Value of Gravitational Constant - Unit, Application, FAQs
The gravitational constant ( $G$ ) is one of the most important fundamental constants in physics, yet it remains one of the most difficult to measure accurately. Introduced by Sir Isaac Newton in his law of universal gravitation, $G$ determines the strength of the gravitational force between two masses. Later measured experimentally by Henry Cavendish using a torsion balance, this constant plays a crucial role in understanding gravity, planetary motion, satellite dynamics, and even Einstein's theory of relativity. The accepted value of the gravitational constant is $6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$. In this article, we will explore the value of G , its SI unit, method of measurement, and its importance in physics in simple and clear terms.
This Story also Contains
- What is the Value of Gravitational Constant?
- How to Measure Gravitational Constant (G)
- SI Unit of Gravitational Constant (G)
- Applications:
What is the Value of Gravitational Constant?
The gravitational constant (G) is the proportionality constant used in Newton's Law of Universal Gravitation. It determines the strength of the gravitational force between two masses.
According to Newton's law:
$F=G \frac{m_1 m_2}{r^2}$
Numerical Value of Gravitational Constant
$G=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$
How to Measure Gravitational Constant (G)
The gravitational constant $G$ is measured using the Cavendish experiment (torsion balance method).
In this experiment:
- Two small lead spheres are attached to a light rod suspended by a thin wire.
- Two large lead spheres are placed near them.
- The small spheres experience gravitational attraction and the rod twists.
- The angle of twist is measured to calculate the tiny gravitational force.
Using Newton's law,
$F=G \frac{M m}{r^2}$
the value of $G$ is calculated.
$G=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$
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SI Unit of Gravitational Constant (G)
The $\mathbf{S I}$ unit of the gravitational constant $G$ is:
$\mathrm{N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$
Derivation of Unit:
From Newton's law of gravitation,
$
\begin{aligned}
F & =G \frac{m_1 m_2}{r^2} \\
G & =\frac{F r^2}{m_1 m_2}
\end{aligned}
$
Substituting SI units:
- $F \rightarrow$ Newton (N)
- $r \rightarrow$ metre (m)
- $m \rightarrow$ kilogram (kg)
$G=\frac{\mathrm{N} \cdot \mathrm{~m}^2}{\mathrm{~kg}^2}$
So,
$
G=\mathrm{N} \mathrm{~m}^2 \mathrm{~kg}^{-2}
$
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Applications:
1. Sir Isaac Newton's Universal Law of Gravity was the first to investigate the Gravitational constant.
2. In this theory of relativity, Einstein expanded on this.
3. This empirical constant is solely used in the research of gravitational impacts in a variety of disciplines.
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NCERT Physics Notes:
Frequently Asked Questions (FAQs)
The gravitational constant is employed in Newton's Law of Gravitation as a proportionality constant. The universal gravitational constant, designated by G and measured in Nm^2/kg^2, is the force of attraction between any two unit masses separated by a unit distance. It is a gravitational physics empirical physical constant. Newton's Constant is another name for it. Everywhere in the cosmos, the gravitational constant has the same value as the universal gravitational constant. G is not the same as g, which signifies the acceleration due to gravity.
G is equal to 6.67 10-11 Newtons kg-2 m2 in SI units. The force is attractive because it is directed in a straight line between the two bodies.
The primary distinction between g and G is that g denotes gravitational acceleration, whereas G denotes the gravitational constant. G's value of gravitational constant varies with altitude, whereas G's value of gravitational constant remains constant. The gravitational constant is a scalar number, while gravitational acceleration is a vector quantity.
The value of gravitational constant of G, 6.67 x 10-11 Nm2kg-2, is known as the Universal Gravitation Constant.
The universal gravitational constant, or G, is named after the fact that its value of gravitational constant is constant and does not vary with location. 6.673 10-11 Nm2/kg2 is the result. This law is universal in that it applies to all bodies, large and tiny, celestial and terrestrial.
