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Q3(i):
Classify the following as scalar and vector quantities.
(i) time period
Solution :
Theoretical Foundation: Scalar vs. Vector Classification
To classify a physical quantity, we must evaluate it against two primary criteria:
- Magnitude: A numerical value representing the size or extent of the quantity.
- Direction: A specific orientation in space required to define the quantity completely.
Definitions per standard physical conventions:
- Scalar Quantity: A physical quantity that is completely described by its magnitude alone. It obeys simple algebraic laws. [Per definition of Scalar fields in Euclidean space].
- Vector Quantity: A physical quantity that possesses both magnitude and direction and adheres to the parallelogram law of vector addition. [Per definition of Vector fields in Euclidean space].
Step 1: Analysis of "Time Period"
The time period represents the duration taken for a phenomenon to complete one full cycle or the interval between two events.
When measuring time period ($T$):
- It possesses a numerical magnitude (e.g., $5 \text{ seconds}$).
- It lacks spatial orientation. Time is treated as a scalar parameter in classical mechanics, moving monotonically forward without an inherent direction vector in three-dimensional space.
Step 2: Graphical Representation of Scalar Nature
Step 3: Logical Conclusion
Since the time period ($T \in \mathbb{R}^+$) is characterized solely by its magnitude and is independent of coordinate geometry directions ($\hat{i}, \hat{j}, \hat{k}$), it fulfills the criteria for a scalar quantity. [Based on the properties of scalar time in Newtonian physics].
Final Solution: Time period is a Scalar quantity.
More Questions from Class 12 Mathematics Vector Algebra EXERCISE 10.1
- Q1: Represent graphically a displacement of 40 km, 30° east of north.
- Q2(i): Classify the following measures as scalars and vectors. (i) 10 kg
- Q2(ii): Classify the following measures as scalars and vectors. (ii) 2 meters north-west
- Q2(iii): Classify the following measures as scalars and vectors. (iii) 40°
- Q2(iv): Classify the following measures as scalars and vectors. (iv) 40 watt
- Q2(v): Classify the following measures as scalars and vectors. (v) $10^{-19}$ coulomb
- Q2(vi): Classify the following measures as scalars and vectors. (vi) $20$ m/s$^2$
- Q3(ii): Classify the following as scalar and vector quantities. (ii) distance
- Q3(iii): Classify the following as scalar and vector quantities. (iii) force
- Q3(iv): Classify the following as scalar and vector quantities. (iv) velocity
- Q3(v): Classify the following as scalar and vector quantities. (v) work done
- Q4(i): In Fig 10.6 (a square), identify the following vectors. (i) Coinitial
- Q4(ii): In Fig 10.6 (a square), identify the following vectors. (ii) Equal
- Q4(iii): In Fig 10.6 (a square), identify the following vectors. (iii) Collinear but not equal
- Q5(i): Answer the following as true or false. (i) $\vec{a}$ and $-\vec{a}$ are collinear.
- Q5(ii): Answer the following as true or false. (ii) Two collinear vectors are always equal in magnitude.
- Q5(iii): Answer the following as true or false. (iii) Two vectors having same magnitude are collinear.
- Q5(iv): Answer the following as true or false. (iv) Two collinear vectors having the same magnitude are equal.
CBSE Solutions for Class 12 Mathematics Vector Algebra
Chapters in CBSE - Class 12 Mathematics
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