Relation between  g ang G

When we throw something up, why does it come down. Have you ever thought about it? The force of gravity pulls that thing down. So what is this gravity?

Newton's law of gravitation:

The attraction force acting between any two objects is proportional to the product of the mass of the objects and inversely proportional to the square of the distance between them.

Suppose two objects with mass m1 and m2 are located at a distance R from each other, then according to Newton's law, the force of attraction between them is F = G m1m2 / R². Where G is a constant, called the universal gravitational constant and whose value is 6.67 X 10‐¹¹ Nm² / kg².

Gravity

An attraction force acts between two bodies according to Newton's gravity. If one of these bodies is earth, then this attraction force is called gravity. That is, gravity is the attraction force through which the earth pulls an object towards its center. The acceleration generated due to this force is called gravitational acceleration (g), which has a value of 9.8 m / s². Gravitational acceleration (g) does not depend on the form, shape, mass, etc. of the object.

What is g ?

AnswerWe know that the Earth pulls every object towards its center. The force of gravity exerted by the Earth is called the force of gravity. this acceleration generated due to the force of gravity is called gravitational acceleration.
1. In another way When an object is left freely above it, it starts falling towards the earth due to the force of gravity and its velocity produces an acceleration which is called gravitational acceleration.
2. Let us display it with g. Its value is 9.81m/sec².
3. Its unit is meter / second² (m/sec²) or newton / kg (N / Kg).
4. Gravitational transfer does not depend on the shape, form, mass, etc. of the object. It is a vector quantity.

Change in value of g. / Change in the value of gravitational acceleration / The value of g at the center of the Earth
1. The standard value of g is 9.8 meters per second.
2. The value of g at the equator is minimum and maximum at the poles because the diameter of the equator is greater than the diameter of the poles and the earth rotates around on its axis.
3. The value of g increases as the earth's rotation speed decreases and the value of g decreases as the rotation speed increases.
4. The value of g decreases above the surface of the earth and increases when it goes down and becomes 0 (at the center) after a time.
5. The value of g at the center of earth becomes 0.
6. The value of g on the moon or The value of gravitational acceleration on the Moon is 1/6 of the gravitational acceleration of the Earth.

What is G ?

1. According to Newton's law of gravity, gravity is the force that acts between any two objects.
2. Each particle of the world attracts each other particle with a force that is proportional to the product of the masses of the two particles and inversely proportional to the square of the distance between them.
3. If the weight of the first body is m1 and the weight of the second body is m2 and the distance between those bodies is r, then according to Newton's law of gravity -

F∝ m1 × m2

F ∝ 1 / r2

F∝ m1 × m2 / r2

F = G m1 m2 / r2

Here, G is called the gravitational constant. This is a constant, so its value will remain the same everywhere. Its value is 6.67259 x 10-¹ Nm² / kg ². Its unit is Newton meter²/ kg² (Nm² / kg ²) or meter³/ kg sec² (m³ / kg sec²). G is a scalar quantity.

Obtain the relation between g & G?

Answer : Consider a body of mass 'm' kept on the surface of earth. Let $M \& R$ be the mass of earth of radius of earth respectively. The gravitational force, by Newton's law of gravitation is,

$F=\frac{G M m}{R^{2}}$ - - - (i)

Where G - Universal gravitational constant let 'g' be the acceleration due to gravity on earth surface, then weight of a body is equal to gravitational force of attraction between the earth \& the given body.

$\therefore$ weight of body = gravitational force

\begin{aligned} \mathrm{mg} &=\frac{\mathrm{GMm}}{\mathrm{R}^{2}} \\ \mathrm{~g} &=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \\ \mathrm{GM} &=\mathrm{gR}^{2} \end{aligned}

This is the relation between g & G.

Where,

• g is the acceleration due to the gravity of any massive body measured in m/s2.
• G is the universal gravitational constant measured in Nm2/kg2.
• R is the radius of the massive body measured in km.
• M is the mass of the massive body measured in kg

The weight of a body on the surface of the earth is defined as P = m and it can be said that it is the attraction of a body towards the center of the earth due to the earth's gravity field g, or how it is also called, the acceleration free fall, or gravitational intensity. Now let's set F_g = P equal and we see that eliminating the mass m on both sides of the equality results in the equation: g = GM / r² which is the equation of the scalar intensity of the Earth's gravitational field and, as a function of the distance r to the center of land.

Difference between g and G

1. The value of gravitational acceleration (g) varies in different places and The value of G is always fixed at every place of the entire universe.
2. The value of 2 g is 9.81 m/s ². The value of G is 6.67259 x 10-¹ Nm²/ kg²
3. g is the vector Quantity. G is a scalar Quantity.
4. g represents gravitational acceleration and is not a constant. G represents the gravitational constant and is a constant.

What is the value of g at the center of the Earth ?
1. The standard value of g is 9.8 meters per second.
2. The value of g at the equator is minimum and maximum at the poles because the diameter of the equator is greater than the diameter of the poles and the earth rotates around on its axis.
3. The value of g increases as the earth's rotation speed decreases and the value of g decreases as the rotation speed increases.
4. The value of g decreases above the surface of the earth and increases when it goes down and becomes 0 (at the center) after a time.
5. The value of g at the center of earth becomes 0.

Is g and G is Same ?
AnswerThe universal gravitational constant (G) is an empirically obtained physical constant, which determines the intensity of the gravitational force of attraction between bodies. It is denoted by "G" and appears in both Newton's law of universal gravitation and Einstein's general theory of relativity.

g = gravity (9.81m / s²)

g = gram (0.001 Kg)

G = giga (10⁹)

G = universal constant of gravitation (6.67x10⁻¹¹Nm² / kg²)

Conclusion: They are not the same and the reason is because they represent very different things, such as those mentioned above.

MCQs on g and G:

1. The S.I. unit of $\mathrm{G}$ is______
(a) $\mathrm{N}-\mathrm{m} / \mathrm{kg}^{2}$
(b) $\mathrm{N}-\mathrm{m}^{2} / \mathrm{kg}^{2}$
(c) $\mathrm{N}^{2}-\mathrm{m}^{2} / \mathrm{kg}$
(d) $\mathrm{N}-\mathrm{m} / \mathrm{kg}$

2. The dimensional formula for $\mathrm{G}$ is______
(a) $L^{\prime} M^{u} T^{-1}$
(b) $L^{2} M^{1} T^{-2}$
(c) $\mathrm{L}^{3} \mathrm{M}^{-1} \mathrm{~T}^{-2}$
(d) $\mathrm{L}^{3} \mathrm{M}^{2} \mathrm{~T}^{2}$

3. The universal constant of gravitation________
(a) has no unitS and dimensions as it is a constant
(b) Its value remains constant in all systems of units
(c) does not depend upon the nature of the medium in which the bodies are placed
(d) It is a force of repulsion

4. If we consider the various aspects of G and g we find that______
(a) Both of them are universal and gravitational constants
(b) they are neither universal nor gravitational
(c) G is a universal constant but g is not a universal constant
(d) g is a universal constant but G is not a universal Constant

5. Universal gravitational constant (G) is________
(a) the gravitational force of attraction between two bodies.
(b) the gravitational force of attraction between two bodies each of unit mass.
(c) the gravitational force of attraction between two bodies separated by unit distance.
(d) the gravitational force of attraction between two bodies each of unit mass, separated from each other by unit distance.

6. The unit of g/G is____
(a) kg/m
(b) kg/m²
(c)m²/kg
(d) m/kg

7. The weight of a body is defined as W = mg. If the weight of a man is 70 kg and if the acceleration due to gravity is
taken as 10 m/s², then the mass of the man is______
(a) 70 kg
(b) 7 kg
(c) 700 kg
(d) 1/7 kg