Chapter 10 — Gravitation
Welcome to HSLC Guru! This page provides complete English-medium notes and question answers for Class 9 Science Chapter 10 — Gravitation, prepared strictly according to the ASSEB (Assam State School Education Board) syllabus. You will find a clear summary, textbook questions and answers, important numerical problems, additional MCQs, fill in the blanks, true/false questions, a glossary, and a formula table to help you score high marks in your examinations.
Summary
Gravitation is the force of attraction that exists between any two objects in the universe due to their masses. Sir Isaac Newton, in 1687, formulated the Universal Law of Gravitation, which states that every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. Mathematically, this law is expressed as F = G m₁m₂/r², where F is the gravitational force, m₁ and m₂ are the masses of the two objects, r is the distance between their centres, and G is the universal gravitational constant. The value of G is 6.67 × 10⁻¹¹ Nm²/kg². The value of G was experimentally determined by Henry Cavendish in 1798. The gravitational force is responsible for keeping the planets in orbit around the Sun, the Moon around the Earth, the existence of the atmosphere around Earth, the flow of water in rivers, and the occurrence of tides.
When an object falls freely under the influence of Earth’s gravitational force only, it is said to be in free fall. The acceleration produced in such a freely falling object due to gravity is denoted by g. The average value of g on the surface of the Earth is 9.8 m/s². The value of g varies slightly from place to place — it is greater at the poles and smaller at the equator, and it decreases as we go higher above the Earth’s surface or deeper inside the Earth. The mass of an object is the quantity of matter contained in it; it is constant everywhere and is measured in kilograms (kg). The weight of an object is the force with which the Earth attracts it, given by W = mg, and is measured in newtons (N). Weight changes with location because g changes. On the Moon, the value of g is about one-sixth (1/6) of that on Earth, so an object weighs only one-sixth of its weight on Earth, while its mass remains the same.
The force acting on an object perpendicular to a surface is called thrust, and the thrust per unit area is called pressure, given by P = F/A. The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m². A sharp knife cuts easily because its small area produces large pressure for the same force. Fluids (liquids and gases) exert pressure in all directions, and the pressure in a fluid increases with depth. When an object is immersed wholly or partially in a fluid, the fluid exerts an upward force on it called the buoyant force or upthrust. Archimedes’ Principle states that when a body is immersed wholly or partially in a fluid, it experiences an upward force equal to the weight of the fluid displaced by it. This principle is used in designing ships, submarines, hydrometers, and lactometers.
The density of a substance is its mass per unit volume (ρ = m/V). The relative density of a substance is the ratio of its density to the density of water at 4°C; it has no unit. An object floats in a fluid if its density is less than the density of the fluid, and sinks if its density is greater than that of the fluid. According to the law of floatation, a body floats when the weight of the fluid displaced by the immersed part equals the weight of the body. Pascal’s Law states that pressure applied at any point of an enclosed liquid is transmitted equally in all directions. This principle is used in hydraulic machines such as hydraulic press, hydraulic brakes, and hydraulic lifts.
Textbook Questions and Answers
1-Mark Questions
Q1. State the universal law of gravitation.
Answer: Every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Q2. What is the value of the universal gravitational constant G?
Answer: The value of G is 6.67 × 10⁻¹¹ Nm²/kg².
Q3. Define free fall.
Answer: The motion of an object falling under the influence of Earth’s gravitational force alone, with no other force acting on it, is called free fall.
Q4. What is the SI unit of pressure?
Answer: The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m².
Q5. What is the value of acceleration due to gravity on the surface of the Earth?
Answer: The value of acceleration due to gravity (g) on the surface of the Earth is 9.8 m/s².
Q6. What is buoyant force?
Answer: The upward force exerted by a fluid on an object immersed in it is called buoyant force or upthrust.
Q7. Why does an iron nail sink in water but a ship made of iron floats?
Answer: The average density of the iron nail is greater than that of water, so it sinks. A ship is hollow and shaped such that its average density (including the air inside) is less than that of water, so it floats.
Q8. What is the weight of an object of mass 10 kg on the Earth?
Answer: W = mg = 10 × 9.8 = 98 N.
Q9. Define relative density.
Answer: The relative density of a substance is the ratio of the density of the substance to the density of water at 4°C. It has no unit.
Q10. State Pascal’s law.
Answer: Pascal’s law states that pressure applied at any point of an enclosed liquid is transmitted equally in all directions throughout the liquid without any loss.
2-3 Marks Questions
Q1. Differentiate between mass and weight.
Answer:
| Mass | Weight |
|---|---|
| It is the quantity of matter contained in a body. | It is the force with which the Earth attracts a body. |
| It is a scalar quantity. | It is a vector quantity. |
| SI unit is kilogram (kg). | SI unit is newton (N). |
| It remains constant everywhere. | It varies from place to place as g varies. |
| It is measured by a beam balance. | It is measured by a spring balance. |
Q2. Why is it easier to walk on sand with flat shoes than with high heels?
Answer: The pressure exerted on the sand depends on the area of contact (P = F/A). Flat shoes have a larger area of contact than high heels, so the pressure exerted on the sand is less, making walking easier. With high heels, the smaller area produces large pressure, causing the heels to sink into the sand.
Q3. State Archimedes’ principle and write any two of its applications.
Answer: Archimedes’ principle states that when a body is immersed wholly or partially in a fluid, it experiences an upthrust (buoyant force) equal to the weight of the fluid displaced by it.
Applications: (i) It is used in designing ships and submarines. (ii) It is used in making instruments like hydrometers (to measure the density of liquids) and lactometers (to measure the purity of milk).
Q4. Why does a sharp knife cut better than a blunt knife?
Answer: A sharp knife has a very small area at its edge. According to P = F/A, when the same force is applied, smaller area produces greater pressure on the object being cut. A blunt knife has a larger area, so it produces less pressure for the same force, and is therefore less effective at cutting.
Q5. Why is the weight of an object on the Moon 1/6th of its weight on Earth?
Answer: The mass and radius of the Moon are smaller than those of the Earth. The acceleration due to gravity on the Moon (g_moon) is about one-sixth that of Earth (g_earth). Since weight W = mg and the mass remains the same, the weight on the Moon = (1/6) × weight on Earth.
Q6. State the conditions under which an object floats or sinks in a liquid.
Answer: (i) If the density of the object is less than the density of the liquid, the object floats. (ii) If the density of the object is greater than the density of the liquid, the object sinks. (iii) If the density of the object is equal to the density of the liquid, the object floats fully submerged just below the surface.
5-6 Marks Questions (with Numericals)
Q1. The mass of the Earth is 6 × 10²⁴ kg and that of the Moon is 7.4 × 10²² kg. The distance between the Earth and the Moon is 3.84 × 10⁸ m. Calculate the gravitational force between them. (G = 6.67 × 10⁻¹¹ Nm²/kg²)
Answer:
Given: m₁ = 6 × 10²⁴ kg, m₂ = 7.4 × 10²² kg, r = 3.84 × 10⁸ m, G = 6.67 × 10⁻¹¹ Nm²/kg²
F = G m₁m₂/r²
F = (6.67 × 10⁻¹¹ × 6 × 10²⁴ × 7.4 × 10²²) / (3.84 × 10⁸)²
F = (6.67 × 6 × 7.4 × 10³⁵) / (14.7456 × 10¹⁶)
F = (296.15 × 10³⁵) / (14.7456 × 10¹⁶)
F ≈ 2.01 × 10²⁰ N
Q2. A stone is dropped from the top of a tower 80 m high. (i) Find the time it takes to reach the ground. (ii) Find the velocity with which it strikes the ground. (Take g = 10 m/s²)
Answer:
Given: u = 0, h = 80 m, g = 10 m/s²
(i) Using h = ut + ½gt²
80 = 0 + ½ × 10 × t²
t² = 16, so t = 4 s
(ii) Using v = u + gt
v = 0 + 10 × 4 = 40 m/s
The stone reaches the ground in 4 seconds with a velocity of 40 m/s.
Q3. A body of mass 50 kg is placed on a horizontal surface of area 0.5 m². Calculate the pressure exerted by the body on the surface. (Take g = 9.8 m/s²)
Answer:
Given: m = 50 kg, A = 0.5 m², g = 9.8 m/s²
Force (Thrust) F = mg = 50 × 9.8 = 490 N
Pressure P = F/A = 490 / 0.5 = 980 Pa (or 980 N/m²)
Q4. The volume of a body of mass 200 g is 100 cm³. Will the body float or sink in water? (Density of water = 1 g/cm³)
Answer:
Density of body ρ = m/V = 200/100 = 2 g/cm³
Since the density of the body (2 g/cm³) is greater than the density of water (1 g/cm³), the body will sink in water.
Relative density = 2/1 = 2.
Q5. Derive the relation F = mg from the universal law of gravitation, and explain why g is independent of the mass of the falling object.
Answer: Let M be the mass of the Earth, m be the mass of an object on the surface of the Earth, and R be the radius of the Earth. According to the universal law of gravitation, the force between the Earth and the object is:
F = G Mm / R²
This force is the weight of the object, so F = mg.
Therefore, mg = G Mm / R², which gives g = GM/R².
Since g depends only on G, M (mass of Earth), and R (radius of Earth), and does not depend on the mass m of the falling object, the acceleration due to gravity is the same for all objects, irrespective of their masses. This is why a heavy stone and a light feather, when dropped together in vacuum, fall at the same rate.
Additional Multiple Choice Questions (MCQ)
Q1. The value of universal gravitational constant G is:
(a) 9.8 Nm²/kg² (b) 6.67 × 10⁻¹¹ Nm²/kg² (c) 6.67 × 10¹¹ Nm²/kg² (d) 9.8 × 10⁻¹¹ Nm²/kg²
Answer: (b) 6.67 × 10⁻¹¹ Nm²/kg²
Q2. The SI unit of pressure is:
(a) newton (b) joule (c) pascal (d) watt
Answer: (c) pascal
Q3. The weight of an object on the Moon is approximately:
(a) equal to its weight on Earth (b) one-sixth of its weight on Earth (c) six times its weight on Earth (d) zero
Answer: (b) one-sixth of its weight on Earth
Q4. Acceleration due to gravity on the Earth’s surface is:
(a) 9.8 m/s² (b) 6.67 m/s² (c) 1.6 m/s² (d) 0 m/s²
Answer: (a) 9.8 m/s²
Q5. The force per unit area is called:
(a) thrust (b) pressure (c) buoyancy (d) weight
Answer: (b) pressure
Q6. A body floats on water because:
(a) its density is greater than that of water (b) its density is less than that of water (c) it has air inside (d) it is heavy
Answer: (b) its density is less than that of water
Q7. The weight of an object of mass 1 kg on Earth is:
(a) 1 N (b) 9.8 N (c) 10 kg (d) 9.8 kg
Answer: (b) 9.8 N
Q8. The principle that pressure applied to an enclosed fluid is transmitted equally in all directions is called:
(a) Archimedes’ principle (b) Pascal’s law (c) Newton’s law (d) Boyle’s law
Answer: (b) Pascal’s law
Q9. Relative density has:
(a) unit kg/m³ (b) unit g/cm³ (c) no unit (d) unit pascal
Answer: (c) no unit
Q10. The upward force exerted by a fluid on an immersed body is called:
(a) thrust (b) pressure (c) buoyant force (d) gravity
Answer: (c) buoyant force
Fill in the Blanks
Q1. The value of acceleration due to gravity on Earth’s surface is __________ m/s².
Answer: 9.8
Q2. The SI unit of weight is __________.
Answer: newton (N)
Q3. The thrust per unit area is called __________.
Answer: pressure
Q4. The relative density of a substance is the ratio of its density to the density of __________.
Answer: water at 4°C
Q5. The principle used in hydraulic machines is __________ law.
Answer: Pascal’s
True or False
Q1. The mass of an object is the same on Earth and on the Moon.
Answer: True
Q2. Pressure decreases with depth in a liquid.
Answer: False (pressure increases with depth)
Q3. The value of g is greater at the equator than at the poles.
Answer: False (g is greater at the poles)
Q4. Archimedes’ principle is used in designing ships and submarines.
Answer: True
Q5. The acceleration due to gravity depends on the mass of the falling object.
Answer: False (g is independent of the mass of the falling object)
Glossary
| Term | Meaning |
|---|---|
| Gravitation | Force of attraction between any two objects in the universe due to their masses. |
| Gravitational Constant (G) | A universal constant equal to 6.67 × 10⁻¹¹ Nm²/kg². |
| Free Fall | Motion of a body falling under the influence of Earth’s gravitational force only. |
| Acceleration due to gravity (g) | Acceleration produced in a freely falling body; on Earth, g = 9.8 m/s². |
| Mass | Quantity of matter in a body; measured in kilograms (kg); constant everywhere. |
| Weight | Force with which Earth attracts a body, W = mg; measured in newtons (N). |
| Thrust | Force acting on a body perpendicular to its surface. |
| Pressure | Thrust per unit area, P = F/A; SI unit pascal (Pa). |
| Buoyant Force | Upward force exerted by a fluid on an object immersed in it. |
| Archimedes’ Principle | An immersed body experiences upthrust equal to the weight of the fluid displaced. |
| Density | Mass per unit volume of a substance. |
| Relative Density | Ratio of the density of a substance to the density of water at 4°C; no unit. |
| Pascal’s Law | Pressure applied at any point of an enclosed liquid is transmitted equally in all directions. |
Formula Table
| Quantity | Formula | SI Unit |
|---|---|---|
| Universal Law of Gravitation | F = G m₁m₂/r² | newton (N) |
| Acceleration due to gravity | g = GM/R² | m/s² |
| Weight | W = mg | newton (N) |
| Equation of motion (free fall) | v = u + gt | m/s |
| Distance in free fall | h = ut + ½gt² | metre (m) |
| Velocity-distance equation | v² = u² + 2gh | m²/s² |
| Pressure | P = F/A | pascal (Pa) |
| Density | ρ = m/V | kg/m³ |
| Relative Density | R.D. = ρ_substance / ρ_water | no unit |
| Pressure in liquid (depth h) | P = hρg | pascal (Pa) |
| Buoyant Force | F_b = V ρ_fluid g | newton (N) |
Keep practising these questions and numericals to master Class 9 Science Chapter 10 — Gravitation. For more chapter-wise notes and ASSEB-aligned study materials, visit HSLC Guru regularly. All the best for your examinations!