Gravitation: JEE Main Previous Year Questions (2021-2026)

 Page 1


JEE Main Previous Year Questions (2021-2026): 
Gravitation  
 
(January 2026) 
 
Q1. Three masses 200 kg , 300 kg and 400 kg are placed at the vertices of an equilateral 
triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 
25 m and with the same centre. The work done in this process ____ J. (Gravitational 
constant G = 6.7 × 10 
-11
 N m
2
 / kg
2
)  
(a) 4.77 × 10 
-7
  
(b) 1.74 × 10 
-7
  
(c) 9.86 × 10 
-6
  
(d) 2.85 × 10 
-7
  
Ans: (b) 
Solution: 
The work done (W) by an external agent to rearrange a system of masses against gravitational 
force is equal to the change in the Gravitational Potential Energy (U) of the system. 
 
For a system of three masses m
1
, m
2
, m
3
 separated by distances r
12
, r
23
, r
31
, the total potential 
energy is the sum of the potential energies of all pairs : 
 
Page 2


JEE Main Previous Year Questions (2021-2026): 
Gravitation  
 
(January 2026) 
 
Q1. Three masses 200 kg , 300 kg and 400 kg are placed at the vertices of an equilateral 
triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 
25 m and with the same centre. The work done in this process ____ J. (Gravitational 
constant G = 6.7 × 10 
-11
 N m
2
 / kg
2
)  
(a) 4.77 × 10 
-7
  
(b) 1.74 × 10 
-7
  
(c) 9.86 × 10 
-6
  
(d) 2.85 × 10 
-7
  
Ans: (b) 
Solution: 
The work done (W) by an external agent to rearrange a system of masses against gravitational 
force is equal to the change in the Gravitational Potential Energy (U) of the system. 
 
For a system of three masses m
1
, m
2
, m
3
 separated by distances r
12
, r
23
, r
31
, the total potential 
energy is the sum of the potential energies of all pairs : 
 
 
Since the masses are at the vertices of an equilateral triangle, all distances are equal 
 
 
Given masses are, 
 
 
So, the work done by external agent is, 
 
The initial side is = L
i
 = 20 m 
The final side is L
f
 = 25 m 
Putting the values, 
Page 3


JEE Main Previous Year Questions (2021-2026): 
Gravitation  
 
(January 2026) 
 
Q1. Three masses 200 kg , 300 kg and 400 kg are placed at the vertices of an equilateral 
triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 
25 m and with the same centre. The work done in this process ____ J. (Gravitational 
constant G = 6.7 × 10 
-11
 N m
2
 / kg
2
)  
(a) 4.77 × 10 
-7
  
(b) 1.74 × 10 
-7
  
(c) 9.86 × 10 
-6
  
(d) 2.85 × 10 
-7
  
Ans: (b) 
Solution: 
The work done (W) by an external agent to rearrange a system of masses against gravitational 
force is equal to the change in the Gravitational Potential Energy (U) of the system. 
 
For a system of three masses m
1
, m
2
, m
3
 separated by distances r
12
, r
23
, r
31
, the total potential 
energy is the sum of the potential energies of all pairs : 
 
 
Since the masses are at the vertices of an equilateral triangle, all distances are equal 
 
 
Given masses are, 
 
 
So, the work done by external agent is, 
 
The initial side is = L
i
 = 20 m 
The final side is L
f
 = 25 m 
Putting the values, 
 
Therefore, the work done in this process is  
Hence, the correct option is (B). 
 
Q2: Given below are two statements : 
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The 
time period of revolution of satellite depends upon the density of earth. 
Statement II: The time period of revolution of the satellite is  (for 
satellite very close to the earth surface), where R
e
 radius of earth and g acceleration due to 
gravity.  
In the light of the above statements, choose the correct answer from the options given below : 
(a) Statement I is true but Statement II is false 
(b) Statement I is false but Statement II is true 
(c) Both Statement I and Statement II are true 
(d) Both Statement I and Statement II are false 
Ans: (c)  
Solution: 
For a satellite revolving in a circular orbit of radius r around the Earth (mass M), the time period 
(T) is given by Kepler's Third Law 
Page 4


JEE Main Previous Year Questions (2021-2026): 
Gravitation  
 
(January 2026) 
 
Q1. Three masses 200 kg , 300 kg and 400 kg are placed at the vertices of an equilateral 
triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 
25 m and with the same centre. The work done in this process ____ J. (Gravitational 
constant G = 6.7 × 10 
-11
 N m
2
 / kg
2
)  
(a) 4.77 × 10 
-7
  
(b) 1.74 × 10 
-7
  
(c) 9.86 × 10 
-6
  
(d) 2.85 × 10 
-7
  
Ans: (b) 
Solution: 
The work done (W) by an external agent to rearrange a system of masses against gravitational 
force is equal to the change in the Gravitational Potential Energy (U) of the system. 
 
For a system of three masses m
1
, m
2
, m
3
 separated by distances r
12
, r
23
, r
31
, the total potential 
energy is the sum of the potential energies of all pairs : 
 
 
Since the masses are at the vertices of an equilateral triangle, all distances are equal 
 
 
Given masses are, 
 
 
So, the work done by external agent is, 
 
The initial side is = L
i
 = 20 m 
The final side is L
f
 = 25 m 
Putting the values, 
 
Therefore, the work done in this process is  
Hence, the correct option is (B). 
 
Q2: Given below are two statements : 
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The 
time period of revolution of satellite depends upon the density of earth. 
Statement II: The time period of revolution of the satellite is  (for 
satellite very close to the earth surface), where R
e
 radius of earth and g acceleration due to 
gravity.  
In the light of the above statements, choose the correct answer from the options given below : 
(a) Statement I is true but Statement II is false 
(b) Statement I is false but Statement II is true 
(c) Both Statement I and Statement II are true 
(d) Both Statement I and Statement II are false 
Ans: (c)  
Solution: 
For a satellite revolving in a circular orbit of radius r around the Earth (mass M), the time period 
(T) is given by Kepler's Third Law 
 
For the equilibrium along the radial direction, 
 
So, the time period of the revolution is, 
 
where G is the universal gravitational constant and M
e
 is the mass of Earth.  
If the satellite is orbiting very close to the Earth's surface, its orbital radius r is approximately 
equal to the Earth's radius, R
e
. 
 
Assuming the Earth is a uniform sphere, its mass M is the product of its volume and density: 
Page 5


JEE Main Previous Year Questions (2021-2026): 
Gravitation  
 
(January 2026) 
 
Q1. Three masses 200 kg , 300 kg and 400 kg are placed at the vertices of an equilateral 
triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 
25 m and with the same centre. The work done in this process ____ J. (Gravitational 
constant G = 6.7 × 10 
-11
 N m
2
 / kg
2
)  
(a) 4.77 × 10 
-7
  
(b) 1.74 × 10 
-7
  
(c) 9.86 × 10 
-6
  
(d) 2.85 × 10 
-7
  
Ans: (b) 
Solution: 
The work done (W) by an external agent to rearrange a system of masses against gravitational 
force is equal to the change in the Gravitational Potential Energy (U) of the system. 
 
For a system of three masses m
1
, m
2
, m
3
 separated by distances r
12
, r
23
, r
31
, the total potential 
energy is the sum of the potential energies of all pairs : 
 
 
Since the masses are at the vertices of an equilateral triangle, all distances are equal 
 
 
Given masses are, 
 
 
So, the work done by external agent is, 
 
The initial side is = L
i
 = 20 m 
The final side is L
f
 = 25 m 
Putting the values, 
 
Therefore, the work done in this process is  
Hence, the correct option is (B). 
 
Q2: Given below are two statements : 
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The 
time period of revolution of satellite depends upon the density of earth. 
Statement II: The time period of revolution of the satellite is  (for 
satellite very close to the earth surface), where R
e
 radius of earth and g acceleration due to 
gravity.  
In the light of the above statements, choose the correct answer from the options given below : 
(a) Statement I is true but Statement II is false 
(b) Statement I is false but Statement II is true 
(c) Both Statement I and Statement II are true 
(d) Both Statement I and Statement II are false 
Ans: (c)  
Solution: 
For a satellite revolving in a circular orbit of radius r around the Earth (mass M), the time period 
(T) is given by Kepler's Third Law 
 
For the equilibrium along the radial direction, 
 
So, the time period of the revolution is, 
 
where G is the universal gravitational constant and M
e
 is the mass of Earth.  
If the satellite is orbiting very close to the Earth's surface, its orbital radius r is approximately 
equal to the Earth's radius, R
e
. 
 
Assuming the Earth is a uniform sphere, its mass M is the product of its volume and density: 
 
Substitute this mass into our time period equation : 
 
Since 3, p, and G are all constants, this equation proves that the time period of a satellite 
orbiting very close to the Earth's surface depends entirely on the density (?) of the Earth.  
Therefore, Statement I is true.  
We also know the formula for the acceleration due to gravity (g) on the surface of the Earth : 
 
Substitute this expression for GM
e
 into the time period equation 
 
Therefore, Statement II is also true. 
As both statement I and statement II are true, so the correct option is (C). 
 
Q3: The escape velocity from a spherical planet A is 10 km/ . The escape velocity from 
another planet B whose density and radius are 10 % of those of planet A , is _____ m/s.  
(a) 1000  
(b) 200v5