Chapter vectors and equilibrium ETEA past MCQs solution and references
Chapter#2: VECTORS & EQUILIBRIUM
VECTORS:
1. The correct representation of
the vector
in the xy-plane
is given. In terms of the rectangular
components as:
2008-94 Med;
a.
b. c.
d.
2. If  is unit vector in the
direction of vector
than; 2009-24 Med, 2015-103 Eng
(a)
(b)
(c)
(d)
Hints:
3. Which one of the following is scalar
quantity? 2012-42
Eng.
(a) Mass (b) Acceleration
(c) Momentum (d) E.
Intensity
4. Which one of the following is
not a vector quantity? 2012-75
Med:
(a) E. F. Intensity (b) G.F Intensity (c)
Magnetic Induction (d) Emf
Answers:
1. (a).
|
3. (a) Mass
|
2.(a)
|
4. (d) Emf
|
Addition, Subtraction & Multiplication
& Products of Vector
1. Two vectors
and
are such that
+
=
–
then select the correct statement: 2015-09 Med
A)
= 0
B)
= 0 C) neither
nor
is zero D)
None of the above
2. Two forces having magnitudes
3.5N and 5.5N are acting on a body. Which one of the following cannot
be the resultant of their possible sum? 2014-53; Med
A) 1.5 N B) 2.5 N C) 4.5 N D) 6.5 N
3. If “x” component of a vector is
3N & Y component is 3N, than angle made by the resultant with n-axis is; 2012-
116 Eng:
(a) 450 (b)
3150 (c) 1350 (d) 2250
Hints: Tanq =
=
q = Tan-1
=Tan-1
=450,
4. The vectors A and B are such
that |A + B| = |A – B|, Then the angle between the two vectors is:
2014-108; Med
a) 0o b) 90o c)
60o d) 180o
5.
is
equal to; 2011-12 Med;
(a) – 1
(b) zero (c)
1 (d) 2
Hints:
6. The horizontal & vertical
component of forces are 10N each. The direction of the resultant force with
x-axis. 2011-9
Eng:
(a)
300 (b) 450 (c) 600 (d) 75
Hints: TanÓ¨
=
7.
Two forces of 12N and 6N applied simultaneously to a body. The maximum
maguitude of their resultant is; 2010-89
Eng:
(a)
24N (b) 30N (c) 18N (d) 36N
Hints:
= max, when = q = 00 ,i.e.
= 12 + 6 = 18N
8. The resultant of a/6N
force & 8N force acting at right angle to each other is of magnitude. 2006-10
Med;
(a)
14N (b) 2N (c) 10N (d) 48N
Hints: when q =
900,
=
=
=
=
= 10N
9. The magnitude of the resultant
two forces is F. The magnitude of each force is F. The angle between the forces
must be: 2006-15,
2007-175, 2009-51Med, 2013-88 Eng:
(a)
300 (b) 600 (c) 450 (d) 1200
10. The magnitude of the resultant
of two forces is 2F. If the magnitude of each force is F, than the angle
between these forces is: 2011-08
Med
(a)
00 (b) 900 (c) 1200 (d) 1800
When q= 00
than R = Maximum Þ
=
2
11.
The vectors
are such that;
(a) 00 (b) 600 (c) 900 (d) 1800
12. The magnitude of i. (ĵ ´ k)
is; 2008-03,
Med:
(a) O (b) 1 (c) -1 (d) 2
Hints : i.
(j × k) = i.i = 1
13. The angle subtended by a vector
WITH X-AXIS… 2010-98,
Med:
(a) 450 (b) 1350 (c) 2250 (d) 3150
Hints:
Tan f= Fy/FxÞf =
Tan-1 1 = 450,
As
it is 4th quadrant; so q with x-axis will be q=3600-f Thus q = 3600 – 450
= 3150
14. If
then its magnitude is; 2010-52, Med:
(a) 9 (b) 5 (c)
3 (d) 1
15. Two forces of magnitude 20N
& 10N act at a point that which one of the following cannot be their
possible sum. 2012-02
Med:
(a)
30N (b) 10N (c) 35N (d) 15N
16. Two concurrent forces have a
maximum resultant of 45N and minimum result of 5N. What is the magnitude of
each these? 2009-44
Med:
(a)
O, 45N (b) 5N, 9N (c) 20, 25N (d) ON, 45N
17.
Let
and
be
any two vectors and q be
the angle between them then |b| cosq
is protection of:
(a)
in the direction of
(b)
in the direction of
(c)
in
the direction of x-axis (d)
in the direction of y-axis
18. The
dot product of force & velocity is equal to; 2011-38, Med:
(a) Power (b) Impulse (c)
Couple (d) Momentum (Power = F.V = FV Cos q)
19. If
Than the angle b/w
2011-13
Eng:
(a)
600 (b) 750 (c) 450 (d) 300
Hints: Cosq =
&q =
Cos-1
20. If
= 1, a = 2, b = 1, the angle b/w them is 2007-121
Med
(a)
300 (b) 600 (c) 900 (d) 450
Hints: A.B
= AB Cosq& Cosq =
&q =
Cos-1
21.
Which of the following is an example of vector product of two vectors? 2011-38, Med:
(a) Linear Momentum (b) Angular Momentum (c) force (d)
Electric flux
22. If the scalar product of two
non-zero vectors A & B is zero, the magnitude of their vector product will
be 2010-65
Eng:
(a)
AB (b) Zero (c) AB Sin f (d) AB Cos q
Hints:
scalar product is zero when q = 90 & A×B = AB sin 90 =
AB
23.
If
then
will be equal
to: 2011-
16 Eng:
(a) AB
(b) Zero (c) AB sin
(d) AB Cos
If each
vector have unit magnitude than
.
is:
2016-35 Med
(a) South (b)
One (c)
North (d) West
A vector
of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum
might be:
2016-118 Med
(a) Zero (b)
3
(c) 12 (d) 47
If
.
= 1, A = 2, B = 1 then the angle between them
is:
2016-177 Med
(a) 300
(b) 600 (c) 900 (d) 450
Hints:
.
= ABcosθ,Cosθ=
.
/AB==1/2
θ= cos-1 (0.5)
Thus cos-1 (0.5) = 60°
A person
walks 10 km north, 20 km east and 10 km south, then the result displacement
is: 2016-01 Eng
(a) 10 km north-east (b) 20 km north-east
(c) 20 km east (d)
20 km west
The sum
of magnitudes of two forces is 10N. the resultant force is 8N and its direction
is perpendicular to minimum force, then the forces are: 2016-02 Eng
(a) 6N & 10N (b) 8N & 8N (c) 4N & 12N (d) 2N & 14N
If
, then what is the angle between
and
? 2016-03Eng
(a) 00
(b) 450 (c) 600 (d) 900
ANSWERS
1. B)
|
7.(c) 18N
|
13. (d) 3150
|
19. (a) 600
|
2. A) 1.5 N
|
8. (c) 10N
|
14. (c) 3
|
20. (b) 600
|
3. (a) 450
|
9. (d) 1200
|
15. (C) 35N
|
21. (b)
Angular Momentum
|
4. b) 90o
|
10(a) 00
|
16. (c) 20,
25N
|
22. (a) AB
|
5.(b) zero
|
11.(c) 900
|
17.(a)
|
23. (a) AB
|
6. (b) 450
|
12. (b) 1
|
18.(a) Power
|
Torque,Equilibrium
& Concurrent Forces
1. In thee dimensional space two
vectors are said to be collinear if they lie ; 2015-129 Eng
A) along the same line B)
along the different lines C)
Above the line D)Below the line
2. Three vectors of equal magnitude
are acting on the three sides of an equilateral triangle. The magnitude of
their resultant is. 2011-15
Med:
(a)
Zero (b) 3 (c)
(d) 1.73
3.
The minimum number of unequal forces whose vector sum can be zero are; 2010-142 Med:
(a)
One (b) Two (c) Three (d) Four
4.
A body is equilibrium must not have; 2012-150
Med;
(a) K.E (b) Momentum (c)
Velocity (d) Acceleration
5.
The minimum number of equal forces that keep the body in equilibrium
are; 2012- 97 Med;
(a) Two (b) Three (c)
Four (d) Five
6. Two or more vectors are said to
be collinear if they are:
2012- 25 Eng:
(a)
Intersecting the same line (b) parallel to
the same line
(c)
perpendicular to the same line (d) both a. and c.
Hints;Two vectors are
collinear if
they have the same direction or are parallel or anti-parallel.
7. If three coplanar forces acting
on a body keep it in equilibrium, then these forces pass are; 2007-
188 Med;
(a) Concurrent (b) Non concurrent (c) Parallel (d) Antiparallel
Hints: When two or more forces act
upon a body and the lines of action of these forces pass through a common
point, the forces are said to be concurrent.
8. The physical quantity which
produces angular acceleration in body.
2011-18,2010- 47 Med
(a) Force (b) Centripetal force (c)
Impulse (d) Torque
9. The direction of torque is:
2009-
46 Med
a. Parallel to the plane of F and r b. Perpendicular to the
plane of F and r
c. Anti – parallel to the plane of F and
rd. is the same as that of the plane of
F and r
10.
The moment arm of force of 0.6N to produce maximum torque of 0.48 N.m is;
2011-23 Eng:
(a) 2.88m (b) 8m (c)
0.8m (d) 0.288m
Hints: T = r×f, r =
=
=
0.8m
11.
Newton’s first law of motion provides:
2011-19 Eng:
(a) 1st condition of
equilibrium (b) 2nd
condition of equilibrium
(c) Complete equilibrium (d) Rotational equilibrium
12. The point at which an applied
force produces linear motion but no rotatory motion is:
2011-22 Med;2010-24 Eng;
(a) Mid-point
(b) Centre of gravity
(c) Optical centre (d)
Pole
13. Two equal, anti parallel and non
concurrent forces that produce only angular acceleration are:
2012- 94 Med;
A) Couple B)
Couple arm C) Collinear forces D) Torque
ANSWERS
1.
A) Along the same line
|
8.
( d) Torque
|
2. (a) Zero
|
9:
b. Perpendicular to the plane of F and r
|
3 (c) Three.
|
10
(c) 0.8m
|
4. (d) Acceleration
|
11. (a) 1st condition of equilibrium
|
5.
(a) Two
|
12. (b) Centre of gravity
|
6.
b) parallel to the same line
|
13. A) Couple
|
7:
(a) Concurrent
|
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