Grade 11 Physics – Chapter: Units and Measurements EXAMINATION PAPER

full Examination Question Paper based on the entire chapter: Units and Measurements, aligned with the NEP 2020 and competency-based learning approach. This paper includes a mix of Competency-Based, Application-Oriented, and Analytical Thinking questions with various formats.

🧪 Grade 11 Physics – Chapter: Units and Measurements

Max Marks: 50
Time: 1 hour 30 minutes
NEP-Based Examination Pattern
Competency-Focused | Application-Oriented | Conceptual Clarity

Section A: Very Short Answer Questions (1 mark each)

(Answer in one sentence or definition. Attempt all questions.)
[1 × 6 = 6 marks]

1. Define a base quantity with an example.

2. Write the dimensional formula of force.

3. What do you mean by dimensional consistency of an equation?

4. Name two physical quantities having the same dimensional formula.

5. Give one example of a dimensionless quantity.

6. Write the SI unit of Planck’s constant.

Section B: Conceptual Understanding (2 marks each)

(Answer in brief: 2–3 lines)
[2 × 5 = 10 marks]

7. Why can't quantities with different dimensions be added or subtracted?

8. Show by dimensional analysis that $x = x_0 + v_0 t + \frac{1}{2} a t^2$ is dimensionally consistent.

9. Differentiate between fundamental and derived quantities.

10. Find the dimensional formula of pressure and write its SI unit.

11. What is meant by the order of accuracy in measurements?

Section C: Application-Based Questions (3 marks each)

(Answer using calculation or short explanation)
[3 × 4 = 12 marks]

12. Derive an expression for the time period of a simple pendulum using the method of dimensions.

13. Two physical quantities have the same dimensions. Does it mean they represent the same physical entity? Justify with an example.

14. If the unit of length is increased by 2%, how much percentage error will be introduced in the measurement of volume?

15. A formula is given as $T = 2\pi \sqrt{m/k}$. Check whether this formula is dimensionally correct. Assume $T$ is time, $m$ is mass and $k$ is spring constant.

Section D: Higher Order Thinking Skills (HOTS) (4 marks each)

(Analytical and creative questions)
[4 × 3 = 12 marks]

16. A new quantity $Z$ depends on mass $m$, acceleration $a$, and time $t$ as:

$$Z = k \cdot m^x a^y t^z$$

Find the values of $x, y, z$ such that $Z$ has the dimensions of energy.

17. The gravitational force between two masses is given by:

$$F = G \frac{m_1 m_2}{r^2}$$

Using dimensional analysis, find the dimensional formula of the gravitational constant $G$.

18. In a lab, a student writes an equation $E = \frac{1}{2} m v$. Another student writes $E = \frac{1}{2} m v^2$.
    (a) Use dimensional analysis to identify which is correct.
    (b) What does this equation represent physically?

Section E: Competency-Based Extended Response (5 marks)

[1 × 5 = 5 marks]

19. You are given three variables:

• mass $m$

• velocity $v$

• radius $r$

You are asked to derive the expression for a physical quantity $Q$, which has the dimensions of angular momentum using dimensional analysis.
(a) Write down the assumed relation.
(b) Derive the values of exponents.
(c) Write the final expression.
(d) Mention one real-life application of this physical quantity.

Here’s the Answer Key for the Grade 11 Physics Chapter: Units and Measurements NEP-Based Examination Paper.

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🧪 Answer Key – Units and Measurements

Max Marks: 50

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Section A: Very Short Answer Questions (1 mark each)

[1 × 6 = 6 marks]

1. Base Quantity: A quantity that is independent of other quantities and is defined arbitrarily, e.g., mass.

2. Dimensional formula of force: $[M^1 L^1 T^{-2}]$

3. Dimensional consistency: An equation is dimensionally consistent if all terms have the same dimensions.

4. Examples: Velocity and speed.

5. Dimensionless quantity: Refractive index or angle (θ in radians).

6. SI Unit of Planck’s Constant:

   J·s (joule second)
   or, in base units:
   kg·m²·s⁻¹

   Explanation:

   • 1 Joule (J) = 1 kg·m²/s²

   • So, J·s = (kg·m²/s²)·s = kg·m²·s⁻¹

   $\text{kg·m}^2\text{s}^{-1}$

   
   

Section B: Conceptual Understanding (2 marks each)

[2 × 5 = 10 marks]

7. Different dimensions represent different physical entities; adding them is meaningless (e.g., adding mass and length).

8. LHS: [L]; RHS: $[L] + [LT^{-1}T] + [LT^{-2}T^2] = [L]$. Hence, it is consistent.

9. Fundamental quantities are independent (e.g., mass), while derived quantities depend on them (e.g., velocity).

10. Pressure = Force/Area = $[MLT^{-2}]/[L^2] = [ML^{-1}T^{-2}]$, SI unit = Pascal (Pa).

11. Order of accuracy refers to the closeness of a measurement to the true value; smaller the error, higher the accuracy.

Section C: Application-Based Questions (3 marks each)

[3 × 4 = 12 marks]

$$T = k l^x g^y m^z \Rightarrow [T] = [L]^x [LT^{-2}]^y [M]^z = L^{x+y} T^{-2y} M^z \Rightarrow x + y = 0, -2y = 1, z = 0 \Rightarrow x = \frac{1}{2}, y = -\frac{1}{2}, z = 0 \Rightarrow T = k\sqrt{l/g}$$

13. No. Velocity and speed have same dimensions but different directions. E.g., velocity is a vector, speed is scalar.

14. Volume ∝ $L^3$
    % Error = 3 × 2% = 6%

$$LHS = [T]; RHS = \sqrt{[M]/[MT^{-2}]} = \sqrt{T^2} = [T] \Rightarrow \text{Yes, dimensionally correct.}$$

Section D: Higher Order Thinking Skills (4 marks each)

[4 × 3 = 12 marks]

Let $Z = m^x a^y t^z$ and Z has dimensions of energy: $[ML^2T^{-2}]$
Acceleration $a = [LT^{-2}]$
So,

$$[M^x][LT^{-2}]^y[T]^z = M^x L^y T^{-2y+z} \Rightarrow x = 1, y = 2, -2y + z = -2 \Rightarrow z = 2 \Rightarrow x = 1, y = 2, z = 2$$

$$F = G \frac{m_1 m_2}{r^2} \Rightarrow G = \frac{F r^2}{m^2} = \frac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]$$

(a) $E = \frac{1}{2} m v$ → $[MLT^{-1}]$;
$E = \frac{1}{2} m v^2$ → $[ML^2T^{-2}]$ → correct
(b) Represents kinetic energy of the body.

Section E: Competency-Based Extended Response (5 marks)

[1 × 5 = 5 marks]

(a) Assume: $Q = m^a v^b r^c$
(b) Angular momentum $[ML^2T^{-1}]$
$m = [M], v = [LT^{-1}], r = [L]$
So,

$$[M^a][LT^{-1}]^b [L]^c = M^a L^{b+c} T^{-b} \Rightarrow a = 1, b + c = 2, -b = -1 \Rightarrow b = 1, c = 1 \Rightarrow Q = mvr$$

(c) Expression: $L = mvr$
(d) Application: Rotational motion, planetary motion, quantum mechanics (electron orbitals)