Class 9 Science

Free Fall

  • Acceleration due to gravitation
  • Calculation of value of g

When an object falls from any height under the influence of gravitational force only, it is known as free fall. In the case of free fall no change of direction takes place but the magnitude of velocity changes because of acceleration.

This acceleration acts because of the force of gravitation and is denoted by ‘g’. This is called acceleration due to gravity.

Acceleration Due to Gravitation

Let mass of the object put under free fall = m.

And acceleration due to gravity = g.

Therefore, according to Newton’s Second Law of Motion which states that Force is the product of mass and acceleration,

F = m × g -----------------(i)

Now, according to Universal Law of gravitation,

`F= G*(M*m)/d^2` ---(ii)

Thus, from above two expressions, we get

`mg = G*(M*m)/d^2`
`=>g = (GMm)/(d^2*m)`
`=>g=(GM)/d^2` ---(iii)

Where, g is acceleration due to gravity,

G is the Universal Gravitational Constant.

M is the mass of earth.

And d is the distance between object and centre of earth.

When object is near the surface of earth

When an object is near the surface of earth, the distance between object and centre of the earth will be equal to the radius of earth because the distance of object is negligible in comparison of the radius of earth.

Let the radius of earth is equal to R.

Therefore, after substituting ‘R’ at the place of ‘d’ we get,

`g = (GM)/R^2` ----(iv)

Since, earth is not a perfect sphere rather it has oblique shape. Therefore, radius at the equator is greater than at the poles.

Since, value of ‘g’ is reciprocal of the square of radius of earth, thus, the value of ‘g’ will be greater at the poles and less at the equator.

And the value of ‘g’ will decrease with increase of distance of object from earth.

Calculation of value of `g`

We know that,

The accepted value of `G` is `6.673xx10^(-11)Nm^2kg^(-2)`

The mass of earth, `M=6xx10^(24)kg`

The radius of earth, `R = 6.4xx10^6m`

Therefore, by using expression `g = (GM)/R^2`, the value of `g` can be calculated.

Therefore, after substituting the value of G, M and R in the expression for ‘g’ we get.

`g=(6.673xx10^(-11)Nm^2kg^(-2)xx6xx10^(24)kg)/(6.4xx10^6m)^2`

`=>g= 9.8\ m\ s^(-2)`

Motion of an object under the influence of gravitational force of earth

The expression for ‘g’ is written as `g=(GM)/R^2`

Since, the value of ‘g’ does not depend upon the mass or distance of an object, therefore, all objects fall over the earth with the same rate.

The equations for motion are as follows:

`v=u+at` ---(i)
`s=ut+1/2at^2` ---(ii)
`v^2=u^2+2as` ---(iii)

Therefore, the equations of motion are also applied to calculate the velocity, distance, etc by replacing ‘a’ by ‘g’. After substituting ‘g’ at the place of ‘a’ we get above equations as follows:

`v=u+g\t` ---(i)
`s=ut+1/2g\t^2` ---(ii)
`v^2=u^2+2gs` ---(iii)

In the calculation; initial velocity (u), final velocity (v), time taken (t), or distance covered (s), the value of ‘g’ is taken as positive in the case of object moving towards earth and taken as negative in the case of object is thrown in opposite direction of earth.


Matter in Our Surroundings

Anything that has both mass and volume is called matter. You can also say that anything which has mass and which occupies space is called matter.

Is Matter Around Us Pure?

Elements and compounds are pure substances. All other substances are mixtures which means they are not pure substances.

Atoms and Molecules

Read about law of conservation of mass, law of constant proportions and Dalton's atomic theory.

Structure of Atoms

Atom is made of three particles; electron, proton and neutron. These particles are called fundamental particles of an atom or sub atomic particles.

Cell: The Fundamental Unit of Life

A cell is capable of independent existence and can carry out all the functions which are necessary for a living being.

Tissue

A groups of cells which is meant for a specific task is called tissue. Tissues are the first step towards division of labour in complex organisms.

Diversity in Living Organisms

Without proper classification, it would be impossible to study millions of organisms which exist on this earth.

Motion

If an object changes its position with respect to a reference point with elapse of time, the object is said to be in motion.

Force & Laws of Motion

Force has numerous effects. Force can set a stationary body in motion. Force can stop a moving body.

Gravitation

Earth attracts everything towards it by an unseen force of attraction. This force of attraction is known as gravitation or gravitation pull.

Work & Energy

When force is exerted on an object and object is displaced, work is said to be done. It means work is the product of force and displacement.

Sound

Sound is a type of energy. Sound travels in the form of wave from one place to another.

Why Do We Fall Ill

Health is a state of physical, mental and social well being. A condition in which the affected person is unable to carry out normal activities is termed as disease.

Natural Resources

Resources which are obtained from nature are called natural resources. Examples: Air, water, soil, wood, etc.

Improvement in Food Production

Food security is said to exist when all people, at all times, have physical and economic access to sufficient, safe and nutritious food to meet their dietary needs and food preferences for an active and healthy life.