# 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

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Objective-I

Objective-II

Exercise

### Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2 Concept of Physics

#### Question 1 :-

Is a vector necessarily changed if it is rotated through an angle?

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?

No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.
Example: Let us add two vectors  𝐴  and  of unequal magnitudes acting in opposite directions. The resultant vector is given by

R= √A²+B²+2ABcos⁡θ

If two vectors are exactly opposite to each other, then

θ = 180º,cos⁡180º = −1

R = √A²+B²−2AB

⇒ R= √(A−B)²

⇒ R= (A−B) or (B−A)

From the above equation, we can say that the resultant vector is zero (R = 0) when the magnitudes of the vectors  𝐴  and   are equal (A = B) and both are acting in the opposite directions.
Yes, it is possible to add three vectors of equal magnitudes and get zero.
Lets take three vectors of equal magnitudes
𝐴 ⃗ , and C ,given these three vectors make an angle of 120º with each other. Consider the figure below:
Lets examine the components of the three vectors.

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.

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?

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 + 0 = jˆ   (Using the property of zero vector)
∴ The resultant of three unit vectors ( iˆ ,−iˆ  and jˆ )  is a unit vector ( jˆ ).

#### Question 5 :-

Can we have physical quantities having magnitude and direction which are not vectors?