The dimensions of angular momentum, latent heat and capacitance are, respectively.
1
2
3
4
Official Solution
Correct Option:
(4)
Angular momentum Latent heat Capacitance
02
PYQ 2018
medium
physicsID: jee-main
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be
determined from a suitable combination of the fundamental physical constants and . Which of the following correctly gives the Planck length ?
1
2
3
4
Official Solution
Correct Option:
(4)
Given Planck length can be determined from suitable combination of and . Therefore,
Equating the exponents, we have
Therefore,
03
PYQ 2019
hard
physicsID: jee-main
If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be : -
1
2
3
4
Official Solution
Correct Option:
(2)
where is dimensionless constant
Hence, Correct answer is option (B) : .
04
PYQ 2020
easy
physicsID: jee-main
The dimension of stopping potential in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :
1
2
3
4
Official Solution
Correct Option:
(2)
05
PYQ 2021
medium
physicsID: jee-main
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity has dimensions of:
1
2
3
4
Official Solution
Correct Option:
(3)
The given quantity is . We can determine the dimensions by analyzing the components of the expression. First, consider the electrostatic force between two charges separated by a distance : . From this, the dimensions of the numerator part can be found: . The dimensions of force are and dimensions of distance squared are . So, . Next, consider the energy of a photon, . From this, the dimensions of the denominator part can be found: . The dimensions of energy are and dimensions of wavelength are . So, . Finally, the dimensions of the entire quantity are the ratio of the dimensions of the two parts: . Therefore, the quantity is dimensionless.
06
PYQ 2022
medium
physicsID: jee-main
Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as and respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :
1
and
2
and
3
and
4
and
Official Solution
Correct Option:
(1)
To find the relation for distance and time between two different systems of units, we will use the given relationships for velocity and acceleration between the two systems.
The relationship for velocity between the two systems is given by:
The relationship for acceleration between the two systems is given by:
We know that velocity is the rate of change of distance with respect to time . Thus, we can write:
Similarly, acceleration is the rate of change of velocity with respect to time . So:
For the system of units 1 and 2, the formulas for length and time can be derived by connecting the given equations for velocity and acceleration.
Equate the expressions of acceleration from both systems using the relation :
Similarly, equate the expressions of velocity:
Solving these two equations, we get:
and
Which simplifies to:
and
Thus, the correct relation for distance and time in the two systems is:
and
This matches the given correct option.
07
PYQ 2022
medium
physicsID: jee-main
Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Time period of oscillation of a liquid drop depends on surf ace tension (S), if density of the liquid is ρ and radius of the drop is r, then is dimensionally correct, where K is dimensionless. Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below.
1
Both (A) and (R) are true and (R) is the correct explanation of (A)
2
Both (A) and (R) are true but (R) is not the correct explanation of (A)
3
(A) is true but (R) is false
4
(A) is false but (R) is true
Official Solution
Correct Option:
(4)
As the equation for first statement is wrong dimensionally. ⇒A is false and R is true.
So, the correct option is (D): (A) is false but (R) is true.
08
PYQ 2022
medium
physicsID: jee-main
Identify the pair of physical quantities which have different dimensions.
1
Wave number and Rydberg’s constant
2
Stress and Coefficient of elasticity
3
Coercivity and Magnetisation
4
Specific heat capacity and Latent heat
Official Solution
Correct Option:
(4)
[S]= ×[ΔT] and, L= ⇒ They have different dimensions The correct option is (D): Specific heat capacity and Latent heat
09
PYQ 2022
easy
physicsID: jee-main
An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 102 Hz
Official Solution
Correct Option:
(1)
The correct answer is 5
Therefore , the frequency of ac source will be 5 × 102 Hz
10
PYQ 2023
hard
physicsID: jee-main
If , and represent resistance, inductive reactance and capacitive reactance Then which of the following is dimensionless :
1
2
3
4
Official Solution
Correct Option:
(2)
All three quantities, , , and , have the same dimension, which is ohms ( ). This implies that is dimensionless.
In electrical circuits, represents resistance, is the inductive reactance, and is the capacitive reactance. These are the three primary components that determine the impedance in an AC circuit. The relationship between these quantities is crucial for understanding the behavior of series RLC circuits.
The formula appears when analyzing the resonant behavior of series RLC circuits. At resonance, the inductive reactance ( ) and the capacitive reactance ( ) cancel each other out, and the impedance is purely resistive. In such a case, the ratio of to the square root of the product of and becomes dimensionless, meaning the quantities involved in this ratio are directly proportional without any physical unit attached to the result.
This dimensionless ratio can be helpful in analyzing the quality factor (Q-factor) of the circuit, which is a measure of the sharpness of the resonance. The Q-factor is defined as the ratio of the energy stored in the system to the energy dissipated per cycle.
The dimensionless nature of the ratio simplifies calculations in circuit analysis and allows for easier comparison of different systems' resonant properties.
11
PYQ 2023
easy
physicsID: jee-main
If the velocity of light , universal gravitational constant and Planck's constant are chosen as fundamental quantities The dimensions of mass in the new system is :
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Express Mass in Terms of Fundamental Quantities
Let be the mass, and let its dimensions in terms of , , and be given by:
Step 2: Write the Dimensional Equation
The dimensions of (Planck’s constant) are . The dimensions of (speed of light) are . The dimensions of (gravitational constant) are . Substituting these dimensions into the equation from Step 1, we get:
Step 3: Equate the Exponents
Equating the exponents of , , and on both sides, we get the following system of equations:
Step 4: Solve the System of Equations
Adding the second and third equations, we get:
Also, from the first equation, . Adding these two equations gives , so . Since , we have . Substituting and into the third equation gives:
Thus, , , and .
Step 5: Write the Dimensions of Mass
Therefore, the dimensions of mass in the new system are:
Conclusion:
The correct answer is option (3).
12
PYQ 2024
medium
physicsID: jee-main
The dimensional formula of latent heat is:
1
2
3
4
Official Solution
Correct Option:
(3)
To determine the dimensional formula for latent heat, we need to understand what latent heat refers to. Latent heat is the heat absorbed or released by a substance during a phase change (such as melting or boiling) without a change in temperature. It is usually expressed in energy per unit mass.
The formula for latent heat (L) is: where is the total heat absorbed or released, and is the mass.
The dimensional formula for heat energy is: . Mass has the dimensional formula .
Since , the dimensional formula of latent heat will be calculated as:
After simplifying, we get:
Therefore, the correct dimensional formula for latent heat is: .
13
PYQ 2024
medium
physicsID: jee-main
If is the permittivity of free space and is the electric field, then has the dimensions:
1
2
3
4
Official Solution
Correct Option:
(2)
To determine the dimensions of , we need to understand the dimensions of each component:
The permittivity of free space, denoted by , has dimensions of . This is derived from the relation for Coulomb's law, or by using the formula for capacitance , where A is area and d is the distance.
The electric field has dimensions of . This arises from the definition , where F is the force with dimensions and is the charge with dimensions .
Now, let's calculate the dimensions of :
has the dimensions of .
Thus, has dimensions .
Performing dimensional multiplication, we have:
Mass:
Length:
Time:
Current:
Thus, the dimensions of are .
The correct answer is therefore: .
14
PYQ 2024
hard
physicsID: jee-main
The dimensions of angular impulse is equal to :
1
2
3
4
Official Solution
Correct Option:
(1)
The correct option is (A): .
15
PYQ 2024
medium
physicsID: jee-main
What is the dimensional formula of in the equation where letters have their usual meaning.
1
2
3
4
Official Solution
Correct Option:
(2)
Given:
where: - is pressure, - is volume, - is the universal gas constant, - is temperature.
Step 1: Dimensions of the Given Quantities - , so the dimension of is:
- The dimensional formula for pressure is:
Step 2: Dimension of From the term having the same dimension as pressure :
Thus, the dimensional formula of is:
Step 3: Calculating the Dimensional Formula of The dimensional formula of is . Therefore, the dimensional formula of is:
Therefore, the correct dimensional formula of is .
16
PYQ 2024
medium
physicsID: jee-main
If G be the gravitational constant and u be thee nergy density then which of the following quantity have the dimension as that the
1
Pressure gradient per unit mass
2
Force per unit mass
3
Gravitational potential
4
Energy per unit mass
Official Solution
Correct Option:
(2)
Dimensional analysis:
This corresponds to the dimensions of force per unit mass. Therefore, Option (2) is correct.
17
PYQ 2024
medium
physicsID: jee-main
The dimensional formula of angular impulse is :
1
[M L–2 T–1]
2
[M L2 T–2]
3
[M L T–1]
4
[M L2 T-1]
Official Solution
Correct Option:
(4)
We need to find the dimensional formula of angular impulse.
Concept Used:
Angular impulse is defined as the product of torque and time. Torque is the rotational analogue of force, given by . The dimensional formula can be derived from this relationship.
Step-by-Step Solution:
Step 1: Write the definition of angular impulse.
Step 2: Find the dimensional formula of torque.
Torque ( ) = Force × Perpendicular Distance
The dimensional formula of force is , and distance is .
Step 3: Find the dimensional formula of time.
Step 4: Combine the dimensions to get the dimensional formula for angular impulse.
Thus, the dimensional formula of angular impulse is [M L² T⁻¹].
18
PYQ 2025
hard
physicsID: jee-main
The pair of physical quantities not having the same dimensions is:
1
Torque and energy
2
Pressure and Young’s modulus
3
Angular momentum and Planck’s constant
4
Surface tension and impulse
Official Solution
Correct Option:
(1)
- Torque has the dimension , and energy also has the dimension , so they have the same dimension.
- Pressure has the dimension , and Young’s modulus has the same dimension .
- Angular momentum has the dimension , and Planck’s constant also has the dimension .
- Surface tension has the dimension , while impulse has the dimension , so they do not have the same dimensions.
19
PYQ 2025
easy
physicsID: jee-main
Match List - I with List - II. Choose the correct answer from the options given below:
1
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
2
(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
3
(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
4
(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
Official Solution
Correct Option:
(4)
Angular Impulse =
Latent Heat =
Electrical Resistivity =
Electromotive Force =
20
PYQ 2025
medium
physicsID: jee-main
Given a charge , current and permeability of vacuum . Which of the following quantity has the dimension of momentum?
1
2
3
4
Official Solution
Correct Option:
(2)
We are given:
Now, we need to find the dimensions of the product . The dimension of is calculated as follows: This simplifies to: Now, we check the dimensions of momentum: We find that the dimensions of are the same as that of momentum. Therefore, the correct answer is:
21
PYQ 2025
hard
physicsID: jee-main
Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.
1
2
3
4
Official Solution
Correct Option:
(1)
The capacitance is defined by the relationship: where is the charge and is the potential difference. The units for are coulombs , and the units for potential are derived from the formula , where (Joules) is energy. The units of energy are , so: Thus, the dimensional formula for capacitance is: Thus, the correct answer is .
22
PYQ 2025
medium
physicsID: jee-main
The equation for real gas is given by , where , , , and are the pressure, volume, temperature and gas constant, respectively. The dimension of is equivalent to that of:
1
Planck's constant
2
Compressibility
3
Strain
4
Energy density
Official Solution
Correct Option:
(2)
From the given equation , we have the following dimensions for each variable: Now, . Thus, the dimensions of correspond to the dimension of compressibility.
23
PYQ 2025
medium
physicsID: jee-main
What is the dimensional formula of (where is permeability and is permittivity of free space)?
1
2
3
4
Official Solution
Correct Option:
(4)
The expression involves the permeability of free space and the permittivity of free space . - The dimensional formula for is , where represents electric current.
- The dimensional formula for is . Now, for , the dimensional formula becomes:
This simplifies to the dimensional formula of as , hence the correct answer is option (4).
24
PYQ 2025
medium
physicsID: jee-main
Match List-I with List-II.
1
(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
2
(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
3
(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
4
(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
Official Solution
Correct Option:
(4)
To match the items from List-I with those in List-II, let's identify the dimensional formulas for each physical quantity.
Permeability of free space (A): The dimensional formula is . Thus, (A) matches with (III).
Magnetic field (B): The dimensional formula is . Thus, (B) matches with (II).
Magnetic moment (C): The dimensional formula is . Thus, (C) matches with (IV).
Torsional constant (D): The dimensional formula is . Thus, (D) matches with (I).
Hence, the correct matching is:
(A)-(III), (B)-(II), (C)-(IV), (D)-(I).
The correct answer is: (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
25
PYQ 2025
medium
physicsID: jee-main
Acceleration due to gravity on the surface of earth is . If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________________ g.
Official Solution
Correct Option:
(1)
The acceleration due to gravity on the surface of the Earth is given by the formula: where: - is the gravitational constant, - is the mass of the Earth, - is the radius of the Earth. If the diameter is reduced to one third of its original value, the new radius becomes: Since mass remains unchanged, the new acceleration due to gravity is: Thus, the acceleration due to gravity increases by a factor of 9. Final Answer: .
26
PYQ 2025
hard
physicsID: jee-main
Match List-I with List-II.
List-I (A) Coefficient of viscosity (B) Intensity of wave (C) Pressure gradient (D) Compressibility
List-II (I) [ML-1T-1] (II) [MT-3] (III) [ML-2T-2] (IV) [M-1LT2]
1
(A)–(I), (B)–(IV), (C)–(III), (D)–(I)
2
(A)–(I), (B)–(II), (C)–(III), (D)–(IV)
3
(A)–(IV), (B)–(II), (C)–(III), (D)–(I)
4
(A)–(IV), (B)–(I), (C)–(II), (D)–(III)
Official Solution
Correct Option:
(2)
The problem requires us to find the dimensional formulas for the physical quantities in List-I and match them with the correct dimensions provided in List-II.
Concept Used:
Dimensional analysis involves expressing physical quantities in terms of fundamental dimensions: Mass (M), Length (L), and Time (T). To find the dimension of a quantity, we use its definition or a formula relating it to other quantities with known dimensions.
Key dimensional formulas used in derivations:
Force
Area
Pressure
Energy/Work
Power
Step-by-Step Solution:
Step 1: (A) Coefficient of viscosity ( )
According to Newton's law of viscosity, the viscous force is given by . We can rearrange this to find the dimensions of .
This matches with (I) in List-II.
Step 2: (B) Intensity of wave (I)
The intensity of a wave is defined as the power transmitted per unit area.
This matches with (II) in List-II.
Step 3: (C) Pressure gradient
Pressure gradient is the rate of change of pressure with respect to distance.
This matches with (III) in List-II.
Step 4: (D) Compressibility (K)
Compressibility is the reciprocal of the Bulk Modulus (B). The Bulk Modulus has the same dimensions as pressure.
This matches with (IV) in List-II.
Final Result:
Based on the derivations, the correct matching is:
(A) Coefficient of viscosity → (I)
(B) Intensity of wave → (II)
(C) Pressure gradient → (III)
(D) Compressibility → (IV)
Therefore, the correct matching is (A)-(I), (B)-(II), (C)-(III), (D)-(IV).
27
PYQ 2025
medium
physicsID: jee-main
Match List-I with List-II. Choose the correct answer from the options given below :
1
(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
2
(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
3
(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
4
(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
Official Solution
Correct Option:
(3)
Let's match the physical quantities in List-I with their corresponding dimensions in List-II.
Mass density is defined as mass per unit volume. The dimension formula is: .
Impulse is defined as the change in momentum. Its dimension is the same as momentum, which is: .
Power is defined as work done per unit time. Its dimension is: .
Moment of inertia is represented as , hence its dimension is: .
Based on the above analysis, we can match them as:
(A) Mass density - (IV)
(B) Impulse - (II)
(C) Power - (I)
(D) Moment of inertia - (III)
Thus, the correct answer is (A)-(IV), (B)-(II), (C)-(I), (D)-(III).
28
PYQ 2025
medium
physicsID: jee-main
The expression given below shows the variation of velocity with time : The dimension of , , and is:
1
2
3
4
Official Solution
Correct Option:
(1)
- The dimension of is . - The dimension of should match the dimension of , i.e., . - For the numerator , dimensions of both terms must be consistent. - has dimensions of , as gives , which balances the dimension of velocity. - has dimensions of , as it has to balance the dimension of velocity when multiplied by . - The denominator has dimensions of , so must have dimensions . Thus, the dimension of , , and is .
29
PYQ 2025
medium
physicsID: jee-main
In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of . If , the value of is:
Official Solution
Correct Option:
(1)
Step 1: Dimensions of Modulus of Elasticity
Modulus of Elasticity (Young's Modulus) = Strain is dimensionless, so the dimension of Modulus of Elasticity = Dimension of Stress. Stress =
Step 2: Dimensions of Torque
Torque =
Step 3: Dimension of the Measured Quantity
The measured quantity is Modulus of Elasticity per unit Torque.
Step 4: Comparing with
Comparing the dimensions:
Step 5: Given
Since we need to compare it with , we take the magnitude of the value . Therefore, the value of is:
30
PYQ 2025
hard
physicsID: jee-main
Match List-I with List-II. Choose the correct answer from the options given below:
1
(A)-(I), (B)-(III), (C)-(I), (D)-(II)
2
(A)-(II), (B)-(IV), (C)-(II), (D)-(III)
3
(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
4
(A)-(I), (B)-(II), (C)-(I), (D)-(IV)
Official Solution
Correct Option:
(4)
(A) Young's Modulus: Young's modulus is the ratio of stress to strain. Its SI unit is , which corresponds to (I).
(B) Torque: Torque is the product of force and distance. The SI unit of force is , and the unit of distance is , so the SI unit of torque is , which corresponds to (II).
(C) Coefficient of Viscosity: The coefficient of viscosity is the ratio of force per unit area to the rate of change of velocity. Its unit is , which corresponds to (I).
(D) Gravitational Constant: The gravitational constant has the unit , which corresponds to (IV). Thus, the correct answer is option (4).
31
PYQ 2025
medium
physicsID: jee-main
The dimensions of a physical quantity are similar to:
1
Electric current
2
Electric field
3
Electric flux
4
Electric charge
Official Solution
Correct Option:
(1)
We are asked to find the dimensions of the quantity . Here, is the permittivity of free space, and is the electric flux. - The dimensions of are given by: - The dimensions of electric flux are: Now, we calculate the dimensions of :
- The dimensions of are: Thus, the dimensions of are:
This corresponds to the dimension of electric current. Therefore, the correct answer is (1) Electric current.
32
PYQ 2025
medium
physicsID: jee-main
The dimensions of a physical quantity are similar to [Symbols have their usual meanings]
1
Electric charge
2
Electric current
3
Electric flux
4
Electric field
Official Solution
Correct Option:
(2)
We are given the quantity , and we need to find its dimensions. - is the permittivity of free space. Its dimensions are: - is the electric flux. The electric flux is given by , where is the electric field and is the area. The dimensions of are: And the dimensions of area are: Thus, the dimensions of electric flux are: Now, we calculate the dimensions of :
- The dimensions of are: Thus, the dimensions of are:
This is the dimension of electric current, as electric current has the dimension of . Therefore, the correct answer is (B) Electric current.
33
PYQ 2025
medium
physicsID: jee-main
In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of . If , the value of is:
Official Solution
Correct Option:
(1)
The modulus of elasticity has dimensions , and torque has dimensions . Step 1: The modulus of elasticity per unit torque has dimensions:
Step 2: Now we compare this with the given dimension and find that , , and . Final Conclusion:
The value of is 2, which corresponds to Option (3).
34
PYQ 2025
medium
physicsID: jee-main
Match List - I with List - II.
List - I
List - II
(A) Latent Heat
(I)
(B) Electromotive Force
(II)
(C) Electrical Resistivity
(III)
(D) Angular Impulse
(IV)
Choose the correct answer from the options given below:
Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.
1
2
3
4
Official Solution
Correct Option:
(1)
The capacitance is defined by the relationship: where is the charge and is the potential difference. The units for are coulombs , and the units for potential are derived from the formula , where (Joules) is energy. The units of energy are , so: Thus, the dimensional formula for capacitance is: Thus, the correct answer is .
36
PYQ 2025
medium
physicsID: jee-main
The coordinates of a particle with respect to origin in a given reference frame is meters. If a force of acts on the particle, then the magnitude of torque (with respect to origin) in -direction is:
Official Solution
Correct Option:
(1)
The torque is given by the cross product of position vector and the force :
where and . The torque in the -direction is the -component of the cross product:
Using the determinant formula for the cross product, we get:
After solving, we find:
Thus, the correct answer is .
37
PYQ 2025
medium
physicsID: jee-main
Acceleration due to gravity on the surface of earth is . If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \_\_\_\_ g.
Official Solution
Correct Option:
(1)
The acceleration due to gravity on the surface of the Earth is given by the formula:
where:
- is the gravitational constant,
- is the mass of the Earth,
- is the radius of the Earth. If the diameter is reduced to one third of its original value, the new radius becomes:
Since mass remains unchanged, the new acceleration due to gravity is:
Thus, the acceleration due to gravity increases by a factor of 9. Final Answer: .
38
PYQ 2026
hard
physicsID: jee-main
The dimensional formula of ( = permittivity of vacuum and = electric field) is . The value of is:
1
2
3
4
Official Solution
Correct Option:
(1)
Concept: The quantity represents energy density of an electric field. Energy density = energy per unit volume. Step 1:Dimension of energy density} Energy dimension: Volume dimension: Thus Step 2:Identify powers} Step 3:Compute required value} However the dimensional balance with the given expression simplifies to
39
PYQ 2026
medium
physicsID: jee-main
Match List-I with List-II.
Choose the correct answer.
1
A-I, B-II, C-III, D-IV
2
A-IV, B-III, C-II, D-I
3
A-III, B-IV, C-II, D-I
4
A-II, B-I, C-IV, D-III
Official Solution
Correct Option:
(3)
Concept:
Dimensional formulas of important physical constants:
Boltzmann constant : relates energy with temperature.
Thus
Stefan–Boltzmann constant : from Stefan’s law
Planck's constant :
Gravitational constant : From Newton’s law Thus
Step 1: {Match the constants.} Hence the correct match is:
40
PYQ 2026
medium
physicsID: jee-main
Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are:
1
2
3
4
Official Solution
Correct Option:
(2)
We are asked to find the dimensional formula for the universal gravitational constant . According to Newton's law of gravitation:
The dimensions of force ( ) are , and the dimensions of mass are , and distance is . Rearranging for , we get:
Substituting the dimensions:
Simplifying, we get the dimensional formula of :
Now, relating this to Planck's constant , whose dimensions are , we can express in terms of . By equating the dimensions, we get the answer . Final Answer: (B)
41
PYQ 2026
medium
physicsID: jee-main
Match List - I with List - II (where h is Planck's constant, G is gravitational constant and c is speed of light):
1
A
2
B
3
C
4
D
Official Solution
Correct Option:
(3)
Step 1: Understanding the Concept: We use dimensional analysis to match units to their expressions in terms of fundamental constants . Step 2: Detailed Explanation: Let . Dimensions: . For Length: . . . . So . Expression: . (Matches A-I). Similarly for Time: . (Matches B-II). For Mass: . (Matches C-III). Step 3: Final Answer: The correct matching is A-I, B-II, C-III.
42
PYQ 2026
hard
physicsID: jee-main
Find dimensions of if
where pressure, density, speed.
1
2
3
4
Official Solution
Correct Option:
(2)
Given equation:
where:
is pressure,
is density,
is speed,
and are quantities for which we need to find the dimensions of .
Step-by-Step Solution:
1. Dimensions of Pressure :
Pressure is force per unit area. The dimensions of force are , and area has dimensions . Therefore, the dimensions of pressure are:
2. Dimensions of :
Since the sum is equal to a constant, the dimensions of both terms must be the same. Therefore, the dimensions of must be .
Let’s assume the dimensions of and are and , respectively. Then, the dimensions of are:
For the dimensions to be consistent with , we must have:
(for mass),
(for length),
(for time).
3. Dimensions of :
From the above, we can solve for the dimensions of and . After solving, we find that:
Final Answer: The dimensions of are .
43
PYQ 2026
medium
physicsID: jee-main
List-I presents some physical quantities and List-II presents their dimensions. Match the two lists appropriately.
1
A (3); B (4); C (2); D (1)
2
A (3); B (1); C (4); D (2)
3
A (2); B (3); C (4); D (1)
4
A (4); B (3); C (1); D (2)
Official Solution
Correct Option:
(2)
Concept: Use basic dimensional formulas of common physical quantities.
Energy (or work)
Potential
Frequency
Planck's constant
Step 1: Work function . Work function is energy.
Step 2: Stopping potential .
Charge dimension
Step 3: Planck's constant .
Step 4: Frequency .
Thus,
44
PYQ 2026
medium
physicsID: jee-main
The potential energy of a particle changes with distance from a fixed origin as , where and are constant with appropriate dimensions. The dimensions of are
1
2
3
4
Official Solution
Correct Option:
(4)
This problem involves dimensional analysis and the principle of homogeneity. The principle of homogeneity states that the dimensions of each term in a physical equation must be identical. Step 1: Determine the dimensions of potential energy and distance . Potential energy has dimensions of work: . Distance has dimensions: . Step 2: Find the dimension of . In the expression , the denominator is . According to the principle of homogeneity, we can only add quantities with the same dimensions. Therefore, dimensions of must be the same as dimensions of . $ A [A] AB AB [M^1 L^{7/2} T^{-2}]$.
45
PYQ 2026
medium
physicsID: jee-main
and represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula corresponds to _________.
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Understanding the Question: We need to find which combination of circuit components matches the given dimensional formula. Step 2: Key Formula or Approach: Know the base dimensions:
(Time constant or period property)
Step 3: Detailed Explanation: Let's analyze option (A): . Dimensions of Resistance : From . Dimensions of : We know resonance frequency . So, . Now, dimensions of : . This matches the target formula exactly. Step 4: Final Answer: The formula corresponds to .
46
PYQ 2026
medium
physicsID: jee-main
Consider the equation , where = magnetic field, = electric field, = permittivity, = distance, = time. The values of and respectively are:
1
1, 1, 1, 1
2
-1, 1, 2, 1
3
1, -1, -2, 1
4
-1, -2, -2, 1
Official Solution
Correct Option:
(1)
Step 1: Understanding the Concept:
We use dimensional analysis to find the powers and . We equate the dimensions of the Left Hand Side (LHS) with the Right Hand Side (RHS). Step 2: Key Formula or Approach:
Dimensions:
- Magnetic field intensity ( ):
- Electric field ( ):
- Permittivity ( ):
- Distance ( ): , Time ( ): Step 3: Detailed Explanation:
Equating dimensions:
Comparing powers of :
Comparing powers of :
Substituting into the equation: .
Comparing powers of : .
Comparing powers of : . Step 4: Final Answer:
The values are .
47
PYQ 2026
easy
physicsID: jee-main
The dimension of is then value of
1
1
2
2
3
3
4
4
Official Solution
Correct Option:
(1)
Step 1: Identify the given expression. The expression is .
Step 2: Understand the physical meaning of the expression. In electromagnetism, the energy stored per unit volume in an electric field is known as the energy density. The formula for energy density is given by:
where is the permittivity of free space and is the electric field strength.
Step 3: Determine the dimensions of energy density. Energy density is defined as energy per unit volume.
The dimensions of energy are . The dimensions of volume are .
Step 4: Calculate the final dimensional formula.
Step 5: Compare with the given form . By comparing with , we get:
Step 6: Calculate the required value . Substituting the values of , , and :
Final Answer: The value is
1. Correct option is (1).
48
PYQ 2026
medium
physicsID: jee-main
Select the quantity with matching dimensions of .
1
2
3
4
Official Solution
Correct Option:
(3)
Concept: Use dimensional formulas of electrical quantities. Step 1: Compute Step 2: Evaluate option (3) Which corresponds to the required dimensional form among the given options. Thus correct quantity is
49
PYQ 2026
hard
physicsID: jee-main
For the circuit shown below, find the current across , .
1
2
3
4
Official Solution
Correct Option:
(2)
Concept: Each upper branch contains a source in series with a resistor. Using source transformation and parallel branch analysis, equivalent current between nodes and can be calculated. Step 1: Convert each source branch Each branch: Thus each becomes a current source with parallel . Step 2: Combine three identical branches Total current contribution: Equivalent resistance of three resistors in parallel: Step 3: Bottom branch resistance Bottom path has two resistors: Step 4: Current division Total resistance between nodes: Using current division for branch :
50
PYQ 2026
easy
physicsID: jee-main
If angular position of a particle is given by . Find angular acceleration at :
1
2
3
4
Official Solution
Correct Option:
(2)
Step 1: State the given expression for angular position. The angular position as a function of time is:
Step 2: Find the angular velocity ( ). Angular velocity is the rate of change of angular position with respect to time.
Step 3: Find the angular acceleration ( ). Angular acceleration is the rate of change of angular velocity with respect to time.
Step 4: Calculate angular acceleration at . Substitute into the equation for :
Final Answer: The angular acceleration is . Correct option is (2).
51
PYQ 2026
hard
physicsID: jee-main
Dimensions of (Universal gravitational constant) in terms of (Planck's constant), (mass), (time) and (length) will be:
1
2
3
4
Official Solution
Correct Option:
(3)
Concept: Dimensional formula of gravitational constant: Dimensional formula of Planck's constant: Step 1: Assume relation.} Step 2: Write dimensions of RHS.} Step 3: Compare with dimensions of .} Equating powers: Mass: Length: Time: Step 4: Solve equations.} From time equation: Choose Then Step 5: Substitute values.}
52
PYQ 2026
easy
physicsID: jee-main
Match the LIST-I with LIST-II Choose the correct answer from the options given below:
1
A-II, B-IV, C-I, D-III
2
A-I, B-IV, C-II, D-III
3
A-II, B-I, C-IV, D-III
4
A-III, B-II, C-IV, D-I
Official Solution
Correct Option:
(1)
Step 1: Identify dimensions of each physical quantity. Spring constant:
Thermal conductivity:
Boltzmann constant:
Inductive reactance:
Step 2: Match with LIST-II. Final Answer:
53
PYQ 2026
easy
physicsID: jee-main
A particle is moving such that its velocity vector at co-ordinate is . Find magnitude of acceleration at .
Official Solution
Correct Option:
(1)
Step 1: Write down the velocity components. , , .
Step 2: Find the acceleration components using the chain rule ( ).
Step 3: Calculate acceleration components at the point . , , .
Step 4: Calculate the magnitude of the acceleration vector . .
Final Answer: .
54
PYQ 2026
medium
physicsID: jee-main
Match the LIST-I with LIST-II: Choose the correct answer from the options given below:
1
A-III, B-IV, C-II, D-I
2
A-I, B-III, C-IV, D-II
3
A-IV, B-III, C-I, D-II
4
A-III, B-IV, C-I, D-II
Official Solution
Correct Option:
(4)
Step 1: Magnetic induction ( ). Magnetic induction is force per unit current per unit length. Its dimensional formula is: Hence, A III. Step 2: Magnetic flux ( ). Magnetic flux is given by . Hence, B IV. Step 3: Magnetic permeability ( ). From , Hence, C I. Step 4: Self inductance ( ). Self inductance is flux per unit current. Hence, D II. Step 5: Final conclusion. The correct matching is A-III, B-IV, C-I, D-II, corresponding to option (4).
55
PYQ 2026
medium
physicsID: jee-main
In Searl's experiment diameter of wire is measured with screw gauge of least count and its value is . Length of wire is with least count and elongation with least count . Weight suspended is then absolute error in Young's modulus is . Then is :
1
1.64
2
1.65
3
1.63
4
1.66
Official Solution
Correct Option:
(2)
Step 1: Write the formula for Young's modulus . .
Step 2: Calculate the value of . .
Step 3: Express the relative error in . .
Step 4: Substitute the given values of absolute errors (least counts) and measurements. , . , . , . .
Step 5: Calculate absolute error . . Comparing with , we find .
Final Answer: Option (2).
56
PYQ 2026
medium
physicsID: jee-main
A satellite is revolving around planet of mass in orbit of radius with time period is . Another satellite is revolving around planet of mass in orbit of radius , with time period . Find .
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: State the formula for the time period of a satellite. , which implies .
Step 2: Set up the ratio for and . .
Step 3: Substitute the given values. , . , . .
Final Answer: Option (3).
57
PYQ 2026
medium
physicsID: jee-main
If stress at from bottom is then find :
Official Solution
Correct Option:
(1)
Step 1: Identify forces at height from the bottom. The total force (tension) at any point is the sum of the load at the bottom ( ) and the weight of the portion of the rod below that point. Let be the weight of the total length . The weight of a section of length is .
Step 2: Write the expression for Stress. Stress = .
Step 3: Calculate Stress at . Substitute into the equation: Stress = .
Step 4: Compare with the given expression to find . The given expression is . Equating the second terms: .
Final Answer: .
58
PYQ 2026
medium
physicsID: jee-main
If and mass of object, then at :- (A) momentum = (B) force = (C) Angular momentum = (D) Torque =
1
A, B, C are correct
2
A, C, D are correct
3
A, C are correct
4
A, B, C, D are correct
Official Solution
Correct Option:
(4)
Step 1: Find velocity and acceleration by differentiating the position vector. Position: Velocity: Acceleration:
Step 2: Calculate values at .
Step 3: Evaluate statement (A) Momentum ( ). . (A is correct)
Step 4: Evaluate statement (B) Force ( ). . (B is correct)
All statements are correct. Final Answer: Option (4).
About Dimensional Analysis - JEE-MAIN
Dimensional Analysis is a vital chapter for JEE-MAIN aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Dimensional Analysis PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Dimensional Analysis carry the most weight. Then, tackle the questions iteratively to solidify your understanding.
