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Ultimate CUET Physics Mastery Guide: Advanced Units, Dimensions & Van der Waals Questions With Full MCQs (CUET-Focused)

Understanding Units and Measurements, Dimensional Analysis, Van der Waals equation, Inductance–Resistance–Charge relations, and Stefan’s & Wien’s constants is crucial for CUET aspirants.

  • CUET Units and Dimensions MCQs

  • CUET Physics advanced dimensional analysis

  • Units and Measurements CUET important questions

  • Dimensional constants CUET

  • Surface tension, stress, Stefan’s constant CUET problems

  • Van der Waals equation dimensional questions CUET

  • Magnetic field & Permittivity dimensional formula CUET

  • Polarization, Luminous flux, Wien’s constant CUET numericals

To help you master these high-scoring topics, here is a comprehensive MCQ collection, each with options and correct answers — exactly in CUET style.

Table of Contents

CUET Physics: Advanced Units & Dimensions MCQs (With Options + Answers)

1. Dimensions of av2\frac{a}{v^2} in Van der Waals equation

a) 1, –1, –2
b) 1, 1, –2
c) 2, 1, –1
d) 1, 1, 1
✔️ Answer: a

2. Match the following (L = inductance, R = resistance, Q = charge)

Quantity Dimensions
(A) Q2R2L\frac{Q^2 R^2}{L} I) M2L4T−5A−2M^2L^4T^{-5}A^{-2}
(B) Q2R3L\frac{Q^2 R^3}{L} II) M0L0T0A1M^0L^0T^0A^1
(C) QR2L\frac{Q R^2}{L} III) ML2T−2ML^2T^{-2}
(D) QRL\frac{Q R}{L} IV) M−1L2T−3A−1M^{-1}L^2T^{-3}A^{-1}

a) A–IV, B–III, C–II, D–I
b) A–III, B–I, C–IV, D–II
c) A–IV, B–III, C–I, D–II
d) A–III, B–IV, C–I, D–II
✔️ Answer: b

3. Set with different dimensions

a) Angular impulse, Planck’s constant, Stefan’s constant
b) Energy density, wave intensity, stress
c) Radius of gyration, angular displacement, Rydberg constant
d) Velocity gradient, acceleration, gravitational potential
✔️ Answer: d

4. Force ∝ velocity² → dimension of constant

a) ML−1TML^{-1}T
b) ML−1ML^{-1}
c) MLT0MLT^0
d) LT−1LT^{-1}
✔️ Answer: b

5. Torque has same dimension as

a) Pressure
b) Impulse
c) Moment of force
d) Acceleration
✔️ Answer: c

6. Dimensionless quantity

a) Thermal conductivity
b) Specific gravity
c) Coefficient of linear expansion
d) Surface tension
✔️ Answer: b

7. Dimension of Luminous flux

a) cd
b) cd·T⁻¹
c) cd·L⁻²
d) cd·L·T⁻¹
✔️ Answer: a

8. Dimensional formula of jωLj\omega L

a) M−1L2T−1Q−2M^{-1}L^2T^{-1}Q^{-2}
b) ML−2T−1Q−2ML^{-2}T^{-1}Q^{-2}
c) ML2T−1Q−2ML^2T^{-1}Q^{-2}
d) ML2T1Q−2ML^2T^1Q^{-2}
✔️ Answer: c

9. Dimensions of A4B3C−2A^4B^3C^{-2}

a) Gas constant
b) Specific heat
c) Stefan’s constant
d) Heat energy
✔️ Answer: c

10. Match List-I with List-II

a) Gravitational potential
b) Stefan’s constant
c) Permittivity
d) Specific heat capacity

a) IV, I, III, II
b) I, IV, II, III
c) III, II, I, IV
d) II, III, IV, I
✔️ Answer: d

11. Pressure gradient dimension

a) ML2T−2ML^2T^{-2}
b) ML−1T−2ML^{-1}T^{-2}
c) MLT−2MLT^{-2}
d) ML−2T−2ML^{-2}T^{-2}
✔️ Answer: d

12. Modulus of elasticity

a) ML−1T−2ML^{-1}T^{-2}, Pascal
b) ML−2T−1ML^{-2}T^{-1}, Pascal
c) ML−1T−2ML^{-1}T^{-2}, Poise
d) ML−2T−1ML^{-2}T^{-1}, Poise
✔️ Answer: a

13. Dimensions of Q5S2PR2\frac{Q^5S^2}{PR^2}

a) Mass
b) Length
c) Time
d) Angle
✔️ Answer: d

14. In the formula X=5YZ2X = \frac{5Y}{Z^2}, X has dimensions of capacitance and Z has dimensions of magnetic field. What are the dimensions of Y?

a) M−1L2T4A2M^{-1}L^{2}T^{4}A^{2}
b) M−2L0T−4A−2M^{-2}L^0T^{-4}A^{-2}
c) M−3L−2T8A4M^{-3}L^{-2}T^{8}A^{4}
d) M−2L−2T6A3M^{-2}L^{-2}T^{6}A^{3}

✔️ Answer: c

15. If S (surface tension), I (moment of inertia), and h (Planck’s constant) are taken as fundamental units, the dimensional formula for linear momentum is:

a) S1/2I1/2h−1S^{1/2} I^{1/2} h^{-1}
b) S3/2I1/2h0S^{3/2} I^{1/2} h^{0}
c) S1/2I1/2h0S^{1/2} I^{1/2} h^{0}
d) S1/2I3/2h−1S^{1/2} I^{3/2} h^{-1}

✔️ Answer: c

16. In terms of G (gravity), h (Planck’s constant), and c (speed of light), the time period is proportional to:

a) Ghc5\sqrt{\frac{Gh}{c^5}}
b) hc3G\sqrt{\frac{hc^3}{G}}
c) c3Gh\sqrt{\frac{c^3}{Gh}}
d) Ghc3\sqrt{\frac{Gh}{c^3}}

✔️ Answer: a

17. If force is given by F=b+ct3F = b + \frac{c}{t^3}, find the dimensions of c.

a) M0LTM^0 L T
b) MLT−1M L T^{-1}
c) MLT−2M L T^{-2}
d) MLT1M L T^{1}

✔️ Answer: d

18. In SI units, the dimensions of ε0/μ0\sqrt{\varepsilon_0 / \mu_0} are:

a) A−1TML3A^{-1} T M L^{3}
b) A−1T2ML−1A^{-1} T^{2} M L^{-1}
c) A0T3M1/2L−1A^{0} T^{3} M^{1/2} L^{-1}
d) A2T3M−1L−2A^{2} T^{3} M^{-1} L^{-2}

✔️ Answer: d

19. Which expression has a dimensional formula different from others?

a) E22ε0\frac{E^2}{2\varepsilon_0}
b) hvhv
c) ρgh\rho g h
d) 12ρv2\frac{1}{2} \rho v^2

✔️ Answer: b

20. If σ is Stefan’s constant and b is Wien’s constant, the dimensions of σb are:

a) LMT3K−3LM T^{3} K^{-3}
b) L−1MT−3K−3L^{-1} M T^{-3} K^{-3}
c) L−1MT2K−3L^{-1} M T^{2} K^{-3}
d) L1MT−3K−3L^{1} M T^{-3} K^{-3}

✔️ Answer: d

21. In μ = A + B/λ², the dimensions of B are the same as:

a) Wavelength
b) Volume
c) Pressure
d) Area

✔️ Answer: d

22. The dimensional formula of Polarization (P) is:

a) L−2A−1T−1L^{-2} A^{-1} T^{-1}
b) ML−1T2A−1M L^{-1} T^{2} A^{-1}
c) L2A−1T1L^{2} A^{-1} T^{1}
d) L−2A1T1L^{-2} A^{1} T^{1}

✔️ Answer: d

23. Which among the following has dimensions of charge?

a) ε0E/ds\varepsilon_0 E / ds
b) ε0E ds\varepsilon_0 E \, ds
c) μ0ε0E ds\frac{\mu_0}{\varepsilon_0} E \, ds
d) ε0μ0E ds\frac{\varepsilon_0}{\mu_0} E \, ds

✔️ Answer: b

24. The dimensional formula of solar constant is:

a) MLT−2M L T^{-2}
b) ML0T−3M L^0 T^{-3}
c) M2L0T−2M^2 L^0 T^{-2}
d) ML2T−2M L^{2} T^{-2}

✔️ Answer: b

25. If momentum P, area A and time T are fundamental quantities, the dimensional formula for energy is:

a) P2AT−2P^{2} A T^{-2}
b) PA−1T−2P A^{-1} T^{-2}
c) PA1/2T−1P A^{1/2} T^{-1}
d) P1/2AT−1P^{1/2} A T^{-1}

✔️ Answer: c

26. Dimension of B22μ0\frac{B^2}{2\mu_0}

a) ML−1T−2M L^{-1} T^{-2}
b) MLT−2M L T^{-2}
c) ML2T−1M L^{2} T^{-1}
d) ML2T−2M L^{2} T^{-2}

✔️ Answer: a

27. If x=IFv2WL4x = \frac{IFv^2}{WL^4}, the dimensions of x are same as:

a) Planck’s constant
b) Force constant
c) Coefficient of viscosity
d) Energy density

✔️ Answer: d

28. The physical quantities having same dimensions are:

a) Couple of force & work
b) Force & work
c) Latent heat & specific heat
d) Work & power

✔️ Answer: a

29. The dimensional formula for thermal conductivity is:

a) MLT−2KM L T^{-2} K
b) MLT−2K−2M L T^{-2} K^{-2}
c) MLT−3K−1M L T^{-3} K^{-1}
d) MLT−3KM L T^{-3} K

✔️ Answer: c

30. If f=hc5Gf = \sqrt{\frac{hc^5}{G}}, f has dimensions of:

a) Area
b) Volume
c) Momentum
d) Energy

✔️ Answer: d

Conclusion

Units and Measurements aren’t just the opening chapter-they form the base of almost every physics questions in CUET,NEET,and JEET.Once you understand dimensional formulas,derived units,and dimensionless constants,solving advanced problems becomes far easier and faster.

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