its way up, its initial upward velocity is constantly decreasing due to the downward acceleration of gravity, g (-9.8 m s⁻²). At the very peak of its trajectory, the object momentarily stops moving upwards before it begins to fall. At this highest point, its vertical velocity is exactly zero (0 m/s). However, its acceleration is not zero. Throughout the entire journey—on the way up, at the peak, and on the way down—the acceleration is constant. It is always equal to the acceleration due to gravity, g (9.8 m s⁻²), and it is always directed vertically downwards towards the center of the Earth. The misconception that acceleration is zero at the peak is incorrect; if it were, the object would remain stationary at that point and not fall back down.
10. Amit buys gold at the poles and hands it over to a friend at the equator. Why might the friend disagree with the weight of the gold? Will they disagree with the mass? Explain your reasoning.
    • Answer: The friend might disagree with the weight of the gold because weight is dependent on the local acceleration due to gravity (g). The value of g is greater at the poles than at the equator because the Earth’s radius is smaller at the poles. Therefore, the same mass of gold will exert a greater downward force (i.e., have a greater weight) when measured at the poles compared to when it is measured at the equator. When the friend weighs the gold at the equator, it will register a slightly lower value than what was recorded at the poles. However, there should be no disagreement about the mass of the gold. Mass is an intrinsic property of the gold, representing the amount of matter it contains. Mass is constant and does not change with location. So, while the weight in Newtons is different, the mass in kilograms is exactly the same.

*****************************************************************************************

Glossary of Key Terms

• Acceleration Due to Gravity (g): The acceleration experienced by an object in free fall due to the Earth’s gravitational force. Its value near the Earth’s surface is approximately 9.8 m s⁻².
• Archimedes’ Principle: The principle that states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
• Buoyancy (or Upthrust): The upward force exerted by a fluid on any object that is partially or fully immersed in it.
• Centripetal Force: A force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.
• Density: The mass of a substance per unit volume.
• Fluid: A substance that can flow and takes the shape of its container; includes all liquids and gases.
• Free Fall: The motion of an object where gravity is the only force acting upon it.
• Gravitational Force: The force of attraction between any two masses in the universe.
• Inverse-Square Law: A law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that quantity. In this context, gravitational force follows this law.
• Mass (m): The measure of an object’s inertia; the amount of matter in an object. It is a constant quantity. Its SI unit is the kilogram (kg).
• Pascal (Pa): The SI unit of pressure, equivalent to one newton per square meter (N/m²).
• Pressure: The force (or thrust) applied perpendicular to a surface per unit area over which the force is distributed.
• Tangent: A straight line that touches a curve or curved surface at a point, but does not cross it at that point.
• Thrust: The force acting on a surface perpendicular to that surface.
• Universal Gravitational Constant (G): The constant of proportionality in Newton’s law of gravitation. G ≈ 6.673 × 10⁻¹¹ N m² kg⁻².
• Universal Law of Gravitation: The law stating that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Weight (W): The force of gravity acting on an object (W = mg). Its SI unit is the Newton (N). It varies with location.