Understanding the Universal Gravitational Constant (G)

The question asks about the value of 'G'. In physics, 'G' represents the Universal Gravitational Constant. This constant appears in Newton's Law of Universal Gravitation, which describes the force of attraction between any two objects with mass anywhere in the universe.

Newton's Law of Universal Gravitation and the Role of G

Newton's law states that the gravitational force ($F$) between two objects is directly proportional to the product of their masses ($m_1$ and $m_2$) and inversely proportional to the square of the distance ($r$) between their centers. Mathematically, this is written as:

Here, 'G' is the constant that makes the proportionality an equality. Its value is determined experimentally and is a fundamental constant of nature.

Determining the Correct Value of G

The accepted value for the Universal Gravitational Constant, G, is approximately:

\(6.67 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{-2}\)

Let's look at the options provided and compare them to the known value and units of the Universal Gravitational Constant, G.

• Option 1: \(9.99 \times 10^{-19} \text{ Nm}^2 \text{ kg}^{-2}\) - The units (\(\text{Nm}^2 \text{ kg}^{-2}\)) are correct for G, but the numerical value and exponent (\(9.99 \times 10^{-19}\)) are significantly different from the accepted value of G.
• Option 2: \(6.67 \times 10^{-9} \text{ m sec}^{-2}\) - The units (\(\text{m sec}^{-2}\) or \(\text{m/s}^2\)) are units of acceleration, not the units for the gravitational constant G. These units are associated with gravitational acceleration, like the acceleration due to gravity on Earth's surface (g). The value \(6.67 \times 10^{-9}\) is also incorrect for G.
• Option 3: \(9.8 \text{ m sec}^{-2}\) - This value and unit (\(\text{m sec}^{-2}\) or \(\text{m/s}^2\)) represent the approximate average acceleration due to gravity on the surface of the Earth (often denoted as 'g'), not the Universal Gravitational Constant 'G'. The value 9.8 is much larger than the exponent \(10^{-11}\) associated with G.
• Option 4: \(6.67 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{-2}\) - The numerical value (\(6.67 \times 10^{-11}\)) and the units (\(\text{Nm}^2 \text{ kg}^{-2}\)) match the internationally accepted value for the Universal Gravitational Constant, G.

Therefore, the value of 'G' that is correct among the given options is \(6.67 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{-2}\).

Revision Table: G vs. g

It is important not to confuse the Universal Gravitational Constant (G) with the acceleration due to gravity (g).

Additional Information on the Universal Gravitational Constant G

The value of G is extremely small, which is why gravitational forces are only noticeable between very large objects like planets, stars, and galaxies. The first successful measurement of G was performed by Henry Cavendish in 1798 using a torsion balance. Measuring G accurately is challenging because the gravitational force between laboratory-sized objects is very weak compared to other forces like electromagnetic forces.

The precise value of G is still an area of active research, with ongoing experiments aiming for higher accuracy, although the value \(6.674 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{-2}\) (or similar values depending on the source and its precision) is widely used.