Understanding the Universal Gravitational Constant (G)

The question asks about the scientist who determined the value of the universal gravitational constant, often represented by the symbol G. This constant is fundamental to understanding gravity.

Sir Isaac Newton formulated the Law of Universal Gravitation, which states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, this is expressed as:

\( F = G \frac{m_1 m_2}{r^2} \)

Here:

• \(F\) is the gravitational force between the two objects.
• \(m_1\) and \(m_2\) are the masses of the two objects.
• \(r\) is the distance between the centers of the two objects.
• \(G\) is the universal gravitational constant.

While Newton's law described how gravity works and introduced the constant \(G\), Newton himself could not determine its value. Determining \(G\) experimentally requires measuring the very weak gravitational force between objects of known masses in a laboratory setting.

The Cavendish Experiment and Determining G

The value of the universal gravitational constant (G) was first determined experimentally by the British scientist Henry Cavendish in the late 18th century. His famous experiment, known as the Cavendish Experiment, used a torsion balance to measure the faint gravitational attraction between lead spheres.

Here's a simplified idea behind the Cavendish experiment:

1. Small lead balls were suspended from a thin fiber (forming a torsion balance).
2. Large lead balls were brought near the small balls.
3. The gravitational attraction between the large and small balls caused the fiber to twist.
4. By measuring the angle of twist and knowing the properties of the fiber and the masses and distances of the balls, Cavendish could calculate the gravitational force.
5. Using Newton's Law of Gravitation (\(F = G \frac{m_1 m_2}{r^2}\)), with known values for \(F\), \(m_1\), \(m_2\), and \(r\), he could solve for \(G\).

This experiment was remarkable for its precision in measuring such a weak force and provided the first reliable value for \(G\).

Examining Other Options

Let's briefly look at the other scientists mentioned:

• Antoine L. Lavoisier: A French chemist considered one of the founders of modern chemistry. His work included the law of conservation of mass. He did not determine the value of G.
• Isaac Newton: As mentioned, Newton formulated the law of gravitation but did not measure the value of the constant G himself.
• John Dalton: An English chemist, physicist, and meteorologist best known for pioneering the modern atomic theory. He did not determine the value of G.

Therefore, based on historical scientific experiments, Henry Cavendish is credited with being the first to determine the value of the universal gravitational constant (G).

Revision Table: Key Facts on Universal Gravitational Constant

Additional Information: Significance of G

The universal gravitational constant (G) is crucial for many calculations in physics and astronomy. Knowing G allows us to:

• Calculate the gravitational force between any two objects with known masses and separation.
• Determine the mass of planets, stars, and other celestial bodies based on their gravitational effects.
• Understand phenomena like orbits, tides, and the formation of galaxies.

The Cavendish experiment was not only significant for determining G but also provided the first accurate measurement of Earth's mass and average density, often referred to as "weighing the Earth."