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Dimensions of Universal Gravitational Constant

Dimensions of Universal Gravitational Constant

The ability to stand, the landing of an airplane and the falling of a ball on the ground are all possible due to the gravitational pull of Earth. It is the force of attraction and also contributes to our ability to stand on Earth. It is the central or gravitational force that acts along the line connecting the centre of two bodies. The gravitational effects are calculated using the gravitational constant, or Universal Gravitational Constant utilised in Newton’s Law of Gravitation and Einstein’s theory of relativity. 

Table of Contents

What is the Universal Gravitational Constant?

The universal gravitational constant is the proportionality constant used in the universal law of gravitation. The force of attraction among two unit masses placed at a unit distance distant is mathematically equivalent to the value of the universal gravitational constant. The gravitational force between two bodies of equal mass kept at an equal distance constitutes the universal gravitational constant. 

The Formula of the Universal Gravitational Constant

Universal gravitational constant was derived by Newton to better explain the force of gravitational attraction.

formula, where f is the force of gravitational attraction, m1 and m2 is the mass of object 1 and 2, and d is the distance between the centre of two objects. 

The SI unit of the universal gravitational constant is formula

Value of Universal Gravitational Constant

Considering the SI unit, the value of the Universal Gravitational Constant is formula. In the CGS system, the value is formula.

Dimensions of Universal Gravitational Constant

In the dimensional formula, mass is depicted as M, length in depicted as L and time is depicted as T. The derivation of the dimensional formula isformula

Practice Problems

Q1. What is the relationship between acceleration due to gravity and the Universal Gravitational constant?

a. formula
formula

The stated formula relates the acceleration due to gravity and Universal Gravitational Constant. In this formula, g is the acceleration due to gravity, G is the Universal Gravitational Constant, M is the mass of the body, and R is the radius of the body. 

Q2. Who actually discovered Universal Gravitational Constant?

  1. Newton
  2. Einstein
  3. Cavendish
  4. Kepler

Ans. c. Cavendish

Newton stated the gravitational law, and Cavendish found the gravitational constant. 

Q3. What is the current status of G or the Universal Gravitational Constant?

  1. The Universal Gravitational Constant is static
  2. The Universal Gravitational Constant is increasing gradually
  3. The Universal Gravitational Constant is decreasing gradually
  4. The Universal Gravitational Constant is decreasing rapidly

Ans. c. The Universal Gravitational Constant is decreasing gradually

Since the world is expanding, the distance between the bodies is increasing. According to the formula, the Universal Gravitational Constant is inversely proportional to the square of the radius, decreasing gradually. 

Frequently Asked Questions 

Q1. What factors influence the Universal Gravitational Constant?
Ans. The Universal Gravitational Constant is a ‘universal constant’ and hence is unaffected by any factors. 

Q2. What are the applications of the Universal Gravitational Constant?
Ans. The Universal Gravitational Constant finds significant application in determinations of the mass of celestial bodies such as the sun, earth and moon. It is also useful in calculating motion prediction and trajectory of astronomical bodies. The Universal Gravitational Constant helps to discover new planets and stars in the universe. 

Q3. What hinders the calculation of the accurate value of the Universal Gravitational Constant?
Ans. The experimental uncertainties, complex data analysis, influence of environmental conditions and sensitivity of measurements limit the calculation of the Universal Gravitational Constant.

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