# Gravitational Force and Gravity

Contents

Gravitation related General Knowledge is one of the most important topic for various type of competitive examinations such as IAS, UPSC, Railway, Banking, SSC, CGL, CHSL, MTS etc. Therefore we have brought to you the proper and appropriate knowledge and concept related Physics by chapter wise.

In this topics we are going to discuss about Gravitation force, Newton’s Law of Gravitation, Center of mass concept, gravity and Gravitational Potential energy.

## Newton’s Law of Gravitation, Gravitational Force:

Definition of Gravitational Force: Every objects in this universe attract each other by a force called gravitation force.

Any two objects in this universe attract each other along a line joining between them. The magnitude of this force of attraction depends on the product of their masses and inversely proportional to the square of the distance between them.

Let us consider two masses, m1 and m2 are separated at a distance r. According to Newtons law of Gravitation if F is the force between these two objects, then, –

Fm1×m2 Where r is constant;

F 1/r2 where m1, m2 are constant;

Combining these two rule we get

Fm1×m2/r2

`or, F = G×m1m2/r2`

Where G is known as Universal Gravitational Constant. The above equation is the mathematical form of Newton’s Law of Gravitation.

### Value of Universal Gravitational Constant:

From Newton’s Law of Gravitation we get

`G = F × r2 / (m1 × m2);`

From the above equation we see that if each masses of two bodies m1 and m2 is 1 kg and they are kept at a distance of 1 meter, then the amount of force by which they attract each other is the Universal Gravitational Constant. It is denoted by ‘G‘. Its unit is Nm2/kg2

The absolute value of Universal Gravitational Constant is 6.67×10 -10 Nm2/kg2. This amount of force is too small that we can not feel. Gravitational force is always directed towards the centre of masses of the bodies. That’s why it is a vector quantity.

### Dimension of G :

The dimension of Universal Gravitational Constant is [M-1L3T-2].

### Gravitational Attraction for Extended Body:

How to calculate the force of attraction for extended bodies or irregular shaped bodies? Now look out the following problem. Object-A and object-B are irregular shaped. While calculating the gravitation force we need to have the distance between them. But how can we obtain the distance? Since they are not point masses.

The problem is solved by considering their centre of masses or centre of gravity. For every object in the universe have particular point where its all the mass is considered to be concentrated. This point is called ‘Centre of Mass‘. For regular shaped and homogeneous objects such as sphere the centre of mass lies on its centre.

## Gravity :

The gravitational force by which our Earth attract an object or body towards its centre is known as gravity. Due to this gravity each object on the earth’s surface fall on earth.

### Gravitational Acceleration :

We know that when a body moves due to application of force, an acceleration is always created on it. How much acceleration will be created? The answer is obtained from the equation –

`Force = Mass * Acceleration;`

This concept is also applicable for the gravity. Thus when Earth attracts an object by its gravity, an acceleration produced on the object. This acceleration is known as ‘Gravitational Acceleration‘ and it is denoted by ‘g‘. The value of ‘g‘ is 9.8 m/s2. It depends on the shape, size and the mass of the body.  Gravitational acceleration is a vector quantity.

Variation of gravitational acceleration on earth surface.

Though the value of gravitational acceleration is considered as constant, but it is not. It vary on earth surface.

• Its value is maximum at the two poles of earth. Why? Because the linear velocity of the surface of pole is less than any other place on the Earth.
• The value of g is minimum at equator. Why? Because linear velocity of the surface of earth is maximum.
• The value of g decreases as the height from the earth surface increases.
• The value of g also decreases as we go inside the earth.

If the angular velocity of the earth become seventeen times its present value, every object on equator well become weightless. Why? Because when angular velocity increase its centrifugal force also increases. This centrifugal force is always opposite to the gravity.

## Gravitational Potential:

The gravitational potential at a point in a gravitational field is measured by the amount of work done in bringing a unit mass form infinity to that point.

It is a scalar quantity and generally it is denoted by V. In gravitational field if you want to move an object from point A to point B, then it required some energy. If you move the object along the direction of field, the energy is negative. And the energy is positive if you move an object opposite to the direction of gravitational force.

If you moves an object from infinite to a some point in the field the potential is given by the following formula.-

`V = -Gm/r, where m is the mass of the object.`

### Potential energy of Earth:

The gravitational potential energy or P.E of Earth is measured by the height you lift an object multiplied by its mass and gravitational acceleration i.e. –

`Gravitational Potential energy of Earth W -= mgh;`

The unit of P.E. is Joul in SI system and erg in c.g.s system.