Gravitational Constant - Class 11 PDF Download

Gravitational Constant

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.

Universal Law of Gravitational

Universal law of Gravitation states –

• Everysingle body in this universe attracts each other with a force which is ∝to the product of their masses and inversely ∝to the square of the distance between them.
• This law holds good for all the bodies in the universe.
• If the product of mass of the bodies increase the force of attraction also increases between themand if the square of the distance between the bodies increases, force decreases.
• Mathematically:-
• Consider 2 boxes having mass m₁ and m₂. The distance between them is r.

• 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 :-

1. 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= 6.67x10^-11Nm²/kg²                        
• Units of G : Nm²/kg²

Schematic drawing of Cavendish’s experiment:-

• S₁ and S₂ are large spheresthat are kept on either side of the ellipse.
• Whenthe big spheres are taken to the other side of the ellipse (shown by dotted circles), the bar AB rotates a little since the torque reverses direction.
• The angle of rotation can be measured experimentally.

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

G=6.67x10^-11Nm²/kg²

F=G m₁m₂/r²

= 6.67x10^-11x 20x10 / (0.1)²

F = 1.3 x 10^-6N