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Gravitational Constant - Class 11 PDF Download


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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.

Gravitational Constant - Class 11

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.

 Gravitational Constant - Class 11 

  • 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

Gravitational Constant - Class 11

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

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FAQs on Gravitational Constant - Class 11

1. What is the gravitational constant?
Ans. The gravitational constant, denoted by G, is a fundamental constant in physics that quantifies the strength of the gravitational force between two objects. It is a measure of the attraction between masses and is used in the calculation of gravitational forces and accelerations.
2. How is the gravitational constant determined?
Ans. The gravitational constant is determined through various experiments, such as measuring the gravitational force between two masses and the distance between them. One of the most famous experiments to determine G is the Cavendish experiment, which involves measuring the gravitational force between two lead spheres using a torsion balance.
3. What is the value of the gravitational constant?
Ans. The value of the gravitational constant is approximately 6.67430 × 10^-11 cubic meters per kilogram per second squared (m^3/kg/s^2). It is a small value, indicating that the gravitational force between objects is weak compared to other fundamental forces.
4. Why is the gravitational constant important?
Ans. The gravitational constant is important because it allows us to understand and calculate the gravitational forces acting between objects. It is a fundamental constant in physics that plays a crucial role in celestial mechanics, astrophysics, and other fields. Without the gravitational constant, we would not be able to accurately describe and study the behavior of celestial bodies, orbits, and the universe as a whole.
5. Is the value of the gravitational constant always the same?
Ans. The value of the gravitational constant, G, is currently considered to be a constant. However, there have been some experimental discrepancies and ongoing research to determine its precise value. Some experiments have reported slightly different values, leading to a small uncertainty in the currently accepted value. Nevertheless, for most practical purposes, the value of G is considered constant and is widely used in scientific calculations.
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