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| Physics 11th Chapter 2 Vectors and Equilibrium Questions Bank |
Physics 1st Year Chapter 2 Vectors and Equilibrium Questions Bank
MCQs
Please select the right answer.
1. The magnitude of the vector 2/3i ̂ −1/3ĵ +2/3k is
2. A body is in dynamic equilibrium only when it is
3. An example of scalar quantity is
4. The magnitude of a vector can never be:
5. |î −j ̂ − 3k| =
6. A⃗ × A⃗ is
7. A body in equilibrium is?
8. A body will be in complete equilibrium when it is satisfying?
9. A central force is that which?
10. A force of 10N is acting along the y-axis. Its component along the x-axis is?
11. A single vector having the same effect as all the original vectors taken together, is called
12. A unit vector is obtained by dividing a vector with:
13. A vector contains more information than a scalar. What is this extra information?
14. Addition of vector obey?
15. An airplane flies 400m due north and then flies 300m south and then flies 1200m. The net displacement is?
16. Angle between A = i and B = i – j is?
17. Arc of a triangle formed by vectors i and (i – j) is?
18. At what angle, the two vectors of the same magnitude have to oriented, if they were to be combined to give a resultant equal to a vector of same magnitude?
19. Cosθ i + Sinθ j is a?
20. Dot product of two non-zero vectors is zero, when angle between them is:
21. Five equal forces of 10N each are applied at one point and all are lying in one place. If the angles between them are equal, the resultant force will be?
22. For a body to be in complete equilibrium,
23. i. (j x k) is equal to
24. If A =Ax i ̂ +Ay j ̂ + Az k and B =Bx i ̂ +By j ̂ + Bz k then:
25. If A= 2̂i −j ̂ + 3k, then the magnitude of vector A is:
26. If 6N force act at right angle to 8N force, then the magnitude of resultant will be:
27. If A ̅ = 2̂i +j ̂ + 2k, then |A ̅| is :
28. If A⃗ + B⃗ = ⃗ B + A⃗, this shows that addition of vectors is
29. If a body is at rest, then it will be in
30. If Ax=Ay , then the angle between the vector A with x-axis will be:
31. If both components of a vector are negative, then resultant lies in:
32. If east, west, north, south, up and down are representing the direction of unit vectors, then east x south has direction along?
33. If the line of action of force passes through axis of rotation or the origin, then its torque is:
34. If the position ̅ and force are in same direction, then torque will be:
35. If the x-component of a vector is positive and y component is negative, then resultant vector lies in what quadrant:
36. If vector A⃗ is acting along y-axis, its y-component is:
37. If vector A lies in the third quadrant, its direction will be:
38. In which quadrant only, the value of ‘tan’ will be positive?
39. In which quadrant the two rectangular components of a vector have same sign?
40. In which quadrant the two rectangular components of a vector have same sign?
41. It is easier to turn a steering wheel with both hands than with a single hand because?
42. Mathematically, unit vector is described as:
43. Maximum number of rectangular components are?
44. Name the quantity which is vector:
45. Null Vector is a vector which has?
46. Out of the following set of forces, the resultant of which triplet cannot be zero?
47. Rectangular coordinate system is also called?
48. SI unit of torque is:
49. The angle between rectangular components of vector is:
50. The cross product î × ̂i =j ̂ ×j ̂ = k ×k is equal to
51. The cross product i ̂ ×j ̂ is equal to
52. The cross product of two vectors is zero when?
53. The cross product of vectors will be minimum when the angle between vectors is
54. The direction of a vector in space is specified by?
55. The direction of torque can be found by:
56. The direction of torque is
57. The direction of vector product is given by:
58. The magnitude of cross-product and dot-product of two vectors are equal, the angle between them is
59. The magnitude of dot and cross product of two vectors are 6√3 and 6 respectively. The angle between them will be
60. The magnitude of i.jxk is?
61. The magnitude of the cross product of two vectors is equal to the dot product between them. The angle between the two vectors?
62. The magnitude of vector product is given by:
63. The magnitudes of rectangular component are equal if its angle with x-axis is:
64. The maximum number of components of a vector maybe?
65. The minimum number of unequal forces whose resultant will be zero:
66. The projection of a vector B⃗ over A⃗ is:
67. The result of two forces of equal magnitudes is also equal to the magnitude of the forces. The angle between the two forces is?
68. The resultant of two forces 30 N and 40 N acting at an angle of 90° with each other is
69. The resultant of two forces of equal magnitudes is also equal to the magnitude of the forces. The angle between the two forces is.
70. The scalar product of two vectors is maximum when they are:
71. The torque acting on a body determines?
72. The unit vector along y-axis is
73. The unit vector in the direction of vector A = 2i – 2j + k is?
74. Three coplanar forces acting on a body keep it in equilibrium. They should therefore be?
75. Torque has zero value, if the angle between ̅ and is
76. Torque is defined as.
77. Two vectors A and B are making angle θ with each other. The projection of vector B on vector A is written as.
78. Two vectors are A = 3i + 2j – k and B = 3i – 2j + k then?
79. Two vectors to be combined have magnitudes 60 N and 35 N. The correct answer for the magnitude of their resultant will be:
80. Unit vector n is along?
81. Vectors A is along y axis, its component along x axis is:
82. What is the angle that the given vector makes with y-axis A = 2i + √.12 j?
83. When two vectors are anti-parallel, the angle between them is:
84. Which is not a correct relation?
85. Which of the following is a scalar quantity?
86. Which of the following pairs does not have identical dimensions?
87. Which of the following statement is correct about force and velocity?
88. Which one is a unit vector?
89. Which one is a vector:
90. Which one is not correct for a vector A = √2i +√2j?
Short Questions
1. A body of mass ‘’m’’ is moving in the downward direction to an inclined plane making an angle 0 to the horizontal.Find the magnitude of the resultant force?
2. By how many manners the two vectors are multiplied?
3. Can a body be in equilibrium under the action of a single force?
4. Can a body rotate about its center of gravity under the action of its weight?
5. Can a force directed north balance a force directed east?
6. Can a vector have a component greater than the vector's magnitude?
7. Can the magnitude of a vector have a negative value?
8. Can the magnitude of the resultant of two vectors be greater than the sum of magnitude of individual vector?
9. Can we talk of a vector of zero magnitude?
10. Can you add zero to a null vector?
11. Define null and equal vectors.
12. Define position vector and give its mathematical expression?
13. Define resultant vector?
14. Define static and dynamic equilibrium.
15. Define the term unit vector.
16. Define the Terms: (i)Unit vector (ii) Position vector (iii)Compontents of a vactor?
17. Define torque.
18. Define vector product?
19. Describe two conditions of equilibrium?
20. Differentiate between static and dynamic equilibrium.
21. Differentiate between Transnational and rotational equilibrium?
22. Give an example of a body which is in motion yet is in equilibrium?
23. Give two conditions of equilibrium.
24. Give two example of vector product?
25. How can we find the values of the rectangular components of a vector?
26. How can we subtract the vectors?
27. How would the two vectors of the same magnitude have to be oriented if they were to be combined to given a resultant equal to a vector of the same magnitudes?
28. If all the components of the vector A₁ and A₂ were reversed how would this alter A₁A₂ ?
29. If one of the components of a vector is not zero can its magnitude be zero?
30. If the body is rotating with uniform or constant velocity,What will be the angular velocity and torque acting on the body?
31. Is it possible to add a vector quantity to a scalar quantity?
32. Is it possible to add a vector quantity to a scalar quantity? Explain.
33. Mention the criterion for positive and negative torque.
34. Show that the scalar product of two vectors is commutative?
35. State condition of rotational equilibrium.
36. State Head to Tail Rule of vector addition?
37. State right hand rule to find the direction of resultant of vector product?
38. Suppose the sides of a closed polygon represent vector arranged head to tail.What is the sum of these vectors?
39. The vector so obtained are called the components of the original vectors and the original vector is called the resultant of the components?
40. The vector sum of three vectors gives a zero resultant. What can be the orientation of the vectors?
41. The vector sums of three vectors give a null vector. What can be orientation of the vectors?
42. Two vectors have unequal magnitude. Can their components be equal in magnitude?
43. Two vectors have unequal magnitude. Can their sum be zero? Explain.
44. Two vectors have unequal magnitudes.Can their sum be zero?
45. Under what circumstances would a vector have components that are equal in magnitude?
46. Under what condition the body will be in complete equilibrium?
47. Vector A lies in xy-plane. For what orientation will both of its rectangular components be negative?
48. What are rectangular components of a vector? At what angle there components are equal?
49. What do you understand by positive and negative torques?
50. What is equilibrium?
51. What is negative of A vector?
52. What is resolution of vectors?
53. What is the physical significance of cross product A× B?
54. What is the torque of a force about the point lying on the axis of rotation?
55. What is the torque of force?
56. When a body is in Translational equilibrium
57. Will the value of vector of zero magnitude?
58. With the help of diagram show that A×B = - B×A?
59. Write any two characteristics of vector product.
60. Write down the names of two examples of scalar product?
61. Write two characteristics of scalar product?
62. You are falling off the edge. What should you do to avoid falling?
Long Questions
1. Explain vector addition by rectangular components.
2. Define and explain scalar product of vectors and write its characteristics.
3. Define and explain vector product of vectors and write its characteristics. Write down the characteristics of dot and cross product.
4. Define and explain torque
5. Write down the condition for a body a to be on complete equilibrium
6. Suppose, in a rectangular coordinate system, a vector A has its tail at the point P (-2, -3) and its tip at Q (3,9).Deterrnine the distance between these two points. ,
7. A certain corner of a room is selected as" the origin of a rectangular coordinate system. If an insect is sitting on an adjacent wall at'a point having coordinates (2,1), where the units are in metres,.what is the distance of the insect from this corner of the room?
8. What is the unit vector in the direction of the vector A=4 i+3j ?
9. Two particlesare located at r₁ =3i+ 7j and r₂=-2i + 3j respectively. Find both the magnitude of the vector(r₂.r₁) and its orientation with respect to the x-axis.
10. lf a vector B is added to vector A, the result is 6i +j. If B is subtracted from A the result is -4 i +7 j. What 'is“the‘ magnitude of vector A?
11. Given that A =2i+3j and B =3i-4j, find the magnitude and angle of (a)C=A+B,and (b) D=3A-2B.
12. Find the angle between the two vectors, A =5 i+ j and B =2.i + 4 j
13. Find the work done when the point of application of the force 3i +2j moves in a straight line from the point (2,-1)to the point (6,4).
14. Show that the three vectors i+j+k, 2i -3j + k and 4i+j-5k are mutually perpendicular.
15. Given that A = i-2j+3k and B=3 i-4 k, find the projection of A on B.
16. Vectors A,B and C are 4 units north, 3 units west and 8 units east, respectively. Describe carefully (a) A x B (b) A x C (c) B x C
"17. The torque or turning effect of force about a given point is given by r x F where r is the
vector from the given point to the point of application of F. Consider a force
F = -3i+j+5k (newton) acting on the point 7i+3j+k (m). What is the torque
in N m about the origin?"
18. The line of action of force, F = i -2j, passes through a point whose position vector is (-j+k ). Find (a) the-moment of F about the origin, (b) the moment of F about the point of which the position vector is i +k.
19. The magnitude of dot and cross products of two vectors are 6√3 and 6 respectively. Find the angle between the vectors
20. A load of 10.0 N is suspended from a clothes line. This distorts the line so that it makes an angle of 15° with the horizontal at each end. Find the tension in the clothes line.