Value of g

# Value of g

## Introduction

The value of “g” represents the acceleration due to gravity, which is a fundamental force that influences the motion of objects on Earth and other celestial bodies. Understanding the value of “g” is crucial in various fields of science and engineering. In this note, we will explore what acceleration due to gravity is, its formula, the unit of “g,” the value of “g” on Earth and the Moon, and how “g” varies on different planets.

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### What is Acceleration Due to Gravity?

Acceleration due to gravity, denoted as “g,” refers to the acceleration experienced by an object in free fall under the influence of Earth’s gravitational force. It represents the rate at which an object gains velocity as it falls toward the Earth’s surface. The value of “g” is approximately constant near the Earth’s surface, but it varies with location and can differ on other celestial bodies.

### Formula of Acceleration due to Gravity (g)

Let us try to find the value of acceleration due to gravity. For this, we will consider the case of a freely falling object. Consider a stone of mass ‘m’ falling freely under the influence of gravity only.

According, to Newton’s second law the force acting on the stone will be:

F = m x g _____(1)

Now, if we consider the mass of the Earth to be ‘M’ and the distance between the stone of mass ‘m’ and the Earth to be ‘d’. As the distance between the center of the stone to the earth’s surface is negligible, we can consider ‘d’ as the radius ‘R’ of the earth. The gravitational force formula is given as,

m x g = G(mxM/R2)

Dividing both sides by the mass of the object ‘m,’

g = G(M/R2)

Unit of Acceleration due to Gravity

The unit of acceleration due to gravity is meters per second squared (m/s2). It represents the rate at which an object accelerates towards the surface of the planet under the influence of gravity.

### Value of g on the Earth

The values of universal gravitational constant, the mass of the earth ‘M,’ and the radius of the earth ‘R’ are,

G = 6.673 x 10-11Nm2kg-2

M= 6 x 1024kg

R = 6.4 x 106m

On substituting them, we get the value of acceleration due to the gravity on the earth as,
g =9.8m/s2

### Value of g on the Moon

The Moon, having a smaller mass than the Earth, has a lower value of acceleration due to gravity compared to Earth. On the surface of the Moon, the value of “g” is approximately 1.6 m/s², which is around 1/6th of the value on Earth. This lower value of “g” on the Moon affects the motion of objects and the behavior of physical processes on its surface.

### Value of g on Different Planet

The acceleration due to gravity varies on different planets due to differences in their mass and size. Here are the approximate values of “g” on some planets in our solar system:

Mars: The value of “g” on Mars is approximately 3.7 m/s², which is around 0.38 times the value on Earth.

Venus: Venus has a value of “g” approximately equal to 8.87 m/s², which is similar to Earth’s “g.”

Jupiter: The value of “g” on Jupiter is about 24.79 m/s², making it approximately 2.53 times the value on Earth.

Saturn: Saturn has a value of “g” approximately equal to 10.44 m/s², which is around 1.07 times the value on Earth.

Uranus: The value of “g” on Uranus is approximately 8.87 m/s², which is similar to Earth’s “g.”

Neptune: Neptune has a value of “g” approximately equal to 11.15 m/s², which is about 1.14 times the value on Earth.

Here’s a tabular form of the acceleration due to gravity (g) on different planets in our solar system:

Planet Acceleration due to Gravity (m/s²)
Mercury 3.7
Venus 8.87
Earth 9.81
Mars 3.71
Jupiter 24.79
Saturn 10.44
Uranus 8.69
Neptune 11.15
Pluto (Dwarf) 0.62

Please note that the values are approximate and may vary slightly depending on factors such as the planet’s mass, radius, and composition. The value for Earth is often used as the standard reference for gravitational acceleration.

### Solved Examples on g:

Example 1: Calculating the acceleration due to gravity on the surface of a planet

Given:

Mass of the planet (M) = 5.972 × 1024 kg

Radius of the planet (r) = 6.371 × 106 meters

Gravitational constant (G) = 6.67430 × 10-11 N(m/kg)2

To determine the acceleration due to gravity (g) on the planet’s surface, we use the formula:

g = (G x M) / r2

Substituting the values

g = (6.67430 × 10-11 x 5.972 × 1024 kg) / (6.371 × 106 m)2

g = (6.67430 × 10-11 x 5.972 × 1024 kg) / 4.049 × 1013 m2

g = 9.8227 m/s2

Therefore, the acceleration due to gravity on the surface of the planet is approximately 9.8227 m/s2.

Example 2: Calculating the weight of an object

Given:

Mass of the object (m) = 60 kg

Acceleration due to gravity (g) on Earth = 9.8 m/s2

To find: Weight of the object (W)

Solution:

Weight is calculated using the formula: W = m x g

Substituting the given values

W = 60 kg x 9.8 m/s2

W = 588 N

Therefore, the weight of the object is 588 Newton.

## Frequently Asked Questions on Value of g

### What is gravity?

Gravity is a fundamental force in nature that attracts objects with mass towards each other. It is responsible for phenomena such as the falling of objects, the motion of planets, and the formation of galaxies.

### Who discovered gravity?

The concept of gravity has been understood and observed since ancient times. However, Sir Isaac Newton's work in the 17th century, particularly his law of universal gravitation, provided a mathematical framework for describing and understanding gravity.

### Is acceleration due to gravity(g) a universal constant?

Acceleration due to gravity (g) is not a universal constant. It varies depending on the location and the mass of the celestial body exerting the gravitational force. On Earth, the average value of acceleration due to gravity is approximately 9.8 m/s². However, on different planets or celestial bodies, the acceleration due to gravity can be significantly different. For example, on the Moon, the acceleration due to gravity is about 1/6th of that on Earth, while on Jupiter, it is much stronger. Therefore, the value of acceleration due to gravity is specific to each celestial body and is not a universal constant.

### How do you calculate 9.8 m/s2?

Gravitational Acceleration Formula is given by: g = G x M / r2 The values of universal gravitational constant, the mass of the earth M, and the radius of the earth R are, G = 6.673 x 10-11Nm2kg-2 M= 6 x 1024kg R = 6.4 x 106m On substituting them, we get the value of acceleration due to the gravity on the earth as, g =9.8m/s2

### What is G in physics?

In physics, G refers to the gravitational constant, also known as the universal gravitational constant. It is denoted by the symbol G and represents the strength of the gravitational force between two objects. The value of the gravitational constant is approximately 6.674 × 10-11 N(m/kg)2 in the International System of Units (SI). It plays a crucial role in the calculation of gravitational forces and is used in various formulas, including Newton's law of universal gravitation. The gravitational constant provides a fundamental constant that helps quantify the force of gravity between objects and is an essential component of gravitational calculations in physics.

### Is gravity the same everywhere in the universe?

Gravity is present throughout the universe, but its strength can vary depending on the masses of the objects involved and the distances between them. Gravity is stronger for objects with larger masses and weaker for objects that are farther apart.

### Where is gravity maximum on the earth?

Gravity is maximum near the surface at the pole. It is slightly stronger at the poles compared to the equator. This is because the Earth is not a perfect sphere but slightly flattened at the poles due to its rotation. As a result, the distance between an object at the poles and the center of the Earth is slightly shorter than at the equator, leading to a slightly stronger gravitational force.

### Is gravitational acceleration zero?

No, gravitational acceleration is not zero. Gravitational acceleration exists whenever there is a gravitational force acting on an object. On Earth, the gravitational acceleration is approximately 9.8 m/s², causing objects to accelerate towards the Earth's surface. However, the value of gravitational acceleration can vary depending on the mass and distance from other celestial bodies.

### What is the SI unit of gravitational acceleration?

The SI unit of gravitational acceleration is meters per second squared (m/s²). Gravitational acceleration represents the rate at which an object accelerates under the influence of gravity. It measures the change in velocity per unit of time and is expressed in terms of meters per second squared.

### What factors does gravitational acceleration depend on?

The formula for gravitational acceleration is as follows: g = G x M / r2 As we can see, Gravitational acceleration depends on several factors. Firstly, it is influenced by the mass of the celestial body. The greater the mass, the stronger the gravitational acceleration. Secondly, the distance from the center of the celestial body affects gravitational acceleration. It decreases as the distance increases. The gravitational constant, denoted as G, is another factor and its value is constant universally. Additionally, local variations in gravitational acceleration can occur due to differences in topography and density variations within Earth's crust. Lastly, the presence of other celestial bodies nearby can influence gravitational acceleration through gravitational interactions.

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