CBSE Class 9 Physics Gravitation (1). Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

**GRAVITATION**

**NEWTON’S UNIVERSAL LAW OF GRAVITATION**

Every object in the Universe attracts every other object with a force which is

(i) directly proportional to the product of their masses, and

(ii) inversely proportional to the square of the distance between their centres. The direction of

the force is along the line joining the centres of two objects.

*F œ* *m*1*m*2 and 2 and Fœ m_{1} m_{2}/r^{2}

*F= G*.*m _{1} m_{2}/r^{2} *where G is a constant proportionality and is called universal gravitational constant.

**UNITS AND VALUE OF GRAVITATIONAL CONSTANT**

F=Gm_{1}m_{2}/r^{2}

*G*.*m _{1}m_{2}=F*

*r*.

^{2}G= F*r*

^{2}/m_{1}m_{2}Unit of G is Nm^{2}/kg^{2}.

If m_{1} = m_{2} = 1 kg, r = 1 then we have G = F Hence, Universal gravitational constant G is numerically equal to the gravitational force of attraction between two bodies, each of unit mass kept at unit distance from each other.

Value of G = 6.67 x 10^{–11} Nm2/kg^{2}

**KEPLER’S LAWS OF PLANETARY MOTION**

**KEPLER’S FIRST LAW**

Every planet revolves around the Sun in an elliptical orbit, with the sun situated at any one of the foci of the ellipse.

**KEPLER’S SECOND LAW**

In the elliptical orbit of the planet, the line joining the centre of the planet to the centre of the Sun sweeps equal intervals of time.

**KEPLER’S THIRD LAW**

The square of time period of revolution of a planet around the Sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.

r^{3} œ T^{2}= r^{3}/T^{2}=constant

where r = radius of orbit = mean distance of planet from the Sun (inm), T = the time period of revolution of planet around the Sun (in second)

**IMPORTANCE OF THE UNIVERSAL LAW OF GRAVITATION**

The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:

(i) the force that binds us to the earth;

(ii) the motion of the moon around the earth;

(iii) the motion of planets around the Sun; and

(iv) the tides due to the moon and the Sun.

**INTEXT QUESTIONS PAGE NO. 134**

**1. **State the universal law of gravitation

**Ans. **The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For two objects of masses *m*_{1} and *m*_{2} and the distance between them *r*, the force (*F*) of attraction acting between them is given by the universal law of gravitation as:

*F= Gm _{1}m_{2}/r^{2}*

Where, G is the universal gravitation constant given by: *G=*6.67*10^{-}^{11}*Nm*^{2} / *kg*^{2}

**2. **Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

**Ans. **Let *M*E be the mass of the Earth and *m *be the mass of an object on its surface. If *R *is the radius of the Earth, then according to the universal law of gravitation, the gravitational force (*F*) acting between the Earth and the object is given by the relation.

*F Gm1m2/r ^{2}*

**FREE FALL**

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.

**EXPRESSION FOR ACCELERATION DUE TO GRAVITATION ‘G’.**

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 x g -----------------(i)

Now, according to Universal Law of gravitation,

*F G*.*M*.*m/d ^{2}*……………. (ii)

Thus, from above two expressions, we get 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,

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