Dimensions PYQs: JEE Mains Physics

1. A ball of radius r and density \(\rho\) dropped through a viscous liquid of density \(\sigma\) and viscosity \(\eta\) attains its terminal velocity at time t , given by \(t = A \rho^{ a } r ^{ b } \eta^{ c } \sigma^{ d }\), where A is a constant and a , b c and d are integers. The value of \(\frac{b+c}{a+d}\) is ___________. 2026 Hard

2. Consider a modified Bernoulli equation.
\(\left( P +\frac{ A }{ Bt ^2}\right)+\rho g ( h + Bt )+\frac{1}{2} \rho V^2=\) constant
If \(t\) has the dimension of time then the dimensions of A and B are _________ , _________ respectively. 2026 Hard

3. Consider the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), where \(H=\) magnetic field; \(E=\) electric field, \(\epsilon=\) permittivity, \(x=\) distance, \(t=\) time. The values of \(p, q, r\) and \(s\) respectively are: 2026 Hard

4. Dimensions of universal gravitational constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are _______. 2026 Medium

5. \(L\), \(C\) and \(R\) represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula \(ML^2 T^{-4} A^{-2}\) corresponds to __________. 2026 Hard

6. Match List - I with List - II.

List - I	List - II
A. Boltzmann constant	I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant	II. \([ML^2T^{-1}]\)
C. Planck's constant	III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant	IV. \([ML^0T^{-3}K^{-4}]\)

Choose the correct answer from the options given below : 2026 Medium

7. Match List-I with List-II.

List-I	List-II
A. Meter (L)	I. \(\sqrt{\dfrac{hc}{G}}\)
B. Second (S)	II. \(\sqrt{\dfrac{Gh}{c^5}}\)
C. Kilogram (M)	III. \(\sqrt{\dfrac{K^2L^2c^3}{Gh}}\)
D. Kelvin (K)	IV. \(\sqrt{\dfrac{Gh}{c^3}}\)

where \(h\) (Planck's constant), \(G\) (gravitational constant) and \(c\) (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below : 2026 Hard

8. Match the LIST-I with LIST-II:

List-I	List-II
A. Spring constant	I. \(ML ^2 T^{-2} K^{-1}\)
B. Thermal conductivity	II. \(ML ^0 T^{-2}\)
C. Boltzmann constant	III. \(ML ^2 T^{-3} A^{-2}\)
D. Inductive reactance	IV. \(MLT ^{-3} K^{-1}\)

Choose the correct answer from the options given below: 2026 Easy

9. Match the LIST-I with LIST-II

List-I	List-II
A. Planck's constant	I. \(ML^2T^{-2}\)
B. Stopping potential	II. \(T^{-1}\)
C. Work function	III. \(ML^2T^{-1}\)
D. Threshold frequency	IV. \(ML^2T^{-3}A^{-1}\)

Choose the correct answer from the options given below: 2026 Medium

10. The potential energy of a particle changes with distance \(x\) from a fixed origin as \(V = \dfrac{A\sqrt{x}}{x + B}\), where \(A\) and \(B\) are constant with appropriate dimensions. The dimensions of \(AB\) are _______. 2026 Easy

11. Given a charge \(q\), current I and permeability of vacuum \(\mu_0\). Which of the following quantity has the dimension of momentum? 2025 Medium

12. If \(\mu_0\) and \(\varepsilon_0\) are the permeability and permittivity of free space, respectively, then the dimension of \(\left(\frac{1}{\mu_0 \varepsilon_0}\right)\) is : 2025 Easy

13. If \(\epsilon_0\) denotes the permittivity of free space and \(\Phi_{\mathrm{E}}\) is the flux of the electric field through the area bounded by the closed surface, then dimension of \(\left(\epsilon_0 \frac{\mathrm{~d} \phi_{\mathrm{E}}}{\mathrm{dt}}\right)\) are that of : 2025 Easy

14. If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is 2025 Easy

15. In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \(\left[M^a L^b T^c\right]\). If \(b=-3\), the value of \(c\) is ________ 2025 Medium

16. In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of \(\left[M^P L^{\circ} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\right]\). The value of P and Q are : 2025 Easy

17. In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of \(\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\), where value of ' Q ' and ' R ' are 2025 Medium

18. Match List - I with List - II.

List - I	List - II
(A) Permeability of free space	(I) \(\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
(B) Magnetic field	(II) \(\left[\mathrm{M} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)
(C) Magnetic moment	(III) \(\left[\mathrm{M} \mathrm{~L} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]\)
(D) Torsional constant	(IV) \(\left[\mathrm{L}^2 \mathrm{~A}\right]\)

Choose\(\text{ }\)the\(\text{ }\)correct\(\text{ }\)answer\(\text{ }\)from\(\text{ }\)the\(\text{ }\)options\(\text{ }\)given\(\text{ }\)below\(\text{ }\): 2025 Easy

19. Match List - I with List - II.

List - I	List - II
(A) Young’s Modulus	(I) \(M L^{-1} T^{-1}\)
(B) Torque	(II) \(M L^{-1} T^{-2}\)
(C) Coefficient of Viscosity	(III) \(M^{-1} L^3 T^{-2}\)
(D) Gravitational Constant	(IV) \(M L^2 T^{-2}\)

Choose the correct answer from the options given below : 2025 Medium

20. Match List - I with List - II.

List-I	List-II
(A) Angular Impulse	(I) \(\left[M^0 L^2 T^{-2}\right]\)
(B) Latent Heat	(II) \(\left[M L^2 T^{-3} A^{-1}\right]\)
(C) Electrical resistivity	(III) \(\left[M L^2 T^{-1}\right]\)
(D) Electromotive force	(IV) \(\left[M L^3 T^{-3} A^{-2}\right]\)

2025 Easy

21. Match List-I with List-II.

List-I	List-II
(A) Mass density	(I) [ML²T^-3]
(B) Impulse	(II) [MLT^-1]
(C) Power	(III) [ML²T⁰]
(D) Moment of inertia	(IV) [ML^-3T⁰]

Choose the correct answer from the options given below : 2025 Easy

22. Match List-I with List-II.

List-I (Physical Quantity)	List-II (Dimensional Formula)
(A) Coefficient of viscosity	(I) [ML⁰T^-3]
(B) Intensity of wave	(II) [ML^-2T^-2]
(C) Pressure gradient	(III) [M^-1LT²]
(D) Compressibility	(IV) [ML^-1T^-1]

Choose the correct answer from the options given below : 2025 Medium

23. Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
(B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
(C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

Choose the correct answer from the options given below : 2025 Medium

24. Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Gravitational constant	(I) \(\left[\mathrm{LT}^{-2}\right]\)
(B) Gravitational potential energy	(II) \(\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]\)
(C) Gravitational potential	(III) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
(D) Acceleration due to gravity	(IV) \(\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below : 2025 Medium

25. The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity) 2025 Medium

26. The electric flux is \(\phi=\alpha \sigma+\beta \lambda\) where \(\lambda\) and \(\sigma\) are linear and surface charge density, respectively. \(\left(\frac{\alpha}{\beta}\right)\) represents 2025 Easy

27. The equation for real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \(\mathrm{ab}^{-2}\) is equivalent to that of : 2025 Medium

28. The expression given below shows the variation of velocity \((v)\) with time (t), \(v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}\). The dimension of ABC is : 2025 Hard

29. The pair of physical quantities not having same dimensions is : 2025 Easy

30. The position of a particle moving on \(x\)-axis is given by \(x(t)=A \sin t+B \cos ^2 t+C t^2+D\), where \(t\) is time. The dimension of \(\frac{A B C}{D}\) is 2025 Easy

31. Which one of the following is the correct dimensional formula for the capacitance in F ? \(\mathrm{M}, \mathrm{L}, \mathrm{T}\) and C stand for unit of mass, length, time and charge, 2025 Easy

32. A force is represented by \(\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}\). Where \(\mathrm{x}=\) distance and \(\mathrm{t}=\) time. The dimensions of \(\mathrm{b}^2 / \mathrm{a}\) are _______. 2024 Hard

33. Applying the principle of homogeneity of dimensions, determine which one is correct. where \(\mathrm{T}\) is time period, \(\mathrm{G}\) is gravitational constant, \(M\) is mass, \(r\) is radius of orbit. 2024 Hard

34. Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______. 2024 Hard

35. Given below are two statements : Statement \((I)\) : dimensions of specific heat is \(\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) Statement \((II)\) : dimensions of gas constant is \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\) 2024 Hard

36. Given below are two statements : \(Statement\) \((I)\) : Planck's constant and angular momentum have same dimensions. \(Statement\) \((II)\) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below : 2024 Hard

37. If \(\varepsilon_0\) is the permittivity of free space and \(E\) is the electric field, then \(\varepsilon_0 E^2\) has the dimensions is _______. 2024 Medium

38. If \(\mathrm{G}\) be the gravitational constant and \(\mathrm{u}\) be the energy density then which of the following quantity have the dimension as that the \(\sqrt{\mathrm{uG}}\)? 2024 Hard

39. If mass is written as \(\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\) then the value of \(P\) will be _______. (Constants have their usual meaning with \(\mathrm{k}\) a dimensionless constant) 2024 Hard

40. Match List \(-I\) with List \(-II\).

	List \(-I\)		List \(-II\)
\(A\).	Coefficient of Viscosity	\(I\).	\([M L^2T^{–2}]\)
\(B\).	Surface Tension	\(II\).	\([M L^2T^{–1}]\)
\(C\).	Angular momentum	\(III\).	\([M L^{-1}T^{–1}]\)
\(D\).	Rotational Kimeatic energy	\(IV\).	\([M L^0T^{–2}]\)

2024 Hard

41. Match List \(I\) with List \(II\)

List - \(I\)	List - \(II\)
\((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below : 2024 Hard

42. The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \(\mathrm{h} / \sqrt{2 m E}\) The dimensional formula for Planck's constant is _______. 2024 Hard

43. The dimensional formula of angular impulse is _______. 2024 Hard

44. The dimensional formula of latent heat is _______. 2024 Hard

45. The equation of state of a real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}\) and \(\mathrm{T}\) are pressure. volume and temperature respectively and \(R\) is the universal gas constant. The dimensions of \(\frac{a}{b^2}\) is similar to that of : 2024 Hard

46. The equation of stationary wave is \(\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)\) Which of the following is NOT correct? 2024 Hard

47. What is the dimensional formula of \(a b^{-1}\) in the equation? \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning. 2024 Hard

48. Dimension of \(\frac{1}{\mu_0 \varepsilon_0}\) should be equal to 2023 Medium

49. If \(R , X _{ L }\). and \(X _{ C }\) represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: 2023 Easy

50. If speed \((V)\), acceleration \((A)\) and force \((F)\) are considered as fundamental units, the dimension of Young’s modulus will be 2023 Hard