In this chapter, we study gravitation, a force that plays an important role not only on Earth but also in the entire universe. From falling objects to the motion of planets and satellites, gravitation explains many everyday as well as astronomical phenomena. This chapter is very important for the SSC board exam as it includes theory questions, definitions, and numerical problems. If you understand the concepts step by step, this chapter becomes easy and scoring.
Table of Contents
Important Concepts of the Chapter
What is Gravitation?
In simple words, gravitation is the force of attraction between any two objects that have mass. Every object in the universe attracts every other object, but this force becomes noticeable only when at least one of the objects is very large, like the Earth or the Sun.
For example, when a stone is released from your hand, it falls down because the Earth attracts it towards its centre. This attractive force is called gravitational force.
Circular Motion and Centripetal Force
When an object moves in a circular path, its direction of motion keeps changing continuously. To change the direction, a force is required.
This force always acts towards the centre of the circular path and is called centripetal force.
In simple words, centripetal force keeps an object moving in a circle instead of flying away in a straight line.
For example, when a stone tied to a string is rotated in a circle, the tension in the string provides the centripetal force. If the string breaks, the stone moves tangentially.
In planetary motion, the gravitational force acts as the centripetal force.
Kepler’s Laws of Planetary Motion
Johannes Kepler studied the motion of planets and gave three important laws:
Kepler’s First Law
Each planet moves around the Sun in an elliptical orbit, with the Sun at one of the foci.
Kepler’s Second Law
The line joining a planet and the Sun sweeps equal areas in equal intervals of time.
This means a planet moves faster when it is closer to the Sun and slower when it is farther away.
Kepler’s Third Law
The square of the time period of revolution of a planet around the sun is directly proportional to the cube of its average distance from the Sun.
These laws helped Newton in formulating the universal law of gravitation.
Newton’s Universal Law of Gravitation
According to Newton, every object in the universe attracts every other object with a definite force.
This force:
- Is directly proportional to the product of the masses of the two objects
- Is inversely proportional to the square of the distance between them
This law explains why planets revolve around the Sun and why objects fall towards the Earth.
Centre of Mass:
- The centre of mass of an object is the point inside or outside the object at which the total mass of the object can be assumed to be concentrated.
- The centre of mass of a spherical object having uniform density is at its geometrical centre.
- The centre of mass of any object having uniform density is at its centroid.
High and Low Tide
You may have observed that the sea level rises and falls regularly along the seashore. This regular rise and fall of sea water is known as tides.
At most places, two high tides and two low tides occur in a day.
Tides are caused mainly due to the gravitational force exerted by the Moon on the Earth.
High Tide
Water directly below the Moon is pulled strongly towards the Moon. This causes the water level at that place to rise, producing a high tide. Another high tide occurs on the opposite side of the Earth due to the Earth–Moon system’s motion.
Low Tide
At places located 90° away from the high tide region, the gravitational pull of the Moon is weaker. This causes water level there becomes minimum, resulting in low tides.
Acceleration Due to Gravity
When an object falls towards the Earth under the influence of gravity, its velocity increases continuously. The rate at which its velocity changes is called acceleration due to gravity and is denoted by g.
The value of g on the surface of the Earth is approximately 9.8 m/s².
This acceleration acts vertically downward towards the centre of the Earth and is the same for all objects at a given place.
Variation in the Value of Acceleration Due to Gravity
The acceleration due to gravity (g) is not the same at all places. Its value changes depending on the position on the Earth.
Causes of Variation in g
The value of g varies due to:
- Shape of the Earth
- Rotation of the Earth
- Height above the Earth’s surface
- Depth below the Earth’s surface
A. Variation of g Along the Surface of the Earth
The Earth is not a perfect sphere. It is bulged at the equator and flattened at the poles. Its radius is largest at equator and lower at poles and hence the value of g is highest at poles (9.832 m/s²) and lowest at equator (9.78 m/s²).
B. Variation of g with Height Above the Earth’s Surface
As we move above the Earth’s surface, the distance from the centre of the Earth increases. When distance r increases, the value of g decreases.
For small heights (like mountains or airplanes), the change in g is very small while For large heights (satellites), the decrease in g is significant.
C. Variation of g with Depth Below the Earth’s Surface
As we go inside the Earth, two things happen: Distance from Earth’s centre decreases and the Mass contributing to gravity also decreases. The combined effect causes the value of g to decrease with depth.
Key points to remember
- g is maximum at the poles
- g is minimum at the equator
- g decreases with height
- g decreases with depth
- g = 0 at the centre of the Earth
Mass and Weight
Mass and weight are often used interchangeably in daily life, but in physics they mean very different things. Understanding this difference is key to learning mechanics and gravitation.
What is Mass?
Mass is the amount of matter contained in an object.
Key points about mass:
- It is a scalar quantity (has magnitude only).
- It does not change from place to place.
- It measures an object’s inertia (resistance to change in motion).
- SI unit: kilogram (kg).
- Measured using a beam balance or electronic balance.
Example:
A book of mass 2 kg will have the same mass on Earth, the Moon, or in space.
What is Weight?
Weight is the gravitational force acting on an object due to a planet or celestial body.
Mathematically:
Weight=Mass×Acceleration due to gravity
W=mg
Key points about weight:
- It is a vector quantity (has magnitude and direction).
- It changes from place to place because gravity varies.
- It depends on the value of g.
- SI unit: newton (N).
- Measured using a spring balance.
Example:
A person weighs less on the Moon than on Earth because the Moon’s gravity is weaker.
Why Does Weight Change but Mass Does Not?
Mass is an intrinsic property of matter. Weight depends on external gravitational force.
- On Earth:
- On the Moon:
So for the same mass:
- Weight on Earth → more
- Weight on Moon → less
Can Weight Be Zero?
Yes. In space or free fall, weight can become zero (called weightlessness), but mass never becomes zero.
Free Fall
When an object moves under the influence of gravitational force alone, it is said to be in free fall.
In free fall:
- Initial velocity is zero
- Acceleration is equal to g
- Mass of the object does not affect the motion
In real life, air resistance affects motion, so true free fall is possible only in vacuum.
Escape Velocity
Escape velocity is the minimum velocity required by an object to escape the gravitational pull of the Earth without coming back.
If an object is thrown upward with velocity less than escape velocity, it will fall back.
If it is thrown with escape velocity or more, it will escape Earth’s gravity completely and will not fall back on the earth.
The escape velocity on Earth is about 11.2 km/s.
Important Laws / Formulae
Gravitational force between two objects
Formula:
F = G × (m₁m₂ / r²)
Where:
F = gravitational force
G = universal gravitational constant
m₁, m₂ = masses of objects
r = distance between their centres
This formula is frequently used in numerical problems in SSC exams.
Acceleration produced by the force
Formula:
a = F/m
Where:
F = gravitational force
m = masses of objects
Newton’s Equations of Motion
Newton’s first equation of motion
v = u + at (This equation is used to find final velocity, acceleration, or time)
Newton’s second equation of motion
s = ut + 1/2 at2 (This equation is used to find distance, time, or acceleration)
Newton’s third equation of motion
v2 = u2 +2as (This equation is useful when time is not given)
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = distance travelled
Acceleration Due to Gravity
Formula:
g = GM / R²
Where:
M = mass of the Earth
R = radius of the Earth
Newton’s equation of motion for free fall
v = gt
s = 1/2 gt2
v2 = 2gs
Centripetal Force
Formula:
F = mv² / r
Used for objects moving in circular motion.
Escape Velocity
Formula:
vesc = √(2gR) or √ 2GM/R
This formula is important for theory questions and numericals.
Important Definitions
- Gravitation – The force of attraction between any two objects having mass.
- Centripetal Force – The force acting towards the centre of a circular path.
- Acceleration Due to Gravity – The acceleration produced in a body due to Earth’s gravitational force.
- Free Fall – Motion of an object under gravity alone.
- Escape Velocity – Minimum velocity needed to escape Earth’s gravity.
Numerical / Process Explanation
For gravitation numericals:
- Write the given values clearly
- Select the correct formula
- Substitute values with proper units
- Perform calculations step by step
For free fall problems:
- Take initial velocity u = 0
- Acceleration a = g
- Use equations of motion carefully
For escape velocity:
- Remember it does not depend on mass of the object
- Only Earth’s radius and g are used
Important Points for SSC Board Exam
- Newton’s law and its formula are very important
- Definitions and Laws are frequently asked (1–2 marks)
- Numerical problems are usually 2–3 marks
- Difference between mass and weight is important
- Free fall concepts are commonly tested
- Escape velocity is often asked as a theory question
- Diagrams related to circular motion may be asked
Quick Revision Summary
- Gravitation is a universal force
- Gravitational force acts between all masses
- Centripetal force keeps objects in circular motion
- Kepler gave three laws of planetary motion
- g on Earth is approximately 9.8 m/s²
- All objects fall with same acceleration in free fall
- Escape velocity on Earth is 11.2 km/s
- Weight depends on gravity, mass does not
By understanding the laws, formulas, and concepts clearly and practising numerical regularly, students can easily score good marks from this chapter in the SSC board examination.