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Q2(i):
Classify the following measures as scalars and vectors.
(i) 10 kg
Solution :
Step 1: Identifying Physical Characteristics
To classify a measure as a scalar or a vector, we analyze two fundamental properties:
- Magnitude: A numerical value representing the quantity.
- Direction: A specific orientation or sense of displacement in space.
[Definition of Scalar: A physical quantity having magnitude but no specified direction.]
[Definition of Vector: A physical quantity having both magnitude and direction.]
Step 2: Analysis of the Given Quantity ($10 \text{ kg}$)
The quantity provided is $10 \text{ kg}$, which represents mass.
| Attribute | Analysis |
|---|---|
| Magnitude | $10$ (A defined numerical value) |
| Unit | $\text{kg}$ (Kilogram, the SI unit of mass) |
| Direction | Mass is an intrinsic property of matter; it possesses no spatial orientation or directionality. [Per Fundamental Physical Definitions] |
Step 3: Visual Representation of Scalar Classification
Step 4: Logical Conclusion
Since the measure $10 \text{ kg}$ only provides information regarding the amount of matter (magnitude) and lacks a directional component, it satisfies the necessary and sufficient conditions for a scalar quantity.
Final Solution: The measure $10 \text{ kg}$ is classified as a scalar.
More Questions from Class 12 Mathematics Vector Algebra EXERCISE 10.1
- Q1: Represent graphically a displacement of 40 km, 30° east of north.
- 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(i): Classify the following as scalar and vector quantities. (i) time period
- 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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