Physics and Mathematics Exercise Questions HC Verma Solutions Ch-2 Concept of Physics Vol-1 for Class-11. Solution of Exercise Questions of Ch-2 Physics and Mathematics HC Verma Concept of Physics . Visit official Website CISCE for detail information about ISC Board Class-11 Physics.

## Physics and Mathematics Exercise Questions HC Verma Solutions Ch-2 Concept of Physics Vol-1 for Class-11

 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 Exercise Questions Page-Number 29 , 30

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### Physics and Mathematics Exercise Questions HC Verma Solutions Ch-2 Concept of Physics Vol-1 for Class-11

(page-29)

#### Question 1:

A vector  𝐴 makes an angle of 20° and  B ⃗  makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.  Question 2:

Let 𝐴 and  B ⃗  be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angle 30° and 60° respectively, find the resultant.  Question 3:

#### Add vectors 𝐴⃗, B⃗ and C⃗ each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.

First, we will find the components of the vector along the x-axis and y-axis. Then we will find the resultant x and y-components.  x-component of  #### Question 4:  #### Question 5:

Refer to figure (2-E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of  First, let us find the components of the vectors along the and y-axes. Then we will find the resultant x and y-components. Question 6:

Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit. Question 7:

A spy report about a suspected car reads as follows. “The car moved 2.00 km towards east, made a perpendicular left turn, ran for 500 m, made a perpendicular right turn, ran for 4.00 km and stopped”. Find the displacement of the car.

The displacement of the car is represented by AD→.  Hence, the displacement of the car is 6.02 km along the direction tan –1  (1/12 ) with positive the x-axis.

#### Question 8:

A carrom board (4 ft × 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the from edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (a) from the centre to the front edge, (b) from the front edge to the hole and (c) from the centre to the hole. Consider that the queen is initially at point A as shown in the figure.
Let AB be x ft. Question 9:

A mosquito net over a 7 ft × 4 ft bed is 3 ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net. (a) Find the magnitude of the displacement of the mosquito. (b) Taking the hole as the origin, the length of the bed as the X-axis, it width as the Y-axis, and vertically up as the Z-axis, write the components of the displacement vector.

Displacement vector of the mosquito,  Question 10:

#### Suppose a⃗ is a vector of magnitude 4.5 units due north. What is the vector (a) 3 a⃗  , (b) —4 a⃗ ?

Given: Question 11:

Two vectors have magnitudes 2 m and 3m. The angle between them is 60°. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.

Let the two vectors be a⃗  = 2 m and b=3 m.

Angle between the vectors, θ = 60° #### Question 12:

Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result. According to the polygon law of vector addition, the resultant of these six vectors is zero. Here, a = b = c = d = e = f (magnitudes), as it is a regular hexagon. A regular polygon has all sides equal to each other. Question 13: Find the angle between them. Question 14:

Prove that To prove: Hence, proved.

#### Question 15: Given: Question 16: . Is the converse true?  Question 17:

A particle moves on a given straight line with a constant speed ν. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that is independent of the position P.  Question 18:

The force on a charged particle due to electric and magnetic fields is given by Suppose Eis along the X-axis and Balong the Y-axis. In what direction and with what minimum speed ν should a positively charged particle be sent so that the net force on it is zero?

According to the problem, the net electric and magnetic forces on the particle should be zero.  So, the particle must be projected at a minimum speed of E/ B along the +ve z-axis( ∅=90) as shown in figure  so that force is zero

#### Question 19:

Give an example for which .

To prove:  Hence, proved.

#### Draw a graph from the following data. Draw tangents at x = 2, 6 and 8. Find the slopes of these tangents. Verify that the curve draw is y = 2x2and the slope of   Question 21:

A curve is represented by y = sin x. If x is changed from find approximately the change in y. 