1. A man of mass 60 kg and a boy of mass 30 kg are standing at a distance of 1 metre. who has more force of attraction? Justify your answer?

An object do not attract another one. They mutually attract. The force of attraction between them,

The same force is applied by elder man on the boy and at the same time boy on the man.

2. Complete the table

3. When an object was taken from the pole region to the regions equator, it found that the weight was decreased. What is the reason for it. Is it has any relationship with the shape of earth. Justify?

The weight of an object is mg. The value of 'g' at the pole regions is more than that at the equator. The value of 'g' is less at the equator. so objects experience decrease in weight at the equator. So objects experience decrease in weight at the equator.

It has relationship with the structure of earth. At the equator, the distance from the centre of earth is more. So the value of g (GM/R2) is decreased.

At the poles value of radius R is less.

So (g = MN/R2) the value of g is more. When the value of 'g' is increased, the weight of the object is also increased.

4. Explain an experiment to show that the acceleration due to gravity do not depends on the mass of the object.

Arrange a coin and feather in a lengthy tube with one end closed keep the tube vertical and observe the fall of coin and feather. Coin reaches the button first. Repeat the experiment by removing the air from the tube. Now both of them reach the bottom at the same time.

5. How mass weight differ each other. Write in a table?      

6. When a weight is taken in one hand we raise the second hand. What is the reason for it?

When a weight is hanged on one side, out centre of gravity changes to that side. One may fall down them. When the free hand is raised, the centre of gravity can be brought back to the previous positions. So the body gets stability also.

7. 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.

8.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.

9. 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 α m₁m₂   ___________________ (1)
(ii) The force between two bodies is inversely proportional to the square of the distance between them.That is,
                F α   1/ r² ___________________ (2)
Combining (1) and (2), we get
                F α m₁m₂ /  r²
Gravitational force, F = Gm₁m₂/ r²
where, G is a constant known as "Universal Gravitational Constant".

10. 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.

11. What is the force of attraction due to a child of mass 20kg and his mother of mass 100kg. 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

12. 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

13. Define acceleration due to gravity.

The uniform acceleration produced in a freely falling body due to the gravitational force 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.

14. Difference between mass and  weight.

 
15. 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.
 

16.  Define weight of an object. Express it mathematically.

     The weight of an object is the force with which it is attracted towards the earth.

By Newton’s Law of Motion,
      F = ma
      F = mg --------(i)
where g = Acceleration produced due to gravitational force of the earth.
Therefore by using (i) and the definition of weight, we get
                W = mg

where    W = Weight of an object
               m = Mass of the object
               g  = Acceleration due to gravitational force of earth.

17. At a given place ,why can we use the weight of an object as a measure of mass of the object ?

We know ,
                 W = mg
The value of 'g' is constant at a given place.Therefore, at a given place, the weight  of an object is directly proportional to the mass of the object, say 'm', i.e., W α m.
It is due to this reason that at a given place, we can use the weight of an object as a measure of mass of the object.

18. Prove that the gravitational force of attraction between two boys (each weighing 35 kg ) sitting 1 metre apart is almost negligible as compared to the force of gravitation between either of the boys and the earth.Mass of the earth = 6 x 10²⁴ kg and radius of the earth = 6.37 x 10⁶ m.

Take G = 6.67 x 10^-11 SI units.
We know,         F = Gm₁m₂ / r²
case (i)         F₁ = G x 35 x 35 / (1)²
                            =  6.67 x 10^-11 x 35 x 35 / (1)²
                            =  8.17 x 10^-8 N
case (ii)        F₂ = G x 6.67 x 10^-11 x 35 x 6 x 10²⁴ / (6.37 x 10⁶ )²
                           = 6.67 x 10^-11 x 35 x 6 x 10²⁴ /(6.37 x10⁶)²
                           ≈ 345.2 N
Let us now compare these two forces,
     F₂ / F₁ = 345.2  N  / 8.17 x 10^-8 N
                 ≈ 4.2 x 10⁹
Thus, the earth attracts either of the  boys with a force 4.2 x 10⁹ times stronger than that existing between the two boys sitting 1 m apart from each other. In other words, the gravitational force of attraction between the two boys sitting 1m apart is almost negligible as compared to the force of attraction between either of the boys and the earth.

19. Derive an expression for acceleration due to gravity on the surface of the earth.Write the S.I .units for 'g' and 'G'.

Let m be the mass of a body, M the mass of the earth, R the radius of the earth and g the acceleration due to gravity. Let F be the force acting on the body.

By the Newton's second law of motion,

The force acting on the body'

               F = ma

                 = mg      -------------------------(i)

By the Newton's Law of Gravitation,

          F = G Mm /R²   ---------------------(ii)

From equations (i) and (ii),we get

       mg = GMm/R²

                         g = GM/R²

The S.I. units of g and G are (ms^-2) and [Nm²kg^-2] respectively.

20. The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon, with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

      Gravitational force with which a body A attracts another body B is equal in magnitude and opposite in direction to the gravitational force with which a body B attracts to the body A. Thus, the magnitude of force with which the earth attracts the moon is equal to the magnitude of force with which the moon attracts the earth. Thus, both the earth and the moon attract each other with equal forces.

21.  A man weighs 600 N on the earth.What is his mass?(take g = 10 m/s²).If he were taken to the moon,his weight would be 100 N.What is his mass on the moon ?What is the acceleration due to gravity on the moon ?

                                        We have W = mg

Here, it is given that :                   Weight of man on earth,W = 600 N

                                                        Mass of man on earth,m = ?        (To be calculated )

                                 Acceleration due to gravity,g(on earth ) = 10 m/s²

Substituting the above values , we get :

                                                                600 = m x 10

So,                                                           m  = 600/10

                                                                      = 60 kg

Thus,the mass of man on the earth is 60 kilograms.Now, the mass of a body remains the same everywhere in the universe.So, the mass of this man on the moon will also be 60 kilograms.

We will now calculate the value of acceleration due to gravity on the moon by using the same formula :

                                                           W = mg

             Weight of man on the moon,W = 100 N

               Mass of the man on moon,m = 60 kg

                Acceleration due to gravity,g = ?

Substituting,

                                                      100 = 60 x g

            So,                                        g  = 100/60

                                                             = 1.66 m/s²

Thus,the acceleration due to gravity on the surface of the moon is 1.66 m/s² .

22.The acceleration due to the surface of the earth is 9.8 m/s². If the radius of the orbit of the spaceship from the centre of the earth is 2R, where R is radius of the earth, find the acceleration due to gravity at  the spaceship.

            We know ,

                                                          F = GmM/R²

where m,M and R stand for mass of a body,mass of the earth and radius of the earth respectively.

                  But,                                 F = mg

        Therefore                               mg = GmM/R²

           or                                           g = GM/R^{2                            ----------------------------------------- (i)}

When the distance from the centre of the earth is 2R, then the acceleration due to gravity (g') becomes,

                                                         g' = GM / (2R)²

                                                            = 1/4 GM/R^{2                     ----------------------------------------- (ii)}

From (i) and (ii) we get,

                                                     g'/g = 1/

or                                                     g' = g/4

                                                            = 9.8 / 4 ms^-2

                                                            = 2.45 ms^-2