# Physics and Mathematics Exercise Questions HC Verma Solutions Ch-2

**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 |

-: Select Topics :-

Exercise

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

(page-29)

**Question 1:**

A vector **𝐴⃗**** **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.

**Answer 1:**

**Question 2:**

Let **𝐴⃗** 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.

**Answer 2:**

**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.

**Answer 3:**

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:**

**Answer 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

**Answer 5:**

First, let us find the components of the vectors along the *x *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.

**Answer 6:**

**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.

**Answer 7:**

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.

**Answer 8:**

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.

**Answer 9:**

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 **?

**Answer 10:**

**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.

**Answer 11:**

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

Angle between the vectors, θ = 60°

**Question 12:**

Let A_{1} A_{2} A_{3} A_{4} A_{5} A_{6} A_{1} 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.

**Answer 12:**

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.

**Answer 13:**

**Question 14:**

Prove that

**Answer 14:**

**To prove:**

Hence, proved.

**Question 15:**

**Answer 15:**

Given:

**Question 16:**

. Is the converse true?

**Answer 16:**

**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.

**Answer 17: **

**Question 18:**

The force on a charged particle due to electric and magnetic fields is given by

Suppose **E⃗ **is along the X-axis and **B⃗ **along 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?

**Answer 18:**

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

.

**Answer 19:**

**To prove:**

Hence, proved.

**Question 20:**

#### 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* = 2*x*^{2}and the slope of

**Answer 20:**

**Question 21:**

A curve is represented by *y* = sin *x*. If *x* is changed from

find approximately the change in *y*.