CHAPTER # 2: VECTORS AND EQUILIBRIUM 1. Which one is a vector: a) Length b) Volume c) Veloc...
CHAPTER #
2: VECTORS AND EQUILIBRIUM
1. Which one is a vector:
a) Length
b) Volume
c)
Velocity
d) Work
2. An example of scalar quantity is
a) Displacement
b) Speed
c) Velocity
d) Torque
3. Name the quantity which is vector:
a) Density
b) Power
c)
Charge
d) Moment of Force
4. Rectangular coordinate system is also called:
a) Polar coordinate system
b) Cartesian coordinate system
c)
Cylindrical
coordinate system
d)
Space
coordinate system
5. The direction of a vector in space is specified by:
a) One angle
b) Two angle
c) Three angle
d)
No angle
6.
If both
components of a vector are negative, then resultant lies in:
a) 1st quadrant
b)
2nd quadrant
c)
3rd quadrant
d)
4th quadrant
7.
In which
quadrant the two rectangular components of a vector have same sign?
a) 1st
b)
2nd
c)
both 1st and 3rd
d)
4th
8.
If the
x-component of a vector is positive and y-component is negative, then resultant
vector lies in what quadrant:
a) 1st quadrant
b)
2nd quadrant
c)
3rd quadrant
d)
4th quadrant
9.
If vector
A lies in the third quadrant, its direction will be:
a) 180 −
b) 360 −
c) 180 +
d)
10. A single vector having the same
effect as all the original vectors taken together, is called
a) Resultant vector
b) Equal vector
c)
Position
vector
d) Unit vector
11. When two vectors are
anti-parallel, the angle between them is:
a) Zero
b) 180°
c)
90°
d) 270°
12. The resultant of two forces 30 N and 40 N acting at
an angle of 90° with each other is
a)
30 N
b)
40 N
c) 50 N
d) 70 N
13. The
magnitude of the vector ̂− ̂+ is:
a) Zero
b) One
c)
Three
d)
14. If 6N force act at right angle to
8N force, then the magnitude of resultant will be:
a) 6N
b)
8N
c) 10N
d)
14N
⃗ ⃗
⃗ ⃗
15. If A
+ B = B + A, this shows that addition of vectors is
a) Associative
b)
Commutative
c) Additive
d) Additive inverse
16. A body is in dynamic equilibrium only when it is
a) At rest
b)
Moving
with a variable velocity
c) Moving with uniform acceleration
d)
Moving
with uniform velocity
17. The unit vector along y-axis is
a)
̂
b)
̂
c)
d)
None
18. Mathematically, unit vector is described as:
b)
|
⃗
|
||||
a)
|
A = A A
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||||
A =
|
⃗
|
||||
c)
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|||||
d)
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A = ⃗
|
||||
A = A . A
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|||||
19. A unit
|
vector is obtained by dividing a vector with:
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||||
⃗ ⃗
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|||||
a)
|
Its
direction
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||||
b)
|
Its
magnitude
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||||
c)
|
Its magnitude and direction
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||||
d)
|
None
|
||||
20. The unit vector in the
direction of vector
A = 2 ̂− 2 ̂+ is:
a) 2 ̂− 2
̂+
c) (2 ̂− 2 ̂+
|
) / 3
|
||
b)
|
(
|
2 ̂− 2 ̂+
|
) / 9
|
d)
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(
|
) / 5
|
|
2 ̂− 2 ̂+
|
|||
1
Written
and composed by Prof. Muhammad Ali Malik, Govt. Degree College, Naushera,
Khushab, 0301-6775811
A =
|
̂−
|
̂
|
21. The
magnitude of a vector ⃗
|
a)
+
b)
−
c)
+
d)
−
22. Vectors A is along y axis, its
component along x axis is:
a)
A
b) A/2
c)
Zero
d) 2A
23. The angle between rectangular
components of vector is:
a) 45°
b) 60°
c) 90°
d) 180°
24. A force of 10N is acting along
x-axis, its component along y-axis is
a) 10N
b) 5N
c) 8.66N
d)
Zero N
25.
|
If vector
|
⃗
|
is acting along y-axis, its
y-component is:
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|||||||||||
a)
|
A
|
|||||||||||||
A
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||||||||||||||
b)
|
cos
|
|||||||||||||
c)
|
||||||||||||||
d)
|
Zero
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|||||||||||||
sin
|
||||||||||||||
26.
|
If
|
= 2 ̂− ̂+ 3
|
, then
the magnitude of vector A
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|||||||||||
is:
|
||||||||||||||
a)
|
4
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|||||||||||||
c)
|
14
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|||||||||||||
b)
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||||||||||||||
None
|
||||||||||||||
d)
|
√14
|
|||||||||||||
27.
|
a) ̂−
|
̂− 3
|
=
|
|||||||||||
b)
|
√5
|
|||||||||||||
c)
|
√7
|
|||||||||||||
d)
|
√11
|
, then
|
is :
|
|||||||||||
28. If
|
√13
|
̅
|
||||||||||||
̅
|
̂+ 2
|
|
|
||||||||||||
= 2 ̂+
|
|
|
|||||||||||||
a)
Zero
b) 3
c) 5
d)
9
29. Dot product of two non-zero
vectors is zero, when angle between them is:
a) 0
b) 30
c) 45
d) 90
30. The cross product ̂× ̂= ̂× ̂= × is equal to
a)
1
b) -1
c)
Zero
d) None
31. The scalar product of two vectors is maximum when
they are:
a)
Parallel
b) Perpendicular
c) Anti-parallel
32. Two vectors A and B are making
angle θ with each other. The projection of vector B on vector A is written as.
⃗
⃗
a) A. B/
⃗
⃗
b) A. B/
c)
cos θ
d) Both a and b are correct.
⃗
⃗
33. The projection of a vector B over A is:
a)
cos
b)
cos
c)
sin
d)
sin
34. If
|
=
|
̂+
|
̂+
|
and
|
=
|
̂+
|
̂+
|
then:
|
|
b)
|
.
|
=
|
+
|
+
|
a)
|
.
|
=
|
+
|
+
|
c)
|
||||
d)
|
.
|
=
|
+
|
+
|
.
|
=
|
+
|
+
|
35. The magnitude of vector product
is given by:
a)
$ sin
b)
$ sin
c)
$ cos
d)
$ tan
36. The direction of vector product
is given by:
a) Head to tail rule
b)
Right
hand rule
c) Left hand rule
d)
Triangular
rule
37. The cross product ̂× ̂is equal to
a)
zero
b) one
c) –
d)
|
|||
Torque
has zero value, if the angle between
and
|
|||
38.
|
is
|
0
|
̅
|
a)
|
°
|
||
b)
|
|||
c)
|
90°
|
||
d)
|
270°
|
||
180°
|
|||
39. ̂. ̂× is equal to
a)
1
b)
0
c) −1
d) −
40. The cross product of vectors will
be minimum when the angle between vectors is
a)
35
b)
90
c)
0
d) 45
41. The direction of torque is
a) Along position vector ̅
b) Parallel to the plane containing ̅and
c)
Along
force
d) Perpendicular to the plane containing ̅and
⃗
⃗
42. A × A is
a)
A
b)
c) 2A
d)
Zero
2
Written
and composed by Prof. Muhammad Ali Malik, Govt. Degree College, Naushera,
Khushab, 0301-6775811
43. If the position ̅and force are in same direction, then
torque will be:
a)
Maximum
b) Minimum
c) Same
d) Negative
44. The direction of torque can be found by:
a) Head to tail rule
b) Right hand rule
c)
Left hand
rule
d) Fleming rule
45. 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?
a) 45°
b)
90°
c)
120°
d) 180°
46. If the line of action of force
passes through axis of rotation or the origin, then its torque is:
a) Maximum
b)
Unity
c) Zero
d)
None of
these
47. The magnitude of a vector can never be:
a) Positive
b)
Negative
c) Positive and negative
d)
None of
these
48. The minimum number of unequal
forces whose resultant will be zero:
a) 2
b)
3
c)
4
d) 5
49. Torque is defined as.
a) Turning effect of force
b) Cross product of force and position vector
c)
Product
of force and moment arm
d) All a, b and c are correct
50. SI unit of torque is:
a) Nm-1
b)
Nm
c)
Nm-2
d)
None
51. A body will be in complete
equilibrium when it is satisfying:
a) 1st
condition of equilibrium
b)
2nd condition of equilibrium
c)
Both 1st and 2nd condition of equilibrium
d)
Impossible
52. For a body to be in complete equilibrium,
a) = 0 D = 0
b) ∑ = 0
c) ∑ = 0
d)
None
53.
If a body
is at rest, then it will be in
a) Static equilibrium
b)
Dynamic
equilibrium
c) Translational equilibrium
d) Unstable equilibrium
54. The magnitudes of rectangular
component are equal if its angle with x-axis is:
a)
45°
b)
90°
c)
30°
d)
0°
55. If , then the angle between the vector A
=
with x
-axis will be:
a) 0
b) 30
c) 45
d) 90
56. The resultant of two forces of equal
magnitudes is also equal to the magnitude of the forces. The angle between the
two forces is.
a)
30o
b)
60 o
c)
90 o
d)
120 o
57. The magnitude of dot and cross
product of two vectors are 6√3 and 6 respectively. The angle between them will be
a)
0°
b) 30°
c)
45°
d)
60°
58. The magnitude of cross-product
and dot-product of two vectors are equal, the angle between them is
a)
Zero
b)
45°
c)
90°
d)
180°
59. Two vectors to be combined have
magnitudes 60 N and 35 N. The correct answer for the magnitude of their
resultant will be:
a) 15 N
b) 20 N
c) 70 N
d)
100 N
Q. No.
|
Ans.
|
Q. No.
|
Ans.
|
Q. No.
|
Ans.
|
1
|
c
|
21
|
c
|
41
|
d
|
2
|
b
|
22
|
c
|
42
|
d
|
3
|
d
|
23
|
c
|
43
|
b
|
4
|
b
|
24
|
d
|
44
|
b
|
5
|
c
|
25
|
a
|
45
|
c
|
6
|
c
|
26
|
c
|
46
|
c
|
7
|
c
|
27
|
c
|
47
|
c
|
8
|
d
|
28
|
b
|
48
|
b
|
9
|
c
|
29
|
d
|
49
|
d
|
10
|
a
|
30
|
c
|
50
|
b
|
11
|
b
|
31
|
a
|
51
|
c
|
12
|
c
|
32
|
a
|
52
|
a
|
13
|
b
|
33
|
b
|
53
|
a
|
14
|
c
|
34
|
a
|
54
|
a
|
15
|
b
|
35
|
b
|
55
|
c
|
16
|
d
|
36
|
b
|
56
|
d
|
17
|
b
|
37
|
d
|
57
|
b
|
18
|
c
|
38
|
a
|
58
|
b
|
19
|
b
|
39
|
a
|
59
|
c
|
20
|
c
|
40
|
c
|
COMMENTS