Gravitation
Universal Law, Free Fall & Buoyancy
In-Text Questions (Page 134)
Q1. State the Universal Law of Gravitation.
Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centers of two objects.
F = G (Mm / d²)
Q2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
F = G (Mm / R²)
Where:
M = Mass of Earth (6 × 1024 kg)
m = Mass of object
R = Radius of Earth (6.4 × 106 m)
G = Universal Gravitational Constant (6.67 × 10-11 Nm²/kg²)
In-Text Questions (Page 136)
Q1. What do you mean by free fall?
When an object falls towards the earth under the influence of earth's gravitational force alone, it is said to be in free fall.
Q2. What do you mean by acceleration due to gravity?
When an object falls freely towards the earth, its velocity changes (increases) due to the gravitational force. This change in velocity involves acceleration, which is called acceleration due to gravity. It is denoted by 'g' and its value is approx 9.8 m/s².
In-Text Questions (Page 138)
Q1. What are the differences between the mass of an object and its weight?
| Mass | Weight |
|---|---|
| Quantity of matter contained. | Force with which earth attracts the object (W=mg). |
| Constant everywhere. | Varies with 'g' (e.g., less on Moon). |
| Scalar quantity. | Vector quantity. |
| SI Unit: kg. | SI Unit: Newton (N). |
In-Text Questions (Page 141)
Q1. Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Pressure is inversely proportional to the area (P = Force/Area). In a thin strap, the area of contact is very small. Hence, the pressure exerted on the shoulders is very large, making it painful to hold.
Q2. What do you mean by buoyancy?
When an object is immersed in a liquid, it experiences an upward force exerted by the fluid. This upward force is called the buoyant force or buoyancy.
Main Textbook Exercises
Q6. What happens to the force between two objects if (i) the mass of one object is doubled? (ii) the distance between the objects is doubled and tripled? (iii) the masses of both objects are doubled?
Formula: F ∝ (Mm)/d²
- (i) Mass doubled: Force becomes 2 times.
- (ii) Distance doubled: Force becomes 1/4th. Distance tripled: Force becomes 1/9th.
- (iii) Both masses doubled: Force becomes 4 times.
Q13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (i) the maximum height to which it rises, (ii) the total time it takes to return to the surface of the earth.
Given: u = 49 m/s, v = 0 (at max height), g = -9.8 m/s² (upward motion).
(i) Height (h): v² - u² = 2gh
0 -
(49)² = 2 × (-9.8) × h
-2401 = -19.6h
h = 122.5 m.
(ii) Time of ascent (t): v = u + gt
0
= 49 - 9.8t
t = 5 s.
Total Time = Ascent + Descent = 5 + 5 = 10 s.
Q19. In what direction does the buoyant force on an object immersed in a liquid act?
The buoyant force acts in the vertically upward direction.
Q21. The volume of 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g/cm³? What will be the mass of the water displaced by this packet?
Density of packet = Mass / Volume = 500 / 350 = 1.42 g/cm³.
Since 1.42 > 1 (Density of water), the packet will sink.
Mass of water displaced = Volume of object
immersed × Density of water
= 350 cm³ × 1 g/cm³ = 350 g.
Gravitation
Gravity, Pressure & Archmedes' Principle
1. Newton's Law of Gravitation
- The force that binds us to the earth.
- The motion of the moon around the earth.
- The motion of planets around the sun.
- The tides due to the moon and the sun.
2. Equations of Motion for Free Fall
Replace acceleration 'a' with 'g' (acceleration due to gravity).
(Replace 's' with height 'h')
Sign Convention:
Downward Motion: g is +ve (9.8 m/s²).
Upward Motion: g is -ve (-9.8 m/s²).
Max Height: v = 0.
Dropped from Rest: u = 0.
3. Thrust and Pressure
Force acting on an object perpendicular to the surface. SI Unit: Newton (N).
Thrust per unit area. P = Force/Area. SI Unit: Pascal (Pa) or N/m².
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: Designing ships, Submarines, Lactometers, Hydrometers.
4. Numerical Examples
A block of wood is kept on a tabletop. The mass of wooden block is 5 kg and its dimensions are 40 cm x 20 cm x 10 cm. Find pressure if kept on 20x10 side.
Force (Weight): mg = 5 × 9.8 = 49 N.
Area: 20 cm × 10 cm = 0.2 m × 0.1 m = 0.02 m².
Pressure: 49 / 0.02 = 2450 N/m².
Relative density of silver is 10.8. The density of water is 10³ kg/m³. What is the density of silver?
Density of Silver = R.D. × Density of Water
= 10.8 × 10³ =
10800 kg/m³.
Key Facts & Definitions
50+ Important Points to Remember
Attractive force between any two objects in the universe.
Force is proportional to product of masses and inversely proportional to square of distance.
Value is 6.673 × 10-11 Nm²/kg². Constant everywhere.
Center-seeking force required for circular motion (provided by gravity for moon).
Motion of an object under the influence of gravity alone.
Acceleration produced during free fall. Average value 9.8 m/s² on Earth.
Value of g is greater at poles and less at equator.
Measure of inertia. Constant everywhere. Scalar quantity.
Force with which earth attracts an object. W = mg.
1/6th of weight on Earth (because gravity on Moon is 1/6th of Earth).
Force acting on an object perpendicular to the surface.
Thrust per unit area (P = F/A).
SI Unit of Pressure. 1 Pa = 1 N/m².
Upward force exerted by a fluid on an immersed object.
Buoyant force = Weight of fluid displaced.
Mass per unit volume. SI Unit: kg/m³.
Ratio of density of substance to density of water. No unit.
Object floats if its density is less than the fluid.
Object sinks if its density is greater than the fluid.
Device to check purity of milk (based on Archimedes' principle).
Device to determine density of liquids.
Gravitational force is inversely proportional to square of distance (1/r²).
g = GM/R² (Independent of mass of the falling object).
Showed all objects fall at same rate in vacuum.
Caused by gravitational pull of moon and sun on ocean water.
Less area = More pressure (e.g., sharp knife, nail tip).
Broad feet increase area, reducing pressure on sand.
Fluids exert pressure in all directions.
Another name for buoyant force.
Because its shape displaces water weighing more than the ship.
Henry Cavendish found the value of G.
Formulated the Universal Law of Gravitation.
Value of g at center of earth is zero.
Sensation of no weight during free fall (e.g., in a lift falling freely).
1000 kg/m³ or 1 g/cm³.
Weight in fluid is less than true weight due to upthrust.
N m² kg⁻².
Directed towards the center of the earth.
Feather and stone fall together in vacuum (no air resistance).
Held to the earth by gravity.
Calculated trajectory of a planet due to gravity.
Governs motion of planets (not in detail in syllabus but related).
Minimum (since g is min).
Maximum (since g is max).
Measures weight.
Measures mass (compares unknown mass with standard mass).
Density of Substance / Density of Water.
Heels exert more pressure (less area).
Wide tires reduce pressure on road.
Floats because cork density < water density.