### CHAPTER 2: Vectors and Equilibrium

(1)               Rectangular coordinate system is also called.

(a)    polar coordinate system
(b)    Cartesian coordinate system
(c)    Cylindrical coordinate system
(d)    Space coordinate system

(2)               The direction of a vector in space is specified by.

(a)    one angle
(b)    two angle
(c)    three angle
(d)    no angle

(3)               Addition of vector obeys.

(a)    commutative law
(b)    distributive law
(c)    associative law
(d)    all given laws in a,  b and c.

(4)               A vector can be multiplied by number. The number may be.

(a)    dimensionless
(b)    dimensional scalar
(c)    negative
(d)    all a, b and c are correct.

(5)               Unit vector is along.

(a)    x-axis
(b)    normal on a surface
(c)    y-axis
(d)    z-axis

(6)               cosθi^  +  sinθj^ is a.

(a)    vector
(b)    unit vector
(c)    vector in the direction at angle with x-axis
(d)    unit vector in the direction at angle θ with x-axis

(7)               Maximum number of rectangular components are

(a)    one
(b)    two
(c)    three
(d)    infinite

(8)               Maximum number of components of a vector may be.

(a)    one
(b)    two
(c)    three
(d)    infinite

(9)        Which one is not correct for a vector             A A = √2  i^  +  √2  j^ ?

(a)    has direction θ=45 with x-axis
(b)   has magnitude 2
(c)    has magnitude 2 and direction θ=45 with y-axis
(d)   has magnitude -2

(10)     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

(11)           What is the angle that the given vector makes with y-axis?
A =  2i^+ √ 12j^

(a)       20 o
(b)   60o
(c)  90o
(d)  120o

(12) In which quadrant the two rectangular components of a vector have same sigh?

(a)    1st
(b)   2nd
(c)    both 1st and 3rd
(d)   4th

(12)           Two vectors A and B are making angle θ with each other. The scalar projection of vector B on vector A is written as.

(a)    A.B/ A
(b)   A.B/ B
(c)    A. cos θ
(d)   Both a and b are correct.

(14)           Two vectors are A = 3i^+2j^ -k^ &  B = 3i^ - 2j^ + k^ , then

(a)    B is antiparallel to A
(b)   B is negative vector of A
(c)    B has negative magnitude
(d)   B is perpendicular to A

(15)           If A=B which of the following is not correct?

(a)    A .B = A^ .B^
(b)     |A|  = |B|
(c)    |A^|  = |B^|
(d)    AB^  = BA^

(16)           i^  .  (j^  x k^)  is equal to.

(a)    1
(b)    i^
(c)    j^
(d)    k^

(17)           Which one is not a correct relation?

(a)    A x B  =  -BxA
(b)    |AxB|  =  - |BxA|
(c)    AxB   =  AB Sinθn^
(d)    BxA  =  AB Sinθ(-n^)

(18)           The direction of vector product is given by.

(a)    head to tail rule
(b)    right hand rule
(c)    left hand rule
(d)    triangular rule

(19)           If east, west, north, south, up and down are representing the direction of unit vectors, then east x south has direction along.

(a)    west
(b)    north
(c)    down
(d)    up

(20)           Null vector is a vector which has.

(a)    zero magnitude
(b)    no specified direction
(c)    both a and b are correct
(d)    both a and b are not correct

(21)           Which one is a unit vector?

(a)    √3 i^  + √3  j^ + √3  k^
(b)    1√3 i^ + 1/ √3 j^ + 1√3 k^
(c)    √3/3 i^ + √3/3 j^  + √3/3  k^
(d)    both b and c are correct

(22)           Angle between two vectors A and B can be determined by.

(a)    their dot product
(b)    their cross product
(c)    head to tail rule
(d)    right hand rule

(23)           The magnitude of cross product is equal to the dot product between the. The angle between the two vector is.

(a)    30o
(b)    45 o
(c)    60 o
(d)    180 o

(24)           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

(25)           The dimension of torque is.

(a)    [ML2T-2]
(b)    [MLT-2]
(c)    [ML2T]
(d)    [ML-2T-2]

(26)           SI unit of torque is.

(a)    N . m
(b)    Joule
(c)    Both a and b are correct
(d)    Neither a nor be is correct

(27)           Torque acting on a body determines.

(a)    acceleration
(b)    linear acceleration
(c)    angular acceleration
(d)    direction of motion of the body

(28)           A body in equilibrium.

(a)    always at rest
(b)    always in uniform motion
(c)    may be at rest or in uniform motion
(d)    may be at rest or in motion\

(29)           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

(30)           Which one is not a type of dynamic equilibrium?

(a)    rotational equilibrium
(b)    translational equilibrium
(c)    static equilibrium
(d)    both a and c are correct answer

(31)           Three coplanar force acting on a body keep it in equilibrium. They should therefore be.

(a)    concurrent
(b)    non concurrent
(c)    parallel
(d)    non parallel

(32)           Which of the following pairs does not have identical dimensions?

(a)    torque and energy
(b)    momentum and impulse
(c)    energy and work
(d)    mass and moment f inertia

(33)           A central force.

(a)    can produce torque
(b)    can’t produce torque
(c)    some time can produce torque some time can’t
(d)    it has no relation with torque

(34)           It is easier to turn a steering wheel with both hands than with a single hand because.

(a)    acceleration force increases on the wheel
(b)    two forces act on the wheel
(c)    two hands provide firm grip
(d)    couple acts on the wheel

(35)           The cross product i^ x j^ is equal to.

(a)    zero
(b)    one
(c)    –k^
(d)    k^

(36)           The unit vector in the direction of vector = 2i^  - 2j^  + k^  is.

(a)    2i^  -  2j^  + k^
(b)    (2i^  -  2j^  + k^) / 9
(c)    (2i^  -  2j^  + k^) / 3
(d)    (2i^  -  2j^  + k^) / 5

(37)           The magnitude of i^ .( j^ x k^)  is.

(a)    0
(b)    1
(c)    -1
(d)    i^
(38)           In which quadrant, only value of ‘tan’ will be positive?
(a)    first
(b)    second
(c)    third
(d)    both 1st and 3rd

(39)      If =  Ax i^ + Ayj^  +  Azk^ = Bx i^  + Byj^ + BzK^ then.

(a) . = AxBx  +   AyBy  +  AzB
(b) . = AxBy   +  AyBz   +  AzBy
(c) . = AyBz   +  AzBy   +  AzBx
(d) . =  AxBz   + AyBy   +  AzBx
(40)      The cross product of two vectors is a negative vector when.
(a)    they are parallel vectors
(b)   they are anti parallel vectors
(c)    they are perpendicular vector
(d)   they are rotated through 270o