JEE Main Previous Year Questions (2025): Mechanical Properties of Solids | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Main Previous Year Questions 
(2025): Mechanical Properties of Solids 
 
Q1: The volume contraction of a solid copper cube of edge length ???? ???? , when subjected to 
a hydraulic pressure of ?? × ????
?? ???? , would be _ _ _ _ ????
?? . 
(Given bulk modulus of copper = ?? . ?? × ????
????
 ?? ?? - ?? ) 
JEE Main 2025 (Online) 28th January Evening Shift 
Ans: 50 
Solution: 
To find the volume contraction of the copper cube, we need to use the formula for volumetric strain 
under pressure, which involves the bulk modulus (K). The volumetric strain is given by the formula: 
Volumetric strain =
? ?? ?? = -
?? ?? 
Where: 
? ?? is the change in volume or volume contraction, 
?? is the original volume of the cube, 
?? is the hydraulic pressure applied, 
?? is the bulk modulus of the material. 
Given: 
Edge length of the cube, ?? = 10 cm = 0 . 1 m 
Hydraulic pressure, ?? = 7 × 10
6
 Pa 
Bulk modulus of copper, ?? = 1 . 4 × 10
11
 Pa 
Calculate the original volume ( ?? ) of the cube: 
?? = ?? 3
= ( 0 . 1 m )
3
= 0 . 001 m
3
 
Calculate the volumetric strain: 
Volumetric strain = -
?? ?? = -
7 × 10
6
1 . 4 × 10
11
= - 5 × 10
- 5
 
Calculate the volume contraction ( ? ?? ): 
? ?? = ?? × Volumetric strain = 0 . 001 m
3
× ( - 5 × 10
- 5
) = - 5 × 10
- 8
 m
3
 
Convert ?? ?? from cubic meters to cubic millimeters: 
1 cubic meter = 10
9
 cubic millimeters. Therefore, 
? ?? = - 5 × 10
- 8
 m
3
× 10
9
 mm
3
/ m
3
= - 50 mm
3
 
Thus, the volume contraction of the copper cube, when subjected to the given hydraulic pressure, is 
50 mm
3
. 
 
Q2: The increase in pressure required to decrease the volume of a water sample by ?? . ?? % is 
?? × ????
?? ????
- ?? . Bulk modulus of water is ?? . ???? × ????
?? ????
- ?? . The value of ?? is _ _ _ _ . 
JEE Main 2025 (Online) 24th January Evening Shift 
Page 2


JEE Main Previous Year Questions 
(2025): Mechanical Properties of Solids 
 
Q1: The volume contraction of a solid copper cube of edge length ???? ???? , when subjected to 
a hydraulic pressure of ?? × ????
?? ???? , would be _ _ _ _ ????
?? . 
(Given bulk modulus of copper = ?? . ?? × ????
????
 ?? ?? - ?? ) 
JEE Main 2025 (Online) 28th January Evening Shift 
Ans: 50 
Solution: 
To find the volume contraction of the copper cube, we need to use the formula for volumetric strain 
under pressure, which involves the bulk modulus (K). The volumetric strain is given by the formula: 
Volumetric strain =
? ?? ?? = -
?? ?? 
Where: 
? ?? is the change in volume or volume contraction, 
?? is the original volume of the cube, 
?? is the hydraulic pressure applied, 
?? is the bulk modulus of the material. 
Given: 
Edge length of the cube, ?? = 10 cm = 0 . 1 m 
Hydraulic pressure, ?? = 7 × 10
6
 Pa 
Bulk modulus of copper, ?? = 1 . 4 × 10
11
 Pa 
Calculate the original volume ( ?? ) of the cube: 
?? = ?? 3
= ( 0 . 1 m )
3
= 0 . 001 m
3
 
Calculate the volumetric strain: 
Volumetric strain = -
?? ?? = -
7 × 10
6
1 . 4 × 10
11
= - 5 × 10
- 5
 
Calculate the volume contraction ( ? ?? ): 
? ?? = ?? × Volumetric strain = 0 . 001 m
3
× ( - 5 × 10
- 5
) = - 5 × 10
- 8
 m
3
 
Convert ?? ?? from cubic meters to cubic millimeters: 
1 cubic meter = 10
9
 cubic millimeters. Therefore, 
? ?? = - 5 × 10
- 8
 m
3
× 10
9
 mm
3
/ m
3
= - 50 mm
3
 
Thus, the volume contraction of the copper cube, when subjected to the given hydraulic pressure, is 
50 mm
3
. 
 
Q2: The increase in pressure required to decrease the volume of a water sample by ?? . ?? % is 
?? × ????
?? ????
- ?? . Bulk modulus of water is ?? . ???? × ????
?? ????
- ?? . The value of ?? is _ _ _ _ . 
JEE Main 2025 (Online) 24th January Evening Shift 
Ans: 43 
Solution: 
The bulk modulus of a material is defined as: 
?? =
- ? ?? (
? ?? ?? )
 
Given: 
Bulk Modulus, ?? = 2 . 15 × 10
9
Nm
- 2
 
Change in volume percentage, 
? ?? ?? = 0 . 2% =
0 . 2
100
= 0 . 002 
To find the required increase in pressure, ? ?? , we rearrange the formula for the bulk modulus: 
?? =
- ? ?? - (
? ?? ?? )
 
Plug in the known values: 
2 . 15 × 10
9
=
? ?? 0 . 002
 
Solving for ? ?? : 
? ?? = 2 . 15 × 10
9
× 0 . 002 
? ?? = 4 . 3 × 10
6
Nm
- 2
 
Since the problem specifies ? ?? = ?? × 10
5
Nm
- 2
, we have: 
4 . 3 × 10
6
= ?? × 10
5
 
?? = 43 
The value of ?? is therefore 43 . 
 
Q3: The fractional compression (
?? ?? ?? ) of water at the depth of 2.5 km below the sea level is 
_ _ _ _ %. Given, the Bulk modulus of water = ?? × ????
?? ?? ?? - ?? , density of water = ????
?? ???? ?? - ?? , 
acceleration due to gravity ?? = ???? ?? ?? - ?? . 
JEE Main 2025 (Online) 29th January Morning Shift 
Options: 
A. 1.0 
B. 1.25 
C. 1.75 
D. 1.5 
Ans: B 
Solution: 
The fractional compression (
? ?? ?? ) of water at a depth of 2.5 km below sea level is calculated as follows: 
Given: 
Bulk modulus of water, ?? = 2 × 10
9
 N / m
2
 
Density of water, ?? = 10
3
 kg / m
3
 
Acceleration due to gravity, ?? = 10 m / s
2
 
Page 3


JEE Main Previous Year Questions 
(2025): Mechanical Properties of Solids 
 
Q1: The volume contraction of a solid copper cube of edge length ???? ???? , when subjected to 
a hydraulic pressure of ?? × ????
?? ???? , would be _ _ _ _ ????
?? . 
(Given bulk modulus of copper = ?? . ?? × ????
????
 ?? ?? - ?? ) 
JEE Main 2025 (Online) 28th January Evening Shift 
Ans: 50 
Solution: 
To find the volume contraction of the copper cube, we need to use the formula for volumetric strain 
under pressure, which involves the bulk modulus (K). The volumetric strain is given by the formula: 
Volumetric strain =
? ?? ?? = -
?? ?? 
Where: 
? ?? is the change in volume or volume contraction, 
?? is the original volume of the cube, 
?? is the hydraulic pressure applied, 
?? is the bulk modulus of the material. 
Given: 
Edge length of the cube, ?? = 10 cm = 0 . 1 m 
Hydraulic pressure, ?? = 7 × 10
6
 Pa 
Bulk modulus of copper, ?? = 1 . 4 × 10
11
 Pa 
Calculate the original volume ( ?? ) of the cube: 
?? = ?? 3
= ( 0 . 1 m )
3
= 0 . 001 m
3
 
Calculate the volumetric strain: 
Volumetric strain = -
?? ?? = -
7 × 10
6
1 . 4 × 10
11
= - 5 × 10
- 5
 
Calculate the volume contraction ( ? ?? ): 
? ?? = ?? × Volumetric strain = 0 . 001 m
3
× ( - 5 × 10
- 5
) = - 5 × 10
- 8
 m
3
 
Convert ?? ?? from cubic meters to cubic millimeters: 
1 cubic meter = 10
9
 cubic millimeters. Therefore, 
? ?? = - 5 × 10
- 8
 m
3
× 10
9
 mm
3
/ m
3
= - 50 mm
3
 
Thus, the volume contraction of the copper cube, when subjected to the given hydraulic pressure, is 
50 mm
3
. 
 
Q2: The increase in pressure required to decrease the volume of a water sample by ?? . ?? % is 
?? × ????
?? ????
- ?? . Bulk modulus of water is ?? . ???? × ????
?? ????
- ?? . The value of ?? is _ _ _ _ . 
JEE Main 2025 (Online) 24th January Evening Shift 
Ans: 43 
Solution: 
The bulk modulus of a material is defined as: 
?? =
- ? ?? (
? ?? ?? )
 
Given: 
Bulk Modulus, ?? = 2 . 15 × 10
9
Nm
- 2
 
Change in volume percentage, 
? ?? ?? = 0 . 2% =
0 . 2
100
= 0 . 002 
To find the required increase in pressure, ? ?? , we rearrange the formula for the bulk modulus: 
?? =
- ? ?? - (
? ?? ?? )
 
Plug in the known values: 
2 . 15 × 10
9
=
? ?? 0 . 002
 
Solving for ? ?? : 
? ?? = 2 . 15 × 10
9
× 0 . 002 
? ?? = 4 . 3 × 10
6
Nm
- 2
 
Since the problem specifies ? ?? = ?? × 10
5
Nm
- 2
, we have: 
4 . 3 × 10
6
= ?? × 10
5
 
?? = 43 
The value of ?? is therefore 43 . 
 
Q3: The fractional compression (
?? ?? ?? ) of water at the depth of 2.5 km below the sea level is 
_ _ _ _ %. Given, the Bulk modulus of water = ?? × ????
?? ?? ?? - ?? , density of water = ????
?? ???? ?? - ?? , 
acceleration due to gravity ?? = ???? ?? ?? - ?? . 
JEE Main 2025 (Online) 29th January Morning Shift 
Options: 
A. 1.0 
B. 1.25 
C. 1.75 
D. 1.5 
Ans: B 
Solution: 
The fractional compression (
? ?? ?? ) of water at a depth of 2.5 km below sea level is calculated as follows: 
Given: 
Bulk modulus of water, ?? = 2 × 10
9
 N / m
2
 
Density of water, ?? = 10
3
 kg / m
3
 
Acceleration due to gravity, ?? = 10 m / s
2
 
The relationship between pressure change and volume change using the bulk modulus is given by: 
?? =
???? h
(
? ?? ?? )
 
Rearranging the formula to solve for the fractional compression: 
? ?? ?? × 100 =
???? h
?? × 100 
Substituting in the given values: 
1000 × 10 × 2 . 5 × 10
3
2 × 10
9
× 100% 
Calculating the result gives: 
= 1 . 25% 
Thus, the fractional compression of water at this depth is 1 . 25%.