Introduction ( Class 11 Physics Gravitation )
- Whenever we throw an object towards the sky it will fall back onto the ground.
- For Example: – A ball comes down when thrown up. Rain drops fall towards the ground; Planets revolve in an elliptical orbit around sunetc.
Planets revolving in the elliptical orbit.
Leaves fall off the tree.
- There is a force due to which all things are attracted towards the earth. This force is known as Gravitation.
- Gravitation is the force of attractionbetween all masses in the universe, especially the force of attraction exerted by the earth on all the bodies near its surface.
- In this chapter we will take a look at gravitation force, its laws, and we will also study about the planetary motion.
Newton’s view of Gravitation
- Newtonwas the first scientist who studied the force of gravitation.
- According to him there is a force which is exerted by the surface of the earth because of which all the objects are attracted towards the surface of the earth.
- He also concluded that all objects in this universe attract each other with a force. This force is Gravitation force.
- F ∝ m1m2
- Force is ∝to the product of masses of 2 bodies.
- F ∝ 1/r2
- Force is inversely proportional to the square of the distance between the 2 bodies.
- Combining above equations:-
- F ∝ m1m2/r2
- F= G m1m2/r2
Where G = universal Gravitational constant.
- Its value is constant and it never changes.
- m1 and m2are masses of 2 bodies.
- r = distance between the bodies.
Gravitational Constant: Cavendish experiment
- Cavendish performed an experiment to calculate the value of G.
- To calculate the value of G he took a wooden plank and attached two 2 balls on either side of the plank and hung this with a thin thread from the top.
- He introduced 2 very big balls and those balls are near the smaller balls.
- He observed that the small balls got attracted to big balls and wooden plank started rotating and as a result the thin thread started twisting.
- This happened because of force of attraction between the small balls and bigger balls.
- He observed that :-
- Plank rotates till twisting force becomes equal to the gravitational force between the balls.
𝛕 = G m1m2/r2
LƟ = G m1m2/r2
- By using the above equation he calculated the value of G,
- G= 6.67×10-11Nm2/kg2
- Units of G : Nm2/kg2
Problem:- Calculate the gravitational force of attraction between 2 lead balls of mass 20kg and 10kg separated by a distance of 10cm?
Answer: m1= 20kg , m2=10kg , r=10cm = 10/100 = 0.1m
= 6.67×10-11x 20×10 / (0.1)2
F = 1.3 x 10-6N
Acceleration due to gravity of the earth
- Acceleration attained due to gravity of earth.
- All the objects fall towards the earth because of gravitational pull of the earth.
- And when abody is falling freely, it will have some velocity and therefore it will attain some acceleration. This acceleration is known as acceleration due to gravity.
- It is a vector quantity.
- Denoted by ‘g’.
- Its value is 9.8m/s2.
Example:-Stones falling from a rock will have some velocity because of which some acceleration. This acceleration is due to the force exerted by the earth on the rocks.This is known as acceleration due to gravity.