Important Questions of Units and Measurements Worksheet for CBSE Class 11 Physics

CBSE Class 11 Physics Important Questions Chapter 1 Units and Measurement are provided here for students. By practising these questions, students get thorough with the important topics of this chapter. Also, they boost their exam preparation for the annual exam. Below are some of the important numerical on units and measurements class 11.

CBSE Class 11 Physics Important Questions Chapter 1 Units and Measurement

Very Short Answer Questions (1 Mark Each)

1. Define the term physical quantity with an example.
2. What are fundamental units? Give two examples.
3. Write the SI unit of surface tension.
4. Convert one light year into meters.
5. How many significant figures are in 0.00450?
6. Define parallax angle.
7. What is the dimension of Planck’s constant (h)?
8. Name a physical quantity that has different units in different systems.
9. State the number of base units in the SI system.
10. What is least count of a vernier caliper?

Short Answer Questions (2-3 Marks Each)

11. Differentiate between accuracy and precision.
12. Convert 1 joule into erg.
13. Express 1 Newton in terms of base SI units.
14. A physical quantity X is given by: X=a²b³/c√d

Find the dimensional formula of X if a, b, c, and d have given dimensions.
15. Define parallax method and explain its application in measuring large distances.
16. State and explain the principle of homogeneity of dimensions.
17. Write down the error formula for measuring a quantity Z, where Z=A⋅B²/C³

How do errors propagate in this case?
18. Explain the importance of dimensional analysis in physics.
19. The diameter of a wire is measured as 0.25 ± 0.01 mm. Find the percentage error.
20. Why is the SI system preferred over the CGS system?

Long Answer Questions (5 Marks Each)

21. Explain the types of errors in measurement with suitable examples.
22. Derive the dimensional formula of universal gravitational constant G using F=Gm₁m₂/r²​​

23. A physical quantity P is given by P =A³B^1/2C²

Find the percentage error in P if the percentage errors in A, B, and C are 1%, 2%, and 3%, respectively.
24. The length and breadth of a rectangular sheet are measured as 4.5 cm and 3.25 cm, respectively. Find the area of the sheet, considering significant figures.
25. The time period T of a simple pendulum is given by T=2π√(l/g)

Check the correctness of this formula using dimensional analysis.
26. Explain systematic errors, random errors, and gross errors with examples.
27. How is parallax method used to measure the radius of the Moon?
28. Explain the significance of order of magnitude with two examples.
29. The period of oscillation T of a simple pendulum is found to be 2.01 s, 2.03 s, 2.04 s, 2.00 s, and 2.05 s. Find the mean absolute error and relative error.
30. If X = A² B³ / C⁴, find the error in X when errors in A, B, and C are given as 2%, 1%, and 3%, respectively.

Solutions

Very Short Answer Questions (1 Mark Each)

1. Physical quantity: A quantity that can be measured and expressed in terms of a unit. Example: Length, mass.
2. Fundamental units: Units that are independent and cannot be derived from other units. Examples: Meter (m), Kilogram (kg).
3. SI unit of surface tension: Newton per meter (N/m).
4. 1 light year in meters: 1 light year=9.46×10¹⁵ m
5. Significant figures in 0.00450: 3 (4, 5, and the trailing zero are significant).
6. Parallax angle: The angle subtended by an object at two different observation points.
7. Dimension of Planck’s constant (h): [h]=[ML²T⁻¹]
8. Example: Energy is measured in Joule (SI unit) and erg (CGS unit).
9. Number of base units in SI: 7.
10. Least count of vernier caliper: 0.01 cm (or 0.1 mm).

Short Answer Questions (2-3 Marks Each)

11. Accuracy vs Precision:

• Accuracy: Closeness to the true value.
• Precision: Reproducibility of measurements.

12. 1 Joule in erg: 1 J=10⁷ 

13. 1 Newton in base SI units: 1 N=1 kg⋅m/s²

14. Dimensional formula of X: Given, X=a²b³/c√d

Substitute the dimensions of a, b, c, and d.

15. Parallax Method:

• Used to measure large distances (e.g., distance of stars).
• The object is observed from two different positions, and the angle subtended is used to calculate the distance.

16. Principle of Homogeneity: The dimensions of LHS and RHS of an equation must be the same.
17. Error formula for Z: ΔZ/Z=ΔA/A+2ΔB/B+3ΔC/C

18. Importance of Dimensional Analysis:

• Checks correctness of formulas.
• Helps in unit conversions.

19. Percentage Error in Diameter:

% Error=(Absolute Error/Measured Value)×100 =(0.010.25)×100=4%

20. SI System is preferred because:

• Universally accepted.
• Based on decimal system.

Long Answer Questions (5 Marks Each)

21. Types of Errors:

• Systematic error: Due to instrument defects.
• Random error: Due to unknown fluctuations.
• Gross error: Human mistakes.

22. Dimensional formula of G: Using F=Gm₁m₂/r²

G=Fr²/m₁m₂

​[G]=[M⁻¹L³T⁻²]

23. Percentage error in P:
    Given, P =A³B^1/2C²

ΔP/P=3ΔA/A+1/2ΔB/B+2ΔC/C

Substituting values: =(3×1)+(0.5×2)+(2×3)=3+1+6=10%

24. Significant Figures in Area Calculation:

A=4.5×3.25=14.625≈14.6 (3 significant figures)

25. Dimensional check for Pendulum: T=2π√(l/g)

[T]=√{L/LT^-2) = T

Matches [T] = [M⁰ L⁰ T¹] ✅.

26. Types of Errors Explained with Examples: (Already covered in Q21).
27. Measuring the Moon’s Radius using Parallax Method:

• Measure the parallax angle from two locations.
• Use trigonometry to find the distance and radius.

28. Order of Magnitude:

• Used to approximate values in powers of 10.
• Example:
  • Earth’s mass: 10²⁴ kg
  • Electron’s charge: 10⁻¹⁹ C

29. Mean Absolute Error and Relative Error:

• Mean value = (2.01 + 2.03 + 2.04 + 2.00 + 2.05) / 5 = 2.026 s
• Mean Absolute Error: ΔT=∑∣T_i−T_mean∣/n​
• Calculate for each value and find the mean error.

30. Error in X:
    Given, X = A² B³ / C⁴

ΔX/X=2ΔA/A+3ΔB/B+4ΔC/C

Substituting given errors: =(2×2)+(3×1)+(4×3)=4+3+12=19%