Gravitation
CBSE Class 9 · Science · Notes, formulas and practice questions
Revise Class 9 Science Gravitation: universal law of gravitation, free fall and acceleration due to gravity, mass and weight, weight on the Moon, pressure, buoyancy, Archimedes' principle and relative density with worked numericals.
Studying Gravitation?
Turn your own textbook pages, a lecture recording or a YouTube video into notes like these — plus flashcards, quizzes and practice questions — in your own language. The Standard plan is free, permanently, and needs no card.
Make notes from your own material — freeWhat this chapter covers
Gravitation begins with a universal observation: a fruit falls to the ground, and the planets remain in orbit around the Sun. Newton's universal law of gravitation gives a single rule to explain both. It states that the force between two masses falls off with the square of the distance between them. When one mass is extremely large, like Earth, this force causes objects to accelerate towards it. Near Earth's surface, the acceleration due to gravity g is about 9.8 m/s², independent of the object's mass.
Because g is constant in free fall, the familiar equations of motion apply with acceleration a equal to g. For a dropped stone with u = 0 you can find the time of fall from h = ½gt² and the speed just before reaching the ground from v = gt or v² = 2gh. The chapter stresses that these equations assume negligible air resistance. It also draws a clean line between mass, which is an intrinsic property, and weight, a force W = mg. On the Moon, where g is smaller, weight becomes about one-sixth, but mass is unchanged.
Later the chapter looks at the same gravitational pull through forces acting on surfaces. Thrust is the perpendicular force on a surface; pressure divides thrust by area, so for a given force, a smaller area gives larger pressure. This explains why sharp blades cut more than blunt ones. When an object is placed in liquid, liquid pressure at greater depth is larger, creating an upward buoyant force. Whether a body sinks or floats depends on whether this force can cancel its weight.
Archimedes' principle sets the buoyant force exactly equal to the weight of displaced liquid. Relative density, the density of a substance divided by density of water, is a convenient way to judge flotation: relative density greater than 1 means it sinks, less than 1 means it floats. This connects density, weight and buoyancy and gives compact numericals for the board exam.
Key terms
- Universal law of gravitation
- Every particle in the universe attracts every other particle with a force directed along the line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. It explains falling bodies, planetary orbits, tides and why everything is pulled towards Earth.
- Acceleration due to gravity (g)
- The uniform acceleration with which a body falls freely towards the Earth's surface under gravity alone. Its value near the surface of Earth is about 9.8 m/s², and it does not depend on the mass, size or shape of the falling body.
- Free fall
- Motion of a body when the only force acting on it is gravity. In free fall, the initial velocity may be zero or non-zero, and the acceleration is g downwards. Air resistance is ignored in school numericals.
- Mass
- The quantity of matter in a body. It is a fundamental property measured in kilograms, and it remains exactly the same whether the body is on the Earth, the Moon or in space.
- Weight
- The gravitational force with which a planet pulls a body; W = mg. It is a vector, measured in newtons, and changes if g changes. On the Moon, a body has only about one-sixth of its Earth weight because the Moon's gravity is weaker.
- Thrust and pressure
- Thrust is the total perpendicular force acting on a surface. Pressure is the thrust acting on unit area, P = F/A. The SI unit of pressure is the pascal (Pa). A smaller area gives a larger pressure for the same thrust.
- Buoyancy
- The tendency of a fluid to exert an upward force on anything immersed in it. As one goes deeper in a liquid, pressure rises, so the upward pressure on the bottom face of an object is greater than downward pressure on top; this difference creates the upthrust or buoyant force.
- Archimedes' principle
- When a body is fully or partially immersed in a liquid, it experiences an upward buoyant force equal to the weight of the liquid displaced by the body. If the buoyant force equals the body's weight, the body floats; if it is less, the body sinks.
- Relative density
- The ratio of density of a substance to the density of water. It is also the ratio of the weight of the body in air to the loss in its weight when fully immersed in water. A relative density less than 1 means the substance floats in water.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Universal law of gravitation | F = Gm₁m₂/r² | F is force of gravity, m₁ and m₂ are the two masses, r is the distance between their centres, and G is the universal gravitational constant, 6.67 × 10⁻¹¹ N m²/kg². |
| Acceleration due to gravity at a planet's surface | g = GM/R² | g is acceleration due to gravity, M is the mass of the planet, R is its radius, and G is the universal gravitational constant. For Earth, M ≈ 6 × 10²⁴ kg and R ≈ 6.4 × 10⁶ m give g ≈ 9.8 m/s². |
| First equation of motion for a freely falling body | v = u + gt | v is final velocity, u is initial velocity, g is acceleration due to gravity (taken positive when the body moves downwards), and t is time. For an upward throw, replace g by −g. |
| Second equation of motion for a freely falling body | h = ut + ½gt² | h is the vertical distance fallen, u initial velocity, t time, g acceleration due to gravity. This holds while the only acceleration is g, i.e., air resistance is neglected. |
| Third equation of motion for a freely falling body | v² = u² + 2gh | v final velocity, u initial velocity, g acceleration due to gravity, h height fallen. It is useful when time is not given. |
| Weight of a body | W = mg | W is weight in newtons, m mass in kilograms, g acceleration due to gravity. On Earth's surface g ≈ 9.8 m/s², on the Moon g ≈ 1.63 m/s². |
| Pressure | P = F/A | P is pressure, F is the perpendicular force on the surface (thrust), A is the area over which the force acts. Pressure is measured in pascal (Pa): 1 Pa = 1 N/m². |
| Relative density from weights in air and water | RD = W/(W − W′) | W is weight of the body in air and W′ is its weight when fully immersed in water, so W − W′ is the loss in weight. RD equals density of the substance divided by density of water. |
Practice questions with answers
1. State the universal law of gravitation and write its mathematical form.
Every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The force is F = Gm₁m₂/r², where G is the universal gravitational constant.
2. What is the difference between mass and weight? Why does weight change on the Moon?
Mass is the quantity of matter in a body and is measured in kilograms; it is the same everywhere. Weight is the force of gravity on the body, W = mg, so it depends on g. On the Moon g is about one-sixth of Earth's value, hence weight is about one-sixth while mass remains unchanged.
3. A ball is dropped from a height of 80 m. Taking g = 10 m/s², calculate the time it takes to reach the ground and its velocity just before impact.
Using h = ut + ½gt² with u = 0, 80 = 0 + ½ × 10 × t² = 5t², so t² = 16 and t = 4 s. Velocity v = u + gt = 0 + 10 × 4 = 40 m/s.
4. The radius of the Earth is 6.4 × 10⁶ m and its mass is 6 × 10²⁴ kg. Use G = 6.7 × 10⁻¹¹ N m²/kg² to find the value of g.
g = GM/R² = (6.7 × 10⁻¹¹ × 6 × 10²⁴)/(6.4 × 10⁶)² = (4.02 × 10¹⁴)/(4.096 × 10¹³) ≈ 9.8 m/s². This agrees with the known value near Earth's surface.
5. A body weighs 90 N on Earth. What is its mass and its weight on the Moon? Take g on Earth as 10 m/s² and gravity on the Moon as one-sixth of that on Earth.
Mass = W/g = 90/10 = 9 kg. Weight on the Moon = (1/6) × 90 = 15 N. Mass remains 9 kg, since mass does not change with location.
6. A force of 500 N acts perpendicular to a surface of area 0.25 m². Compute the pressure exerted on the surface.
Pressure P = F/A = 500/0.25 = 2000 N/m² = 2000 Pa. A larger area would give a smaller pressure for the same force.
7. Using Archimedes' principle, explain why a solid iron nail sinks in water but a hollow iron ship floats.
The buoyant force on a body equals the weight of the water it displaces. A solid nail has high density, so the weight of water displaced is smaller than its own weight, causing it to sink. A ship is hollow with a large volume and low average density; it displaces a large weight of water, so the buoyant force equals its weight and it floats.
8. A metal object weighs 40 N in air and 34 N in water. Calculate the buoyant force and the relative density of the metal.
Buoyant force = loss of weight = 40 − 34 = 6 N. Relative density = weight in air / loss of weight in water = 40/6 ≈ 6.67. Since its relative density is greater than 1, the metal sinks in water.
9. Why do sharp knives cut better than blunt ones? Use your understanding of pressure.
Pressure = thrust/area. A sharp knife edge has a very small surface area, so the same force produces a far greater pressure than a blunt edge with a larger area. This higher pressure penetrates material more easily.
10. The apparent loss in weight of an object when fully immersed in a liquid is found to equal the weight of the liquid displaced. Which principle is being applied? How does it explain whether an object floats or sinks?
This is Archimedes' principle. If the weight of liquid displaced when the object is immersed is less than the object's weight, the object sinks. If the buoyant force can equal the object's weight, the object floats. For a floating body, the weight of the displaced liquid equals the body's own weight.
Studying Gravitation?
Turn your own textbook pages, a lecture recording or a YouTube video into notes like these — plus flashcards, quizzes and practice questions — in your own language. The Standard plan is free, permanently, and needs no card.
Make notes from your own material — free