Cavendish’s Experiment.
Currently, as my chaotic brain is attracted to the level of a waggish class 9 student. So, frankly speaking, I don’t have an extravagant or plenteous or immeasurable amount of knowledge regarding this topic.
Most part of this writing is extracted from books like- 1) Six Easy Pieces (By- Sir Richard P Feynman)
2) New Simplified Physics (By- S.L. Arora)
3) Concept of Physics (By- H.C. Verma)
In 1687, Newton in his writing Philosophiae Naturalis Principia Mathematica provided the theory of how bodies move in space & time. Not only this but he also developed the much needed complex mathematics to analyse these motions.
In addition to this, he also put forward the conceivable postulate of the law of Universal Gravitation. According to it, every particle in this universe attracted every other particle towards it with a force directly equivalent to the product of their masses and inversely proportional to the square of the distance of those particles from their center of masses. Howsoever, due to this valuable theory, there is an apocryphal that “Newton was inspired by an apple hitting his head”.
Nearly 71 years later, in 1736 Sir Henry Cavendish carried out the famous Cavendish’s experiment. As we know, Gravitation extends over enormous distances and if there is any force between any pair of objects or bodies. Then, most certainly we ought to be able to calculate this force between those objects.
Instead of only calculating the forces between stars, why can’t we calculate or see a ball on a table move towards another ball on that same table? The difficulty of this experiment when done in such a simple form we concluded that the reason was that the force was very weak & delicate.
Then,
How to measure this force?
The whole experiment should be done with extreme care like while doing the experimentation the whole system most certainly should be inside a vacuum chamber, making sure nothing is electrically charged and so on.
Steps for setting up…
- At first, two identical spheres of lead each of mass “m” are connected to the ends of a light rod like a dumb-bell.
- It is then suspended by a quartz fibre or Torsion fibre as shown.
- Two large lead spheres of mass “M” are placed on opposite sides in such a way that all four of them lie on the same horizontal plane.
following the law of gravitation, F = G(Mm)/R2
the small spheres get attracted towards the larger ones…
4. The force of the two spheres form a couple and start exerting a torque.
5. As the torque deflects the rod a restoring torque thereafter acts to equal the gravitational torque here.
The angle of deflection θ is measured by the angle of deflection of the light beam with the help of a lamp and a scale.
LET L be the length of the rod.
Then, deflecting torque= F x L or G(Mm)/R2 x L
Restoring torque= kθ
(k is restoring torque per unit angle of twist and is known as torsion constant)
In the rotational equilibrium, both the torques are equal and opposite.
Therefore,
G(Mm)/R2 x L = kθ
or G= kθR2 / MmL
Hence, from this experiment, we concluded that the value of G happens to be or is currently accepted to be 6.67 x 10 ^-11Nm²/kg².
This experiment by Cavendish even led to the calculation of the earth’s mass and this is the reason the experiment is also known as “weighing of the earth”.
Atlast, before ending I would like to quote few lines by one of my favourite books based on physics written by Richard Feynman….
It is hard to exaggerate the importance of the effect on the history of science produced by this great success of the theory of gravitation. Compare the confusion, the lack of evidence, the incomplete knowledge that prevailed in the earlier ages, when there were endless debates and paradoxes, with the clarity and simplicity of this law this fact that all the moons and planets and stars have such a simple rule to govern them, and further that man could understand it ad deduce how the planets should move! This is the reason for the success of the sciences in the following years, for it gave hope that the other phenomena of the world might also have such beautiful simple laws :)
