HC Verma solutions,Physics and Mathematics, Objective-II, Concepts of Physics - Part 1" - Chapter 2, Answers and Explanations

Objective - II

1. A situation may be described by using different sets of co-ordinate axes having different orientations. Which of the following do not depend on the orientation of the axes?
  (a) the value of a scalar
  (b) component of a vector
  (c) a vector
  (d) the magnitude of a vector

Answer: (a), (c), (d) 

Explanation: Sets of co-ordinate axes are simply lines of references to describe the position and orientation of vectors or similar things. Their orientations cannot change (a) the value of scalar, (b) a vector or (d) the magnitude of a vector. But when a vector is resolved along axes, the component is dependent on the angle between the vector and the axis along which it is being resolved. This angle will vary if the orientation of axes is changed. So the component of a vector will depend upon the orientation of the axes.

2. Let vectors C = A + B .
  (a) |C| is always greater than |A|  
  (b) It is always possible to have  |C| < |A| and |C|  < |B| 
  (c) C is always equal to A+B 
  (d) C is never equal to A+B  

Answer: (b) 

Explanation:  Two vectors are added by "parallelogram law of addition" not by mathematical addition. Vectors A and B are placed with their tails at a point without changing their directions. Taking them as two adjacent sides of a parallelogram, the parallelogram and the diagonal from tails is drawn. This diagonal gives the sum of the two vectors. Depending on the directions and magnitudes of two vectors, the length of this diagonal (which represents the magnitude of the sum) may be 
   (i) greater or less than the magnitude of vector A which makes option (a) false,
  (ii) equal to or less than the sum of magnitudes of  A and B makes option (c) false,
  (iii) equal to the sum of magnitudes of  A and B if  A and B are collinear and having the same direction. That makes the option (d) false.
Only option (b) is true because it is always possible to have  |C| < |A| and |C|  < |B| . See this condition in the figure below:-

Sum of two vectors by triangle law of addition

3. Let the angle between two nonzero vectors A and B be 120° and its resultant be C. 
  (a) C must be equal to |A-B| 
  (b) C must be less than |A-B| 
  (c) C must be greater than |A-B| 
  (d) C may be equal to |A-B| 

Answer: (c) 

Explanation:  |A-B| means the numerical difference of the magnitudes of  A and B. The answer may be explained through the following diagram:- 
 

The magnitude of resultant and difference of magnitudes of two vectors

   
In left figure: In triangle OCD angle ODC =120° so angle COD<120°. Hence OC>CD because in a triangle side opposite the greater angle is greater. So C > |A-B|

In right figure: In triangle OCD angle ODC =120° so angle OCD<120°. Hence OC>OD because in a triangle side opposite the greater angle is greater. So C > |A-B|

4. The x-component of the resultant of several vectors
  (a) is equal to the sum of the x-components of the vectors  
  (b) may be smaller than the sum of the magnitudes of the vectors
  (c) may be greater than the sum of the magnitudes of the vectors
  (d) may be equal to the sum of the magnitudes of the vectors 

Answer: (a), (b), (d) 

Explanation:  Only (c) is wrong because the sum of the magnitudes of the vectors is the numerical sum while x-component of the resultant vector is the algebraical sum of the x-component of the vectors and will never be greater than the former. 

5. The magnitude of the vector product of two vectors A and B may be
  (a) greater than AB                        (b) equal to AB
  (c) less than AB                             (d) equal to zero  

Answer: (b), (c), (d) 

Explanation:  Magnitude of the cross product of two vectors A and B is ABsinθ and value of sinθ varies between 1 to -1. So ABsinθ can vary between AB to -AB ie it can be either equal to or less than AB or even equal to zero. But it can not be greater than AB.   

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CHAPTER- 18 - Geometrical Optics

Questions for Short Answers

CHAPTER- 17 - Light Waves

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1-Q10

EXERCISES - Q11-Q20

EXERCISES - Q21-Q30

EXERCISES - Q31-Q41

CHAPTER- 16 - Sound Waves

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES -Q-21 TO Q-30

EXERCISES -Q-31 TO Q-40

EXERCISES -Q-41 TO Q-50

EXERCISES -Q-51 TO Q-60

EXERCISES -Q-61 TO Q-70

EXERCISES - Q-71 TO Q-80

EXERCISES - Q-81 TO Q-89

CHAPTER- 15 - Wave Motion and Waves on a String

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES - Q-21 TO Q-30

EXERCISES - Q-31 TO Q-40

EXERCISES - Q-41 TO Q-50

EXERCISES - Q-51 TO Q-57 

CHAPTER- 14 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q-1 TO Q-10

EXERCISES- Q-11 TO Q-20

CHAPTER- 13 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES Q-1 TO Q-10

EXERCISES- Q11 TO Q20

EXERCISES Q-21 TO Q30

EXERCISES Q-31 TO Q35

CHAPTER- 12 - Simple Harmonic Motion

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q1 TO Q10

EXERCISES- Q11 TO Q20

EXERCISES- Q21 TO Q30

EXERCISES- Q31 TO Q40

EXERCISES- Q41 TO Q50

EXERCISES- Q51 TO Q58 (2-Extra Questions)

CHAPTER- 11 - Gravitation

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q_1 to Q_10

EXERCISES -Q-11 TO Q-20

EXERCISES -Q 21 TO 30

EXERCISES -Q 31 TO 39

CHAPTER- 10 - Rotational Mechanics

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q-1 TO Q-15

EXERCISES - Q-16 TO Q-30

EXERCISES Q-31 TO Q-45

EXERCISES Q-46 TO Q-60

EXERCISES Q-61 TO Q-75

EXERCISES Q-76 TO Q-86

CHAPTER- 9 - Center of Mass, Linear Momentum, Collision

Questions for Short Answers

Objective - I

Objective - II

EXERCISES Q-1 TO Q-10

EXERCISES Q-11TO Q-20

EXERCISES Q-21 TO Q-30

EXERCISES Q-31 TO Q-42

EXERCISES Q-43 TO Q-54

CHAPTER- 8 - Work and Energy

Click here for → Question for Short Answers

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)

Click here for → Exercises (31-42)

Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

Click here for → Questions for Short Answer 

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → EXERCISES (11-20)

Click here for → EXERCISES (21-30)

CHAPTER- 6 - Friction

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Click here for → OBJECTIVE-I

Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)

For more practice on problems on friction solve these- "New Questions on Friction".

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CHAPTER- 5 - Newton's Laws of Motion

Click here for → QUESTIONS FOR SHORT ANSWER

Click here for→ Newton's laws of motion - Objective - I

Click here for → Newton's Laws of Motion - Objective -II

Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 28 to 42)

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CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    

Click here for "The Forces" - OBJECTIVE-I

Click here for "The Forces" - OBJECTIVE-II

Click here for "The Forces" - Exercises

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CHAPTER- 3 - Kinematics - Rest and Motion

Click here for "Questions for short Answers"

Click here for "OBJECTIVE-I"

Click here for EXERCISES (Question number 1 to 10)

Click here for EXERCISES (Question number 11 to 20)

Click here for EXERCISES (Question number 21 to 30)

Click here for EXERCISES (Question number 31 to 40)

Click here for EXERCISES (Question number 41 to 52)

CHAPTER- 2 - "Physics and Mathematics"

Questions for Short Answers

Objective - I

Objective - II

Exercises (1 - 19)

Exercises (20 - 35)