• Amal Augustine
• November 28, 2025

Dimensions Mastering & Units: Advanced MCQs for NEET, JEE & CUET Aspirants

Understanding dimensions, units, and measurement systems is a core skill for Physics students preparing for NEET, JEE and CUET. These concepts connect mathematical reasoning with physical laws, making them essential for solving complex numerical and theoretical questions. This blog brings together unique dimensional-analysis MCQs, units-based reasoning problems, fundamental constants, conversion-based questions, and derived units—all in one structured guide.

Along the way, we use important keywords such as SI units, dimensional formula, inductance, magnetic flux, permeability, Planck’s constant, astronomical unit, surface tension, specific resistance, mobility, solar constant, torque, Young’s modulus, CGS units, order of magnitude, fundamental quantities, and more.
This makes the post both exam-relevant and conceptually strong.

Understanding Dimensions in Terms of Derived Quantities

1. What is the dimension of energy in terms of linear momentum (P), area (A) and time (T)?

Options:
a) P¹A¹T⁻¹
b) P²A²T⁻¹
c) P¹A¹/²T⁻¹
d) P¹/²A¹/²T⁻¹
Answer: c

---

Units, Measurements & Astronomical Scales

2. How many astronomical units are there in 1 metre?

a) 6.68×10¹² AU
b) 6.68×10⁻¹⁰ AU
c) 6.68×10¹⁰ AU
d) 6.68×10⁻¹² AU
Answer: d

---

Range of Physical Quantities

3. The range of masses we study in physics is:

a) 10⁻²⁷ to 10⁶⁰ kg
b) 10⁻²⁷ to 10⁵⁵ kg
c) 10⁻³⁰ to 10⁵⁵ kg
d) 10⁻³⁰ to 10⁶⁰ kg
Answer: c

---

Dimensionless Quantities

4. A dimensionless physical quantity:

a) may have a unit
b) always has a unit
c) never has a unit
d) does not exist
Answer: a

---

5. One minute of arc (1′) in radians is nearly:

a) 2.91×10⁻⁴ rad
b) 4.85×10⁻⁴ rad
c) 4.80×10⁻⁶ rad
d) 1.75×10⁻² rad
Answer: a

---

Thermal Effects & Dimensional Impact

6. On heating a copper sphere, which physical quantity changes by the highest percentage?

a) Radius
b) Area
c) Volume
d) Length
Answer: c

---

Units Across Different Measuring Systems

7. One angstrom (Å) equals:

a) 10⁻⁶ mm
b) 10⁻⁷ mm
c) 10⁻⁸ mm
d) 10⁻⁹ mm
Answer: b

---

Fundamental Ideas in Physics

8. Two principal thrusts in physics:

a) Diversification and complete
b) Unification and simplification
c) Unification and reduction
d) Diversification and simplification
Answer: c

---

Expressing μ₀ Using Fundamental Constants

9. The permeability μ₀ in terms of e, m, c, h:

a) h/me²
b) hc/me²
c) h/ce²
d) mc²/he²
Answer: c

---

Capacitors in Quantum-Scale Units

10. If capacitance is expressed using e, a₀, h, c:

a) u = e²h/a₀
b) u = hc/e²a₀
c) u = e²c/ha₀
d) u = e²a₀/hc
Answer: d

---

Derived Units in New Fundamental Systems

11. Dimensions of mass if F, V, T are fundamental:

a) FVT⁻¹
b) FVT⁻²
c) FV⁻¹T⁻¹
d) FV⁻¹T
Answer: d

---

Mobility & Dimensional Analysis

12. Dimensions of mobility:

a) M⁻²T²A
b) M⁻¹T²A
c) M⁻²T³A
d) M⁻¹T³A
Answer: b

---

Surface Tension in E–V–T System

13. Dimensional formula of surface tension with energy E, velocity V, time T:

a) EV⁻¹T⁻²
b) EV⁻²T⁻²
c) E⁻²V⁻¹T⁻³
d) EV⁻²T⁻¹
Answer: b

---

Identifying Physical Quantities from Dimensions

14. A quantity with MaLbTc is pressure when:

a) a = 1, b = 0, c = –1
b) a = 1, b = 1
c) a = 0, b = –1, c = –2
d) a = 1, b = –1, c = –2
Answer: d

---

Constants With Dimensions

15. Dimensional constant in the list:

a) Refractive index
b) Dielectric constant
c) Relative density
d) Gravitational constant
Answer: d

---

Solar Constant as a Dimensional Quantity

16. Dimensional formula of solar constant:

a) [M⁰L⁰T⁰]
b) [MLT⁻²]
c) [ML²T⁻²]
d) [ML⁰T⁻³]
Answer: d

---

Conceptual Applications

17. Energy/time has dimensions same as:

a) momentum
b) power
c) torque
d) electric field
Answer: b

---

Self-Inductance & Magnetic Properties

18. Dimensions of coefficient of self-inductance:

a) ML²T⁻²A⁻²
b) ML²T⁻²A⁻¹
c) MLT⁻²A⁻²
d) MLT⁻²A⁻¹
Answer: a

---

19. Dimensions of magnetic field in M, L, T, C:

a) MLT⁻¹C⁻¹
b) MT²C⁻²
c) MT⁻¹C⁻¹
d) MT⁻²C⁻¹
Answer: c

---

20. Correct dimensions of gravitational constant:

a) M⁻¹L³T⁻²
b) MLT⁻¹
c) ML⁻¹T⁻²
d) ML²T⁻²
Answer: a

---

21. Mass in F–L–T system:

a) FL⁻¹T²
b) FL⁻¹T⁻²
c) F⁻¹L⁻¹T⁻¹
d) FL²T²
Answer: a

---

22. Dimensional formula of magnetic flux:

a) ML²T⁻²A⁻¹
b) ML³T⁻²A⁻²
c) L²T⁻²A⁻²
d) M²T⁻¹A⁻²
Answer: a

---

23. Dimensions of viscosity:

a) ML⁻¹T⁻¹
b) MLT⁻¹
c) MLT⁻²
d) ML²T⁻²
Answer: a

---

24. Physical quantities NOT having same dimensions:

a) torque & work
b) momentum & Planck’s constant
c) stress & Young’s modulus
d) speed & (μ₀ε₀)⁻¹/²
Answer: b

---

25. Pair with equal dimensions:

a) torque & work
b) stress & energy
c) force & stress
d) force & work
Answer: a

---

26. Ratio of Planck’s constant to moment of inertia has dimensions of:

a) time
b) frequency
c) angular momentum
d) velocity
Answer: b

---

Heat, Mass, and Microscopic Quantities

27. Dimensions of torque:

a) MLT⁻²
b) ML²T⁻²
c) ML²T⁻¹
d) ML²T⁻²
Answer: b

---

28. Dimensions of specific heat:

a) ML²T⁻²K
b) ML²T⁻²K⁻¹
c) ML²T⁻²K⁻¹
d) L²T⁻²K⁻¹
Answer: d

29. If P, Q, and R are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity?

A) (P − Q) / R
B) PQ − R
C) PQ / R
D) (PR − Q²) / R
Correct Answer: A

30. Which of the following pairs has same dimensions?

A) Angular momentum and Planck’s constant
B) Dipole moment and electric field
C) Both (a) and (b)
D) None of these
Correct Answer: A

Final Thoughts

These MCQs strengthen your conceptual base in dimensional analysis, units and measurements, derived quantities, and fundamental constants—topics that consistently appear in NEET, JEE and CUET.