Units, Dimensions & Measurements – Full Quiz

Total: 57 Questions • Click the correct answer to check instantly

1. The magnitude of any physical quantity:

Correct Answer: 1
The numerical value changes with the measurement method and instrument sensitivity.

Different measurement methods give slightly different results.

2. What is the unit of measurement of solid angle?

Correct Answer: 1
The SI unit of solid angle is steradian.

Plane angle → radian; solid angle → steradian.

3. Newton-second is the unit of:

Correct Answer: 3
Impulse and momentum share the same unit: Newton-second.

4. Which is NOT a unit of energy?

Correct Answer: 4
Watt is the SI unit of power, not energy.

5. Candela is the SI unit of:

Correct Answer: 2

6. Universal time is based on:

Correct: 3

7. Which has same dimensions as energy?

Correct: 4

8. Which pair does NOT have same dimensions?

Correct: 2

9. Which pair has same dimensions?

Correct: 3

10. A unitless quantity:

Correct: 3

11. Ratio of Planck’s constant to moment of inertia has dimension of:

Correct: 1

12. Dimension of Planck’s constant equals:

Correct: 3

13. Physical quantities NOT having same dimensions:

Correct: 3

14. 100 dyne (CGS) is equal to in MKS:

Correct: 3

15. If new units: L=4m, M=4kg, T=2s, then 32 units of energy =

Correct: 1

16. Assertion–Reason (Dimensional analysis)

Correct: 1

17. If L=2.331 cm, B=2.1 cm, L+B = ?

Correct: 3

18. 9.99 m − 0.0099 m (significant figures) =

Correct: 3

19. 97.52 ÷ 2.54 (significant figures) =

Correct: 1

20. A silver wire has mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and length (4 ± 0.04) cm. The maximum percentage error in the measurement of its density will be:

Correct: 1 (4%)
Density ∝ m / (r²l). Percentage error ≈ (Δm/m) + 2(Δr/r) + (Δl/l) ≈ 4%.

21. Time period (2.00 ± 0.05) s → correct representation:

Correct: 3

22. Copper sheet heated → area increases by:

Correct: 1

23. Mean absolute error in pendulum experiment:

Correct: 2

24. Accuracy of measurement is determined by:

Correct: 2

25. Percentage error in volume of cylinder:

Correct: 3

26. Vernier least count formula:

Correct: 3

27. Least count of vernier caliper (20 VSD = 16 MSD):

Correct: 4

28. LC when 1 cm is divided into 5 parts, n MSD = (n+1) VSD:

Correct: 2

29. Screw gauge least divisions needed for 5 mm wire:

Correct: 1

30. Vernier constant when MSD = 1 mm & VSD = 0.9 mm:

Correct: 3

31. The vernier constant of a vernier caliper is 0.001 cm. If 49 main scale divisions coincide with 50 vernier scale divisions, then the value of 1 main scale division is:

Correct: 2 (0.5 mm)
Let 1 MSD = x cm, 1 VSD = y cm.
49x = 50y and LC = x − y = 0.001 cm ⇒ solving gives x = 0.05 cm = 0.5 mm.

32. In a vernier caliper, the ten smallest divisions of the vernier scale are equal to the nine smallest divisions on the main scale. If the smallest division on the main scale is a half millimeter, then the vernier constant is:

Correct: 3 (0.05 mm)
9 MSD = 10 VSD. 1 MSD = 0.5 mm ⇒ 9 × 0.5 = 10 VSD ⇒ 1 VSD = 0.45 mm.
LC = MSD − VSD = 0.5 − 0.45 = 0.05 mm.

33. Which of the following is dimensionless?

Correct: 1
Poisson’s ratio is a ratio of strains (dimensionless/ dimensionless).

All ratios of same-type quantities are dimensionless.

34. The dimension of impulse is the same as that of:

Correct: 2
Impulse = Force × time = change in momentum ⇒ same dimensions as momentum.

35. Which of the following has the same units as work?

Correct: 1
Work and torque both have units of N·m in SI.

36. The dimensional formula of pressure is:

Correct: 1
Pressure = Force / Area = (MLT⁻²)/L² = ML⁻¹T⁻².

37. Which one of the following is NOT a base (fundamental) SI unit?

Correct: 4
Joule is a derived unit (for energy); others are base units.

38. The SI unit of coefficient of viscosity is:

Correct: 2

39. Dimensional formula of gravitational constant G is:

Correct: 1
From F = G m₁m₂ / r² ⇒ G = Fr² / (m₁m₂) ⇒ (MLT⁻²·L²)/M² = M⁻¹L³T⁻².

40. Which quantity has the same dimensions as power?

Correct: 1
Power = work/time = force × velocity.

41. The dimensional formula of electric charge is:

Correct: 1
Charge Q = current × time ⇒ [Q] = [A][T].

42. Which quantity is dimensionless?

Correct: 1

43. Which among the following has units of N·m⁻²?

Correct: 1

44. Number of significant figures in 0.002304 is:

Correct: 2 (4 significant figures)
0.002304 ⇒ significant digits are 2, 3, 0, 4 (leading zeros ignored).

45. Which measurement shows the highest accuracy (greatest significant figures)?

Correct: 3
2.000 cm has four significant figures and indicates the finest precision.

46. Measurement error decreases when we:

Correct: 2
Smaller least count → finer resolution → reduced instrumental error.

47. If radius r has 2% error, error in area πr² is approximately:

Correct: 3
Area ∝ r² ⇒ percentage error ≈ 2 × 2% = 4%.

48. Pitch of screw gauge = 1 mm, circular scale = 100 divisions. Least count is:

Correct: 1
LC = pitch / number of divisions = 1 mm / 100 = 0.01 mm.

49. If a Vernier caliper has 1 mm MSD and 10 VSD = 9 MSD, the least count is:

Correct: 1
10 VSD = 9 mm ⇒ 1 VSD = 0.9 mm. LC = MSD − VSD = 1 − 0.9 = 0.1 mm.

50. The dimensional formula of work is the same as that of:

Correct: 1

51. The SI unit of energy density is:

Correct: 2

52. Which of the following is NOT dimensionless?

Correct: 4
Force constant (spring constant k) has unit N/m ⇒ dimensions ML⁰T⁻² / L = ML⁻¹T⁻².

53. Dimensional formula of angular velocity is:

Correct: 1

54. Which one is a derived SI unit?

Correct: 3
Pascal (Pa) = N/m² is derived from base units.

55. Which physical quantity has dimensional formula MLT⁻¹?

Correct: 2
Momentum p = mv ⇒ [p] = M × LT⁻¹ = MLT⁻¹.

56. A physical quantity that has a unit but no dimension is:

Correct: 2
Solid angle (steradian) has a defined unit but is dimensionless.

57. Dimensional formula of Young’s modulus is the same as that of:

Correct: 1
Young’s modulus = stress/strain = (Force/Area)/dimensionless = pressure-like ⇒ ML⁻¹T⁻².

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Units and Measurement Notes