Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2
Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2. Concept of Physics. Step by Step Solution of Questions for short answer of Ch-2 Physics and Mathematics. Visit official Website CISCE for detail information about ISC Board Class-11 Physics.
Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2
| Board | ISC and other board |
| Publications | Bharti Bhawan Publishers |
| Ch-2 | Physics and Mathematics |
| Class | 11 |
| Vol | 1st |
| writer | H C Verma |
| Book Name | Concept of Physics |
| Topics | Solution of Question for short answer |
| Page-Number | 27,28 |
-: Select Topics :-
Question for Short Answer
Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2 Concept of Physics
(page-27)
Question 1 :-
Is a vector necessarily changed if it is rotated through an angle?
Answer 1 :-
Yes. A vector is defined by its magnitude and direction, so a vector can be changed by changing its magnitude and direction. If we rotate it through an angle, its direction changes and we can say that the vector has changed.
Question 2:-
Is it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?
Answer 2:
No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.
Example: Let us add two vectors 𝐴 ⃗ and B ⃗ of unequal magnitudes acting in opposite directions. The resultant vector is given by
R= √A²+B²+2ABcosθ
If two vectors are exactly opposite to each other, then
θ = 180º,cos180º = −1
R = √A²+B²−2AB
⇒ R= √(A−B)²
⇒ R= (A−B) or (B−A)
Yes, it is possible to add three vectors of equal magnitudes and get zero.
Lets take three vectors of equal magnitudes
So, along the x – axis , we have:
Hence, proved.
Question 3 :-
Does the phrase “direction of zero vector” have physical significance? Discuss it terms of velocity, force etc.
Answer 3 :-
A zero vector has physical significance in physics, as the operations on the zero vector gives us a vector.
For any vector 𝐴 ⃗ , assume that
The significance of a zero vector can be better understood through the following examples:
The displacement vector of a stationary body for a time interval is a zero vector.
Similarly, the velocity vector of the stationary body is a zero vector.
When a ball, thrown upward from the ground, falls to the ground, the displacement vector is a zero vector, which defines the displacement of the ball.
Question 4 :-
Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?
Answer 4 :-
Yes we can add three unit vectors to get a unit vector.
No, the answer does not change if two unit vectors are along the coordinate axes. Assume three unit vectors iˆ, −iˆ and jˆ along the positive x-axis, negative x-axis and positive y-axis, respectively. Consider the figure given below:
The magnitudes of the three unit vectors ( iˆ, −iˆ and jˆ ) are the same, but their directions are different.
So, the resultant of iˆ and −iˆ is a zero vector.
–> Now, jˆ + 0⃗ = jˆ (Using the property of zero vector)
∴ The resultant of three unit vectors ( iˆ ,−iˆ and jˆ ) is a unit vector ( jˆ ).
Page no 28 –
Question 5 :-
Can we have physical quantities having magnitude and direction which are not vectors?
Answer 5 :-
Yes, there are physical quantities like electric current and pressure which have magnitudes and directions, but are not considered as vectors because they do not follow vector laws of addition.
Question 6 :-
(a) Two forces are added using triangle rule because force is a vector quantity.
(b) Force is a vector quantity because two forces are added using triangle rule.
Answer 6 :-
Two forces are added using triangle rule, because force is a vector quantity. This statement is more appropriate, because we know that force is a vector quantity and only vectors are added using triangle rule.
Question 7 :-
Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?
Answer 7 :-
No, we cannot add two vectors representing physical quantities of different dimensions. However, we can multiply two vectors representing physical quantities with different dimensions.
Example: Torque,
Question 8 :-
Can a vector have zero component along a line and still have nonzero magnitude?
Answer 8 :-
Example: Consider a two dimensional vector 2iˆ + 0jˆ . This vector has zero components along a line lying along the Y-axis and a nonzero component along the X-axis. The magnitude of the vector is also nonzero.
Now, magnitude of 2iˆ + 0jˆ
Question 9 :-
Let ε1 and ε2 be the angles made by 𝐴 ⃗ and –𝐴 ⃗ with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of 𝐴 ⃗.
Answer 9 :-
The direction of – 𝐴 ⃗ is opposite to 𝐴 ⃗.So, if vector 𝐴 ⃗ and −𝐴 ⃗ make the angles ε1 and ε2 with the X-axis, respectively, then ε1 is equal to ε2 as shown in the figure:
Here, tan ε1 = tan ε2
Because these are alternate angles.
Thus, giving tan ε does not uniquely determine the direction of −𝐴 ⃗.
Question 10 :-
Is the vector sum of the unit vectors i ⃗ and i⃗ a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?
Answer 10 :-
No, the vector sum of the unit vectors i ⃗ and i ⃗ is not a unit vector, because the magnitude of the resultant of i ⃗ and j ⃗ is not one.
Magnitude of the resultant vector is given by
Yes, we can multiply this resultant vector by a scalar number 1/√2 to get a unit vector.
Question 11 :-
Answer 11 :-
Question 12 :-
Can you have 𝐴 ⃗ × B ⃗ = 𝐴 ⃗ ⋅ B ⃗ with A ≠ 0 and B ≠ 0 ? What if one of the two vectors is zero?
Answer 12 :-
No, we cannot have 𝐴 ⃗ × B ⃗ = 𝐴 ⃗ ⋅ B ⃗ with A ≠ 0 and B ≠ 0. This is because the left hand side of the given equation gives a vector quantity, while the right hand side gives a scalar quantity. However, if one of the two vectors is zero, then both the sides will be equal to zero and the relation will be valid.
Question 13 :-
Answer 13 :-
If 𝐴 ⃗ × B ⃗ = 0, then both the vectors are either parallel or antiparallel, i.e., the angle between the vectors is either 0∘ or 180∘.
𝐴 ⃗ B ⃗ sin θ nˆ=0……… (∵ sin0º=sin180º=0)
Both the conditions can be satisfied:
(a) 𝐴 ⃗ = B ⃗ , i.e., the two vectors are equal in magnitude and parallel to each other
(b) 𝐴 ⃗ ≠ B ⃗ , i.e., the two vectors are unequal in magnitude and parallel or anti parallel to each other.
Question 14 :-
Answer 14 :-
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