Dimension of Gravitational Constant

Dimensional Formula for Gravitational Constant is [M^-1 L³ T^-2]. The Gravitational Constant is represented by ‘G‘. It is Newton’s gravitational constant and gives the constant of proportionality in Newton’s Universal law of gravitation which is the basis of our understanding of non-relativistic gravity.

In this article, we will discuss the ‘Gravitational Constant,’ its unit, dimensional formula, and the derivation of the Gravitational Constant.

Gravitational Constant (G)
Dimensional Formula	M-1 L3 T-2
SI Unit	Nm3 kg-2
Value	6.6743 × 10-11 m3 kg-1 s-2
Formula	G = F × r2 × (m1m2)-1

Dimensional Formula for Gravitational Constant

The dimensional formula of gravitational constant is

M^-1 L³ T ^-2

where M denotes mass, L denotes length, and T denotes time.

Derivation of Dimensional Formula for Gravitational Constant

We can derive the dimensional formula for gravitational constant as follow:

As we know, from Newton’s law of gravitation,

Force (F) = (Gm₁m₂) × r^-2

Gravitational Constant (G) = F × r² × (m₁m₂)^-1 ……(1)

As, Force (F) = Mass × Acceleration

Dimensionally, Force (F) = M × [LT^-2]

The dimensional formula of force = M¹ L¹ T^-2 ……(2)

On substituting equation (2) in equation (1) we get,

Gravitational Constant (G) = F × r² × [m₁ m₂]^-1

G = [M¹ L¹ T^-2] × [L]² × [M]^-2

G = [M^-1 L³ T^-2]

Hence, the universal gravitational constant is dimensionally represented as M^-1 L³ T^-2.

What is Gravitational Constant?

Gravitational constant describes the intrinsic strength of gravity and can be used to calculate the gravitational pull between two objects. It is a physical constant derived using Newton’s Law and is represented by the letter G. According to Newton’s law of gravitational constant the attractive force between two objects (F) is equal to G times the product of their masses (m_1, m₂) divided by the square of their distance (r²).

Mathematically,

F ∝ m₁m₂ / r²

F = G m₁ m₂ / r²

Here, G is proportional constant called Gravitational Constant.

G is equal to 6.6743 × 10^-11 m³ kg^-1 s^-2.

Read more about Universal Gravitational Constant.

Gravitational Constant Formula

As we know, from Newton’s law of gravitation,

Force (F) = G m₁ m₂ / r²

Gravitational Constant (G) = F × r² × (m₁m₂)^-1

Read More,

• Gravitational Force
• Difference between Coulomb Force and Gravitational Force
• Gravitational Potential Energy

Dimensional Formula for Gravitational Constant: FAQs

What is Universal Gravitational Constant?

According to Newton’s Law, the force of gravitational attraction is the force that is dependent on the masses of both bodies and is inversely proportional to the square of the distance that separates the center of the bodies. The constant proportionality present in Newton’s equation of gravitational force is called the universal gravitational constant.

What is SI Unit of Gravitational Constant?

The SI unit of gravitational constant (G) is Nm³ kg^-2

What is Value of Gravitational Constant?

The value of Universal gravitational constant is given by 6.6743 × 10^-11 m³ kg^-1 s^-2

What is Dimensional Formula of Gravitational Constant?

The dimensional formula of the gravitational constant is M^-1 L³ T ^-2

What is Formula for Gravitational Constant?

The formula of Gravitational Constant (G) = F × r² × (m₁m₂)^-1

Why is G called Universal Constant?

The value of G does not depend on the nature and size of the bodies and remains same in the whole universe, therefore it is known as Universal constant.

What is Dimension of F= GMmR²?

F= GMmR² represents the Universal gravitational constant whose dimension is M^-1 L³ T ^-2 .

What are the Dimensional Formula of small g?

The unit of ‘g’ is m/s² and so its dimensional formula is M⁰L¹T^-2.