Ask a Teacher

will you please give some class notes based on chapter gravitation

1.State the Universal law of Gravitation. Why do we say that the law is universal?

   The Universal law of Gravitation was given by Newton. So it is also known as Newton's Law of  gravitation.

According to Universal Law of Gravitation : Every body in the Universe attracts every other body with a force which is directly proportional to the product of their masses and inversely  proportional to the square of the distance between them.

The law is universal because it is applicable to all objects; whether the objects are big or small,whether they are celestial or terrestrial.

2.What is the importance of Universal Law of Gravitation?

     1. It is the gravitational force between the sun and the earth, which makes the earth to move around the sun with a uniform speed. Similarly, it is the gravitational force between the earth and the moon, which makes the moon to move around the earth with uniform speed. In fact, it is the gravitational force which is responsible for the existence of our solar system.
2. The tides (rising and falling of water level in sea) are formed in sea due to the gravitational pull exerted by the sun and the moon on the surface of water.
3. It is the gravitational pull of the earth, which holds our atmosphere in place. It is the gravitational pull of the earth, due to which the rain drops fall towards the earth and the rivers flow towards the sea.
4. It is the gravitational pull of earth, which keeps us and other bodies firmly on the ground.
5. The gravitational pull of the earth, which keeps the enormous amount of water in oceans in place and prevents it from flowing.

3. Derive the formula to find the magnitude of the gravitational force between two objects on the surface of the earth.

Consider  two bodies A and B of masses m₁ and m₂ are lying at a distance r from each other. Let the force of attraction between these two bodies be F.  Now, according to the Universal law of Gravitation.

(i). The force between two bodies is directly proportional to the product of  their masses.That is ,
                F ? m₁m₂   ___________________ (1)
(ii) The force between two bodies is inversely proportional to the square of the distance between them.That is,

                F ?   1/ r² ___________________ (2)
Combining (1) and (2), we get
                F ? m₁m₂ /  r²
Gravitational force, F = Gm₁m₂/ r²

where, G is a constant known as "Universal Gravitational Constant".

4. What will happen to the gravitational force,

       a. When the distance between the two bodies is doubled?

       b. When the  distance between the two bodies is halved?

(a)   F = Gm₁m₂/r²

       F₁= Gm₁m₂ / (2r)²

           = F/ 4

The gravitational force becomes one fourth.

(b)     F= Gm₁m₂/ r²

      F₂ = Gm₁m₂ / (r/2)²

           = 4F

The gravitational force becomes  four times.

5. What is the force of attraction due to a child of mass 20 kg and his mother of mass 100 kg. If the distance between them is 20cm?  Take G = 6.67 x 10^-11 Nm²/ kg².

Given m = 20kg 

           M = 100kg

           F = GmM/r²

              = 6.67 x 10^-11x 20 x 100 / (20/100)²

             = 6.67 x 10^-11 x 2000 x 25 / 1

             = 3.335 x 10^-6 N

6. The mass of the earth is 6 x 10²⁴ kg and that of the moon is 7.4 x 10²² kg.  If the distance between  the earth and the moon be 3.84 x 10⁵ km. Calculate the force exerted by the earth on the moon. (G = 6.67 x 10^-11 Nm²/kg²).

The force exerted by one body on another body is given by the Newton's formula:

 F = Gm₁m₂/r²

Here, mass of earth, m₁= 6 x 10²⁴ kg

  mass of the moon, m₂ = 7.4 x 10²² kg

And, Distance between the earth and moon, r = 3.84 x 10⁵ km

                                                                              = 3.84 x 10⁵ x 1000 m

                                                                              = 3.84 x 10⁸m

Putting these values in the above formula, we get

                  F = 6.67 x 10^-11 x 6 x 10²⁴ x 7.4 x 10²² / (3.84 x 10⁸)²

                     = 2.01 x 10²⁰ N

7. Define acceleration due to gravity.

The uniform acceleration produced in a freely falling body due to the gravitational fore of the earth is known as acceleration due to gravity and it is denoted by the letter g.The value of g does not depend on the mass of the body.  The value of g changes slightly from place to place but for the most of the purposes it is taken as 9.8m/s². Thus, the acceleration due to gravity, g = 9.8m/s².

8. Difference between mass and  weight.

9. What is the ratio of SI units to CGS units of gravitational constant?

SI unit of  G is Nm²kg^-2

CGS unit of G is dyne cm²g^-2

The required ratio is

Thus, the ratio of SI unit to CGS unit of G is 10³.

11.