We know that an object in circular motion keeps on changing its direction. Due to this, the velocity of the object also changes.
A force called Centripetal Force acts upon the object that keeps it moving in a circular path. It is exerted from the centre of the path.
Without the Centripetal Force objects cannot move in circular paths, they would always travel straight. For Example, The rotation of Moon around the Earth is possible because of the centripetal force exerted by Earth.
Why does Apple fall on Earth from a tree? – Because the earth attracts it towards itself.
Can Apple attract the earth? – Yes. It also attracts the earth as per Newton’s third law (every action has an equal and opposite reaction). But the mass of the earth is much larger than Apple’s mass thus the force applied by Apple appears negligible and Earth never moves towards it.
Newton thus suggested that all objects in this universe attract each other. This force of attraction is called Gravitational Force.
The Universal Law of Gravitation
Newton’s Law of gravitation states that every object in the universe attracts every other object by a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F∝M∗m Fα1/d2 F=G Mm/r2 where G is the universal gravitation constant. Value of G = 6.673∗10−11Nm2Kg−2
Free fall
When an object falls towards the earth due to earth’s gravity and no other force is acting upon it, the object is said to be in free fall state. Free falling objects are not even resisted by the air.
g = 9.8 m/s2 is also called the Free-fall Acceleration.
Consider the equations of motion given in different scenarios
When an object at rest falls towards earth – its initial velocity is zero v = gt s = t + (1/2) gt2 2 g s = v2
When an object with some initial velocity (u) falls towards earth – v = u + gt s = ut + (1/2) gt2 2 g s = v2 – u2
When an object with some initial velocity (u) falls towards earth – v = u + gt s = ut + (1/2) gt2 2 g s = v2 – u2
Acceleration due to gravity
Whenever an object falls towards the Earth there is an acceleration associated with the movement of the object. This acceleration is called acceleration due to gravity.
Denoted by: g SI Unit: m s-2 We know that, F= ma Therefore, F = mg
The following figure demonstrates the mathematical derivation of ‘g’
The force (F) of gravitational attraction on a body of mass m due to earth of mass M and radius R is given by
We know from Newton’s second law of motion that the force is the product of mass and acceleration. ∴ F = ma
But the acceleration due to gravity is represented by the symbol g. Therefore, we can write F = mg ….. (2)
From the equation (1) and (2), we get
When body is at a distance ‘r’ from the centre of the earth then:
Value of ‘g’ may vary at different parts of the earth
From the equation g = GM/ r2 it is clear that the value of ‘g’ depends upon the distance of the object from the earth’s centre.
This is because the shape of the earth is not a perfect sphere. It is rather flattened at poles and bulged out at the equator.
Hence, the value of ‘g’ is greater at the poles and lesser at the equator. However, for our convenience, we take a constant value of ‘g’ throughout.
We can find the value of acceleration due to gravity by the following
Difference between mass and weight:
Mass
Weight
Mass is defined as the quantity of a matter in an object.
The weight of an object is the force by which the gravitational pull of the earth attracts the object.
Mass is the scaler quantity.
Weight is the vector quantity.
The mass of an object is always constant as it depends upon the inertia of the object.
The weight of an object can vary at different locations because of change in gravitational force of the earth.
Masses can never be zero
Weight can be zero at the places there is no gravitational force
Denoted as: m
Denoted as: WF = mg Where m = mass of object a = acceleration due to gravity Similarly, W is force, so W = mg
SI Unit: kg
SI Unit: N
Thrust
The force that acts in the perpendicular direction is called thrust.
It is similar to force applied to an object
It is a vector quantity.
Pressure
The force that acts per unit area of the object is pressure.
It is the thrust per unit area.
Pressure is denoted by ‘P’
P = thrust/ area = force/ area = F/A
SI unit: N/m2 or Pa (Pascal)
Buoyancy
Whenever an object is immersed in a liquid, the liquid exerts a buoyant force or upthrust in the opposite direction of the gravitational force. This is also called the Force of Buoyancy.
It depends upon the density of the fluid.
Therefore an object is able to float in water when the gravitational force is less than the buoyant force.
Similarly, an object sinks into the water when the gravitational force is larger than the buoyant force.
Pressure in Fluids
The pressure exerted by a fluid in a container is transmitted undiminished in all directions on the walls of the container.
Archimedes’ Principle
The upward force exerted by a fluid on an object is known as upthrust or buoyant force.
The magnitude of buoyancy depends on the density of the fluid. If the density of an object is less than the fluid, it will float. If the density of the object is greater than the fluid, it will sink.
According to the Archimedes’ principle, 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.
Relative Density
When density can be expressed in comparison with water’s density it is called Relative Density. It has no unit because it is a ratio of two similar quantities.
Relative density = Density of a substance/ Density of water
Why water is chosen as a reference?
Water is present everywhere on earth so it becomes easier to evaluate the density of a substance in relation to water.
How relative density can be used as a measure to determine in an object will sink or float in water?
Relative density of an object
Float / Sink
Greater than 1
Sink in water
Less than 1
Float in water
Write the answer of the following questions.
Which scientist is credited with formulating the law of universal gravitation? a) Isaac Newton b) Albert Einstein c) Galileo Galilei d) Johannes Kepler
What is the SI unit of gravitational force? a) Newton b) Joule c) Kilogram d) Watt
The force of gravity between two objects depends on: a) The mass of both objects and the distance between them b) The mass of one object only c) The distance between the objects only d) The speed of the objects
If the distance between two objects is doubled, how does the gravitational force between them change? a) It becomes four times as strong b) It becomes half as strong c) It becomes one-fourth as strong d) It remains the same
What happens to the gravitational force between two objects if the mass of one of the objects is doubled? a) The force doubles b) The force halves c) The force quadruples d) The force remains the same
Which of the following is not an example of gravitational force? a) A person standing on the ground b) A satellite orbiting Earth c) A magnet attracting an iron nail d) An apple falling from a tree
The acceleration due to gravity on Earth’s surface is approximately: a) 10 m/s^2 b) 5 m/s^2 c) 9.8 m/s^2 d) 15 m/s^2
What happens to the gravitational force between two objects if the distance between them is tripled? a) It becomes nine times weaker b) It becomes three times weaker c) It becomes three times stronger d) It remains the same
Which law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers? a) Kepler’s First Law b) Kepler’s Second Law c) Newton’s First Law d) Newton’s Law of Universal Gravitation
Two objects with masses 5 kg and 10 kg are separated by a distance of 2 meters. What is the gravitational force between them? a) 0.05 N b) 0.5 N c) 5 N d) 50 N
What would happen to the gravitational force between two objects if the distance between them is increased by a factor of 3? a) It decreases by a factor of 3 b) It increases by a factor of 3 c) It decreases by a factor of 9 d) It increases by a factor of 9
A satellite orbits Earth in a circular path. What force keeps the satellite in its orbit? a) Gravitational force b) Magnetic force c) Frictional force d) Tension force
If the mass of an object is doubled, how does its weight change near the surface of the Earth? a) It doubles b) It halves c) It quadruples d) It remains the same
What is the approximate value of the acceleration due to gravity on the surface of the Moon? a) 1.6 m/s^2 b) 3.2 m/s^2 c) 6.4 m/s^2 d) 9.8 m/s^2
Which planet in our solar system experiences the strongest gravitational force at its surface? a) Jupiter b) Mars c) Earth d) Mercury
What is the gravitational force acting on a 50 kg person standing on the surface of the Earth? a) 50 N b) 500 N c) 5 N d) 5000 N
If the radius of the Earth were doubled while its mass remained the same, what would happen to the weight of an object on its surface? a) It doubles b) It halves c) It quadruples d) It remains the same