9th Class Physics Unit No. 5 Gravitation (Exercise Solution)

UNIT No. 5

Gravitation

(Exercise Solution)

5.1        Encircle the correct answer from the given choices.

 i.               Earth's gravitational force of attraction vanishes at

(a) 6400 km                  (b) infinity                  (c) 42300 km              (d) 1000 km

ii.              Value of g increases with the

(a) increase in mass of the body

(b) increase in altitude

(c) decrease in altitude

(d) none of the above

iii.               The value of g at a height one Earth's radius above the surface of the Earth is:

(a)          2 g                   (b)      1/2 g                (c)        1/3 g                (d)       1/4 g

iv.               The value of g on moon's surface is 1.6 ms^-2. What will be the weight of a 100 kg body on the surface of the moon?

(a)          100 N             (b)       160 N              (c)        1000 N            (d)      1600 N

v.               The altitude of geostationary orbits in which communication satellites are launched above the surface of the Earth is:

(a)          850 km            (b)       1000 km          (c)        6400 km          (d)       42,300 km

vi.               The orbital speed of a low orbit satellite is:

(a)          zero                 (b)       8 ms^-1              (c)        800 ms^-1          (d)       8000 ms^-1

Answers to Multiple Choice Questions (MCQs)

i.	(b)	ii.	(c)
iii.	(d)	iv.	(b)
v.	(d)	vi.	(d)

 

5.2         What is meant by the force of gravitation?

Ans:  The force due to which everybody of universe attracts every other body is called force of gravitation.

5.3         Do you attract the Earth, or the Earth attracts you? Which one is attracting with a larger force? You or the Earth.

Ans: You attract the earth with the same force that the earth attracts you. However, this force  has more effect on you because you are much lighter than Earth.

5.4         What is a field force?

Ans:  A force which is acting on a body by another body whether the body is in contact with other body or not, is called field force. It is a noncontact force                                                         

           Examples:

                        i.          Gravitational Force

                      ii.          Electrostatic force.

                    iii.          Magnetic force

5.5         Why earlier scientists could not guess about the gravitational force?

Ans:  Earlier scientists could not guess the force of gravitation between two masses, because it is of very small value. it could be detected only by the very sensitive instrument which was not invented at that time.

5.6        How can you say that gravitational force is a field force?

Ans:  The gravitational force exists around earth and it is acting on the bodies whether the bodies are in contact with each other or not, so we can say that gravitational force is a field force.

5.7         Explain, what is meant by gravitational field strength?

Ans:  In the gravitational field of the earth, the gravitational force per unit mass is called the gravitational field strength of the earth.

At any place its value is equal to the value of g at that point. Near the surface of the earth, the gravitational field strength is 10 Nkg^-1. 

5.8        Why law of gravitation is important to us?

Ans: The law of gravitation is important for us because it is used to calculate

                        i.          The Gravitational force of attraction between two masses.

                      ii.          The mass of the earth.

                    iii.          The acceleration due to gravity at any place on the earth. 

5.9        Explain the law of gravitation.

Ans: Statement

            “Everybody 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 their masses”

            Mathematically

\[F = G\frac{m_{1}m_{2}}{d^{2}}\]

5.10     How the mass of Earth can be determined?

Derivation for the Mass of Earth

Consider a body of mass m on the surface of the Earth as shown in figure below

Let the mass of the Earth be M_e  and radius of the Earth be R. The distance of the body
from the centre of the Earth will also be equal to the radius R of the Earth. According to the law of gravitation, the gravitational force F of the Earth acting on a body is given
by

\[F = G\frac{mM_{e}}{R^{2}}\] 

But the force with which Earth attracts a body towards its centre is equal to its weight w. Therefore

F= w = mg ------------------- (2)

By comparing equation (1) and (2)

\[mg = G\frac{mM_{e}}{R^{2}}\]

\[g = G\frac{M_{e}}{R^{2}}\]

\[M_{e}= \frac{R^{2}g}{G}\]

Here

g = gravitational acceleration = 10 ms^-2

 

R = Radius of the earth = 6.4x10⁶ m

 

G = gravitational constant = 6.67x10^-11 Nm²kg^-2

Mass M of the Earth can be determined on putting these values in equation (3)

\[M_{e}= \frac{(6,4X10^{6}))^{2}(10))}{6.67X10^{-11}}\]

M_e= 6x10²⁴ kg

Thus, mass of the Earth is 6 x 10²⁴ kg.

 

5.11     Can you determine the mass of our moon? If yes, then what you need to know?

Ans: Yes, we can determine the mass of the moon by the following formula

\[M_{m}= \frac{R^{2}g}{G}\]

         Above equation shows that we need to know the following quantities

                        i.          Gravitational acceleration on the surface of the moon i.e. g

                      ii.          Radius of the moon i.e. R.

                    iii.          Gravitational constant G. 

5.12   Why does the value of g vary from place to place?

Ans: The value of gravitational acceleration ‘g’ at any place depends upon its distance from the centre of earth. As different places have different distances from the centre of earth there for the value of ‘g’ have different values at these places.

                                                                        OR

Ans: The value of gravitational acceleration ‘g’ at any place depends upon its distance from the centre of earth. As distance from the centre of earth varies from place to place therefor the value of g varies from place to place.

5.13     Explain how the value of g varies with altitude.

Ans: Altitude is the height of an object or place above sea level. It is denoted by ‘h’. The value of g varies with altitude by the relation

\[g = G\frac{M_{e}}{(R+h)^{2}}\]

            This equation shows that value of g decrease with the increase in altitude.

            Example

     At a height equal to one earth radius above the surface of earth i.e. (h=R), value of g    becomes one fourth of its value on the surface of earth.

5.14     What are artificial satellites?

Ans:  An object that revolves around a planet is called a satellite. The moon revolves around the Earth so moon isa natural satellite of the Earth.

Scientists have sent many objects into space. Some of these objects revolve around
the Earth. These are called artificial satellites. 

5.15     How Newton's law of gravitation helps in understanding the motion of satellites?

Ans   A gravitational force of attraction exists between the Earth and the satellite. This force provides the required centripetal force to the satellite to revolve around the Earth. In this way law of gravitation is very important to understand the motion of satellite.

5.16     On what factors the orbital speed of a satellite depends?

Ans:  The speed of satellite is given by the relation

\[v_{o} = \sqrt{g_{h}(R+h)}\]

          This equation shows that the speed of satellite depends upon the

·         The gravitational acceleration i.e., g_h

·         The distance of the satellite from the centre of earth i.e. (R+h) 

5.17     Why communication satellites are stationed at geostationary orbits?

Ans:  Communication satellites and weather satellites are often given geostationary orbits, so that the satellite antennas that communicate with them do not have to move to track them but can be pointed permanently at the position in the sky where they stay. A geostationary orbit is a particular type of geosynchronous orbit.

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