Gravitation, Class 9th Notes

THESE NOTES ARE PREPARED ACCORDING TO JKBOSE SYLLABI IN SIMPLIFIED AND CONCISE  PATTERN

Q. Define Gravitation? Explain the universal law of Gravitation?

                                                          Or

State the universal law of Gravitation? Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

Ans: Gravitation is a non contact force of attraction between two bodies by virtue of their mass.

Universal law of Gravitation 

The law states that every object attracts other object mutually.

This force of attraction is directly proportional to product of the masses of two bodies i.e M1, M2

   =>         F       ∝   M1  ×   M2

It is also Inversely proportional to square of distance, "R" between them.

=>           F     ∝           1    
                                        2
                                      R
                             

=>           F    ∝     M1 × M2
                                        2
                                      R

 =>          F     =   G  M1× M2

                                     2
                                   R

The "G" is universal gravitation constant. Its
                             -11   2   2
value is 6.67 × 10 Nm/ kg.


Q. What is meant by acceleration due to gravity? Which factors affect the acceleration due to gravity.

                                                                      Or

What do you mean by free fall?

Ans: The rate of change of velocity of an object due to gravity of earth is called acceleration due to gravity. It is denoted by "g"
                                           2
The value of g is 9.8 m/s .

Factors affecting 'g'

The g is more at poles and less at equator.

The g decreases as we move upwards from surface of earth.

The g decreases as we move inside the earth.

The g is zero at the centre of earth.


Q. Define inverse square law?

Ans: It states that gravitational force between two bodies is inversely proportional to square of distance between them.

i.e             F     ∝           1    
                                          2
                                       R

In other words, If the distance is doubled, the gravitational force becomes 1/4 times.

Q. Derive the relation between Universal Gravitation constant "G" and acceleration due to gravity, "g"

Ans:
From the newtons 2nd law of motion, we know that,

               F   =   M  A

Under the influence of gravity, the acceleration will be taken as g, so,

                F   = m g   ......... I

The gravitational force is given by,

 
         F     =   G  M× m   ......  II
                                 2
                              R


From equation I and II, we get,

      m g   =       G  M× m  
                                 2
                              R
    

            g      =    G  M
                                 2
                              R

The acceleration due to gravity on surface 
                                2

Of earth is 9.8 m/s .


Q. What is the difference between mass and weight of body.

Ans:
A. Mass is the measure of inertia of body where as weight is force with which it is attracted to earth

B. Mass is scaler quantity whereas weight is vector quantity.

C. The SI Unit of mass is kilogram (kg) whereas the SI Unit of weight is newton

D. Mass of object is constant where as weight of object varies.


Q. Why is the weight of object 1/6th on moon than earth?

Ans: The mass and radius of earth is greater than moon, so weight of object on earth is 6 times than moon.

   Textual Questions  

Q. How does force of gravity between two objects change when distance between them is reduced to half?

Ans: When the distance between two objects is reduced to half, the force will become 4 times.



Q. Gravitational force on surface of moon is 1/6 as strong as earth. What is weight of 10 kg object on both moon amd earth?

Ans: Mass of object, m = 10 kg

Weight of object, W  = m g
Here,                                         2
       m   = 10 kg, g  =  9.8 m/s

           W  =   10 × 9.8  
    
             W   =  98 N

Weight on moon is 1/6th of earth, therefore weight on moon = 1/6  × 98
        =            16.3 N.




Q. A ball is thrown vertically upwards with the velocity of 49 m/s, Calculate

A. The maximum height it will reach

B. Total time it takes to return to surface of earth.

Ans:  Given,
        Initial velocity,  U = 49 m/s
        Final velocity, V   =  0 m/s
        Distance,       S   =   ?        
                                                        2
         Acceleration, A  =  9.8  m/s

We have,
               2        2    
            V    -   U    =    2   A    S
             0   -    49×49  =   2 ×  -9.8 ×  S  
      
            S   =     49 × 49
                           2 × - 9.8
            S  =    -  122.5 M
Therefore maximum height is 122.5 m
Minus sign indicates object moves upwards and is decelerating.

Total time taken, T = 

         V    =    U  +  AT
         0     =   49  - 9.8 × T
       -  T  =   49
                   9.8
        T   =  5 sec

Therefore total time taken is upward time and downward time i.e
      T    =   5 × 2    = 10 seconds.

Q. A stone is released from the top of tower at the height of 19.6 m. Calculate its final velocity just before touching the ground.

Ans: Given,
   Initial Velocity, U  =  0
   Final velocity, V    =  ?
   Distance,   S        =  19.6
  Acceleration, A   =  9.8 

We have, 
              2        2    
            V    -   U    =    2   A    S
              2 
           V    -  0   =   2 × 9.8  ×  19.6
              2
            V    =   19.8  ×  19.8
        
          V   =  √19.8× 19.8
        
           V    =   19.8

Therefore, Final Velocity is 19.8 m/s.




Q. A stone is thrown vertically upwards with initial velocity of 40 m/s. Take g as 10m/s2. Find the maximum height reached by stone, What is net displacement and total distance covered by stone.

Ans: Given,
     
         Initial velocity, U   =    40 m/s
         Final Velocity, V    = 0 m/s
                                                          2
        Acceleration, A    =  - 10 m/s
        Distance,        S    =   ?

We have,

              2        2    
            V    -   U    =    2   A    S
            0  -   40×40  =  2  × -10 × S
            S    =   40  × 40
                              20
           S   =   80 m,

Therefore, Maximum height it will reach is 80m.
Total distance travelled is upward and down ward distance,i.e , 80 × 2 = 160 m.

Net displacement is Zero.




Q. A ball is thrown vertically upwards and returns after 6s. Find i. Velocity,  ii. maximum height it reaches. iii. Position after 4 seconds.



Ans:  Given,

         Initial Velocity,  U   = ?
         Final Velocity, V   =   0
        Acceleration ,   A   =  - 9.8
         Time taken,  T   = 3 sec because time of ascent is equall to time of descent i.e 6/2 = 3.

We have,
           V   =  U   +     AT
           0   =  U  +   ( -  9.8 × 3)
          U   =   29.4 m/s.

Therefore initial velocity is 29.4 m/s.

For Maximum height,
We have,

               2        2    
            V    -   U    =    2   A    S
          0  -    29.4 × 29.4  =   2  × (-9.8) S

          S   =   29.4  × 29.4
                        2  ×  9.8

         S   =  - 44.1   m

There fore maximum height is 44.1 m upwards.



Q. What is the importance of Universal law of gravitation.

Ans:  It defines the force that binds us to earth.

It defines the motion of moon around the Planets and planets around sun.

It explains the tides due to sun and moon. 

Q. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Ans: All the objects fall at constant acceleration called as acceleration due to gravity. This acceleration does not depend on the mass of the object. Hence, heavy objects do not fall faster than a light object.



Q. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 10^24 kg and radius of the earth is 6.4 × 10^6 m.)

Ans: Given,

Mass of Earth (M1) = 6 x 10^24

Mass of Object (M2) = 1

Radius of Earth (r ) = 6.4 x 10^6

Gravitational force (F) = ?

We know,

F  = G M1 x M2

                  R^2

F = 6.67 x 10^-11  x   6 x 10^24 x 1

                                     6.4 x 10^6

F =   6.67    x   6   x 10^{^-11 + 24 - 12}

           6.4 x 6.4

F = 0.977 x 10

F = 9.77 Newton

 

 

Q. 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?

Ans: The earth attracts moon with exactly the same force as the with which moon attracts earth.

According to the Universal law of gravitation;

        F = G Me Mm

                     R^2

 

Where, Me is the Mass of Earth and Mm is the mass of the moon. This equation defines the gravitational force between the two bodies and is same for both of the bodies.

 

Q. If the moon attracts the earth, why does the earth not move towards the moon?

Ans: The earth and the moon attract each other with the same force. However, the earth does not move towards the moon because it has more mass than the moon.



Q. What happens to the force between two objects, if

(i) the mass of one object is doubled?

Ans: We Know that, Gravitational Force is directly proportional to the Mass of the object.

So, when the mass of an object is doubled, the gravitational force also doubles.



(ii) the distance between the objects is doubled and tripled?

We Know that, Gravitational Force is inversely proportional to the Square of the distance between the two bodies.

So, when the distance is doubled, the gravitational force reduces by four times.

And, when the distance is tripled, the gravitational force reduces by nine times.



(iii) the masses of both objects are doubled?

Ans: We Know that, Gravitational force is directly proportional to the product of the masses of two bodies.

So, when the masses of both objects is doubled, the gravitational force increases by four times.



Q. What is the acceleration of free fall?

Ans: The acceleration of a free fall on the surface of earth is 9.8 m/s^2s





Q. What do we call the gravitational force between the earth and an object?

Ans: The gravitational force between the earth and an object is called the weight of the object.



Q. Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of g is greater at the poles than at the equator.]

Ans: The weight of the gold is the product of mass and acceleration due to the gravity.

                                                                        W = mg

Since, the acceleration due to gravity is more at the poles than the equator. So, the gold will weigh more at the equator than poles. Hence, Amit’s friend will not agree with the gold bought.



Q. Why will a sheet of paper fall slower than one that is crumpled into a ball?

Ans: A sheet of paper has more surface area than a crumpled ball of paper. It will face more air resistance and will fall slowly.



Q. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 10^24 kg and of the Sun = 2 × 10^30 kg. The average distance between the two is 1.5 × 10^11 m.

Ans: Given,

Mass of Earth (M1) = 6 x 10^24 Kg

Mass of Sun (M2) = 2 x 10^30 Kg

Distance (R) = 1.5 x 10^11 m

Force of Gravity (F) = ?

We Know that,

F = G M1 M2

            R^2

 

F = 6.67 x 10^-11  x   6 x 10^24 x 2 x 10^30

                                            (1.5 x 10^11)^2

 

F = 6.67 x 6 x 2 x 10^ ^{-11 + 24 +30 - 22}

           2.25

 

F = 35.57 x 10^21 Newton

 

Q. A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.

Ans: Given,

Height of Tower (S) = 100 m

Initial Velocity of Stone 2 = 25 m/s

Acceleration due to gravity = 10 m/s^2

For Stone 1, Let it meets stone 2 at 100 – x distance,

We Know,

S = UT + ½ gT^2

100 – x = 0T +1/2 x 10 x T^2

100 – x = 5T^2 ---------- Equation I

For Stone 2, Let it meet stone 1 at distance x from th ground.

We Know,

S = UT + ½ gT^2

x = 25T + ½ x -10 x T^2 (- Sign indicates that the stone is decelerating)

x = 25T – 5T^2 -------- Equation II

On adding equation I and II, We get

100 – x + x = 5T^2 + 25T – 5T^2 (Opposite values will cancel)

100 = 25 T

T = 100/25

T = 4 Seconds.

Therefore, the two stones will meet after 4 seconds.



Now, to know the distance at which both the stones will meet, we will add the value of Time in equation I,

i.e. 100 – x = 5 T^2

100 – x = 5 (4)^2

100 – x = 5 x 16

100 – x = 80

x = 100 – 80

x = 20 m.

Therefore, both the stones will meet 20 meters above the ground.

 

         
                                                      .................................................. 

Click here for other NCERT notes.