Textbook Solutions: Gravitation

 Page 1


Gravitation 
Exercise 
Q. 1. Study the entries in the following table and rewrite them putting the 
connected items in a single row. 
 
 
Answer : 
 
 
 
Page 2


Gravitation 
Exercise 
Q. 1. Study the entries in the following table and rewrite them putting the 
connected items in a single row. 
 
 
Answer : 
 
 
 
 
Q. 2. A. Answer the following question. 
 
What is the difference between mass and weight of an object. Will the mass and 
weight of an object on the earth be same as their values on Mars? Why? 
Answer : Following are the difference between the weight and mass of an object. 
 
i. Since mass is the amount of the matter present in the body, and amount of matter (ex: 
bones, blood, skin etc) is same everywhere. Therefore the mass of the object on earth 
will be same as that on mars. 
 
ii. Whereas the weight of an object on Earth and Mars will be different as accelearation 
due to gravity (g) is different for Earth and Mars and we know that Weight= Mass × g 
Q. 2. B. Answer the following question. 
 
What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) 
centripetal force? 
Page 3


Gravitation 
Exercise 
Q. 1. Study the entries in the following table and rewrite them putting the 
connected items in a single row. 
 
 
Answer : 
 
 
 
 
Q. 2. A. Answer the following question. 
 
What is the difference between mass and weight of an object. Will the mass and 
weight of an object on the earth be same as their values on Mars? Why? 
Answer : Following are the difference between the weight and mass of an object. 
 
i. Since mass is the amount of the matter present in the body, and amount of matter (ex: 
bones, blood, skin etc) is same everywhere. Therefore the mass of the object on earth 
will be same as that on mars. 
 
ii. Whereas the weight of an object on Earth and Mars will be different as accelearation 
due to gravity (g) is different for Earth and Mars and we know that Weight= Mass × g 
Q. 2. B. Answer the following question. 
 
What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) 
centripetal force? 
Answer : (i) Free Fall: Whenever an object moves under the influence of the force of 
gravity alone, it is said to be in Free Fall. During free fall initial velocity of object is 
zero and force of air also acts on an object. Thus real free fall is possible only in 
vacuum because there is no air. 
 
For Example: 
a) When an object is dropped from the top of the table it falls down only due to 
gravitational force hence it is under free fall. 
b) An apple falling from the tree. 
But when we are standing on the ground, flying in a flight we are not in free fall because 
other forces except gravitational force are also acting. 
(ii) Acceleration due to gravity: The acceleration which is gained by an object 
because of the gravitational force is called acceleration due to gravity. Its S.I unit is 
m/s
2
. It is denoted by ‘g’ and its value at surface of earth is 9.8m/s
2
. 
It is a vector quantity (have both magnitude and direction) and it is directed towards the 
center of the earth. The value of acceleration due to gravity is not fixed it changes from 
place to place Like at moon ‘g’ value is one-sixth of value on earth. 
(iii) Escape velocity: The minimum value of initial velocity at which an object to escape 
from the gravitational pull/force of the earth and never comes back to the earth is called 
as the escape velocity. 
The escape velocity from earth is about 11.186 km/s, means if an object travels 11.186 
km in 1 sec it will escape from earth’s gravitational pull. All the satellites and rockets are 
launched with velocity equal to escape velocity in order to escape from the earth’s 
gravity. 
(iv) Centripetal force: The force that acts on an object to keep it moving along the 
circular path with constant speed is called as the centripetal force. 
It is given by Fc =  
It is directed towards the center of the circle (of radius ‘r’) in which the object is moving 
(with velocity ‘v’). 
Example: The stone tied to a piece of string whirl in circle due to centripetal force only. 
Page 4


Gravitation 
Exercise 
Q. 1. Study the entries in the following table and rewrite them putting the 
connected items in a single row. 
 
 
Answer : 
 
 
 
 
Q. 2. A. Answer the following question. 
 
What is the difference between mass and weight of an object. Will the mass and 
weight of an object on the earth be same as their values on Mars? Why? 
Answer : Following are the difference between the weight and mass of an object. 
 
i. Since mass is the amount of the matter present in the body, and amount of matter (ex: 
bones, blood, skin etc) is same everywhere. Therefore the mass of the object on earth 
will be same as that on mars. 
 
ii. Whereas the weight of an object on Earth and Mars will be different as accelearation 
due to gravity (g) is different for Earth and Mars and we know that Weight= Mass × g 
Q. 2. B. Answer the following question. 
 
What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) 
centripetal force? 
Answer : (i) Free Fall: Whenever an object moves under the influence of the force of 
gravity alone, it is said to be in Free Fall. During free fall initial velocity of object is 
zero and force of air also acts on an object. Thus real free fall is possible only in 
vacuum because there is no air. 
 
For Example: 
a) When an object is dropped from the top of the table it falls down only due to 
gravitational force hence it is under free fall. 
b) An apple falling from the tree. 
But when we are standing on the ground, flying in a flight we are not in free fall because 
other forces except gravitational force are also acting. 
(ii) Acceleration due to gravity: The acceleration which is gained by an object 
because of the gravitational force is called acceleration due to gravity. Its S.I unit is 
m/s
2
. It is denoted by ‘g’ and its value at surface of earth is 9.8m/s
2
. 
It is a vector quantity (have both magnitude and direction) and it is directed towards the 
center of the earth. The value of acceleration due to gravity is not fixed it changes from 
place to place Like at moon ‘g’ value is one-sixth of value on earth. 
(iii) Escape velocity: The minimum value of initial velocity at which an object to escape 
from the gravitational pull/force of the earth and never comes back to the earth is called 
as the escape velocity. 
The escape velocity from earth is about 11.186 km/s, means if an object travels 11.186 
km in 1 sec it will escape from earth’s gravitational pull. All the satellites and rockets are 
launched with velocity equal to escape velocity in order to escape from the earth’s 
gravity. 
(iv) Centripetal force: The force that acts on an object to keep it moving along the 
circular path with constant speed is called as the centripetal force. 
It is given by Fc =  
It is directed towards the center of the circle (of radius ‘r’) in which the object is moving 
(with velocity ‘v’). 
Example: The stone tied to a piece of string whirl in circle due to centripetal force only. 
The diagram below illustrates the centripetal force acting on an object towards the 
center. 
 
Q. 2. C. Answer the following question. 
 
Write the three laws given by Kepler. How did they help Newton to arrive at the 
inverse square law of gravity? 
Answer : Johannes Kepler studied about the planets motion and their positions and. He 
noticed that motion of the planets follows a certain law. He gave three laws describing 
the planetary motion. These are known as Kepler’s laws which are as follows: 
Kepler’s First law: The orbit of planet is an ellipse with sun at one of the foci. The 
figure below illustrates the elliptical orbit of earth with sun at its focus. 
 
Kepler’s Second law: The line joining the planet and the Sun sweeps equal areas in 
equal intervals of time. 
 
Page 5


Gravitation 
Exercise 
Q. 1. Study the entries in the following table and rewrite them putting the 
connected items in a single row. 
 
 
Answer : 
 
 
 
 
Q. 2. A. Answer the following question. 
 
What is the difference between mass and weight of an object. Will the mass and 
weight of an object on the earth be same as their values on Mars? Why? 
Answer : Following are the difference between the weight and mass of an object. 
 
i. Since mass is the amount of the matter present in the body, and amount of matter (ex: 
bones, blood, skin etc) is same everywhere. Therefore the mass of the object on earth 
will be same as that on mars. 
 
ii. Whereas the weight of an object on Earth and Mars will be different as accelearation 
due to gravity (g) is different for Earth and Mars and we know that Weight= Mass × g 
Q. 2. B. Answer the following question. 
 
What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) 
centripetal force? 
Answer : (i) Free Fall: Whenever an object moves under the influence of the force of 
gravity alone, it is said to be in Free Fall. During free fall initial velocity of object is 
zero and force of air also acts on an object. Thus real free fall is possible only in 
vacuum because there is no air. 
 
For Example: 
a) When an object is dropped from the top of the table it falls down only due to 
gravitational force hence it is under free fall. 
b) An apple falling from the tree. 
But when we are standing on the ground, flying in a flight we are not in free fall because 
other forces except gravitational force are also acting. 
(ii) Acceleration due to gravity: The acceleration which is gained by an object 
because of the gravitational force is called acceleration due to gravity. Its S.I unit is 
m/s
2
. It is denoted by ‘g’ and its value at surface of earth is 9.8m/s
2
. 
It is a vector quantity (have both magnitude and direction) and it is directed towards the 
center of the earth. The value of acceleration due to gravity is not fixed it changes from 
place to place Like at moon ‘g’ value is one-sixth of value on earth. 
(iii) Escape velocity: The minimum value of initial velocity at which an object to escape 
from the gravitational pull/force of the earth and never comes back to the earth is called 
as the escape velocity. 
The escape velocity from earth is about 11.186 km/s, means if an object travels 11.186 
km in 1 sec it will escape from earth’s gravitational pull. All the satellites and rockets are 
launched with velocity equal to escape velocity in order to escape from the earth’s 
gravity. 
(iv) Centripetal force: The force that acts on an object to keep it moving along the 
circular path with constant speed is called as the centripetal force. 
It is given by Fc =  
It is directed towards the center of the circle (of radius ‘r’) in which the object is moving 
(with velocity ‘v’). 
Example: The stone tied to a piece of string whirl in circle due to centripetal force only. 
The diagram below illustrates the centripetal force acting on an object towards the 
center. 
 
Q. 2. C. Answer the following question. 
 
Write the three laws given by Kepler. How did they help Newton to arrive at the 
inverse square law of gravity? 
Answer : Johannes Kepler studied about the planets motion and their positions and. He 
noticed that motion of the planets follows a certain law. He gave three laws describing 
the planetary motion. These are known as Kepler’s laws which are as follows: 
Kepler’s First law: The orbit of planet is an ellipse with sun at one of the foci. The 
figure below illustrates the elliptical orbit of earth with sun at its focus. 
 
Kepler’s Second law: The line joining the planet and the Sun sweeps equal areas in 
equal intervals of time. 
 
 
In the above figure A1 = A2 according to law. 
Kepler’s Third law: The Square of its period of revolution around the Sun is directly 
proportional to the cube of the mean distance of a planet from the Sun. 
If ‘r’ is the average distance of the planet from the sun and ‘T’ is the period of revolution 
then according to third law; 
 
 
Inverse Square law of gravity: We know that centripetal force F is given by ; 
F =  
Where v = velocity of the planet = 
Distance travelled in one revolution=2pr 
Where r = radius of the orbit. 
V =  
F =