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__Chapter 2__

__Vectors and Equilibrium__

**Encircle the most appropriate answer among the following options**

*1. A scalar quantity can be described by choose which one is correct:*

(a) Magnitude

(b) Unit

**(c) Magnitude and unit **

(d) Number

*2. A vector quantity can be described by magnitude, unit and choose which one is correct:*

**(a) Direction **

(b) Rotation

(c) Dimension

(d) Unit vector

*3. Choose one Which among of the following is a vector quantity choose which one is correct: *

(a) Energy

(b) Power

(c) Work

**(d) Momentum**

*4. Choose Which among of the following is a scalar quantity choose which one is correct: *

**(a) Mass **

(b) Displacement

(c) Force

(d) Torque

*`5. Two lines are drawn at right angle to each other are known as choose which one is correct:*

(a) Coordinate axis

(b) xy-axis

(c) Components

**(d) Cartesian axis**

*6. A vector which gives the direction of a given vector is called choose which one is correct:*

**(a) Unit vector **

(b) Position vector

(c) Null vector

(d) Negative vector

*7. Choose one among the following When a vector is divided by its magnitude we get choose which one is correct:*

(a) Null vector

**(b) Unit vector**

(c) Zero vector

(d) Position vector

*8. Pick out the scalar quantity among the following choose which one is correct:*

(a) Force

(b) Torque

**(c) Time **

(d) Velocity

*9. Pick out the vector quantity among the following choose which one is correct:*

(a) Power

(b) Energy

**(c) Force **

(d) Mass

*10. The magnitude of a null vector is choose which one is correct:*

(a) One

**(b) Zero**

(c) Double

(d) Negative

*Il. Null vector is a vector having zero magnitude and choose which one is correct:*

**(a) Arbitrary direction **

(b) No direction

(c) Specific direction

(d) Opposite direction

*12. Unit vector of a vector A describes choose which one is correct:*

(a) Direction of a given vector

(b) Magnitude of a given vector

(c) Shape of a given vector

**(d) All of above**

*13. The unit vector of among vector is determined choose which one is correct:*

(a) By multiplying the vector with its own magnitude

**(b) By dividing the vector with its own magnitude**

(c) Both (a) and (b)

(d) None of these

*14. Unit vector is used to specify choose which one is correct:*

**(a) Direction of a vector **

(b) Position Of a vector

(c) Magnitude of a vector

(d) Dimension of a vector

*15. An example of a scalar quantity choose which one is correct:*

(a) Displacement

(b) Acceleration

(c) Force

**(d) Speed**

*16. An example of a vector quantity choose which one is correct:*

(a) Speed

(b) Work

**(c) Acceleration **

(d) Mass

*17. A vector which has magnitude one is called choose which one is correct: *

(a) Null vector

**(b) Unit vector**

(c) Resultant vector

(d) Position vector

*18. A vector which has zero magnitude is called choose which one is correct: *

**(a) Null vector **

(b) Unit vector

(c) Resultant vector

(d) Position vector

*19. The sum of two or more vectors is equal to a single vector which is called choose which one is correct:*

(a) Component of vector

(b) Product vector

(c) Null vector

**(d) Resultant vector**

*20. Resultant of two vectors of magnitude 24 and 7 is 25. The angle between them is choose which one is correct:*

**(a) 90 ^{o}**

(b) 180^{o}

(c) 360^{o}

(d) 270^{o}

*21. When a vector A is multiplied by a negative number then its direction choose which one is correct:*

(a) Remains same

**(b) Changed by 180 0**

(c) Does not change

(d) None of these

*22. When a vector A is multiplied by a positive number then its direction choose which one is correct:*

(a) Remains same

(b) Changed by 180^{o}

**(c) Does not change**

(d) None of these

*23. The splitting up of a vector into its components is called choose which one is correct:*

(a) Sum of vector

(b) Subtraction of a vector

**(c) Resolution of a vector **

(d) None of these

*24. The angle between two rectangular components is choose which one is correct:*

(a) 600

**(b) 900**

(c) 1800

(d) 2700

*25. The resultant of two anti-parallel vectors A and B is choose which one is correct:*

(a) A +B

**(b) A – B**

(c) Zero

(d) None of these

*26. Two vectors having same magnitude and direction are called choose which one is correct:*

(a) **Equal vectors **

(b) Unequal vectors

(c) Null vectors

(d) None of these

*27. The sum of two equal and opposite vectors is a vector called choose which one is correct:*

(a) Equal vector

(b) **Null vector**

(c) Position vector

(d) Unit vector

*28. The resultant of three vectors whose magnitude are 3 units in east, 12 units in north and 4 units vertically upwards is*

(a)

(b) **13**

(c)

(d) 19

*29. What is the resultant of 3N and 4N forces acting at right angle to each other choose which one is correct:*

(a) 90 N

(b) **5 N**

(c) 7

(d) 1 N

*30. If a force of 10 N makes an angle of 30 0 with x-axis, its x-component is given by choose which one is correct:*

(a) 86.6 N

(b) 0.866 N

(c) **8.66 N **

(d) None of these

*31. Choose one among the following Two forces of 10 N and 7 N respectively are acting to an object. The minimum value of resultant is choose which one is correct:*

(a) 0 N

(b) 10N

(c) 7 N

(d) **3 N**

*32. Choose one among the followingTwo forces act together on a body, the magnitude of their resultant is greatest when the angle between the forces is choose which one is correct:*

(a) 45^{0}

(b) 60^{0}

(c) **0 ^{0}**

(d) 180^{o}

*33. The position vector in xy-plane is written as choose which one is correct:*

**(a) r = x+ y**

(b) r = y + z

(c) r = y + z

(d) None of these

*34. The position vector in xz-plane is written as choose which one is correct:*

(a) r = x+ y

(b) r = y + z

**(c) r = x + z**

(d) None of these

*35 The position vector in yz-plane is given by choose which one is correct:*

(a) r = x+ z

(b) r = x + y

**(c) r = y + z**

(d) r = x + y+ z

*36. If a force of 50 N is acting along x-axis, then its component along y-axis will be choose which one is correct:*

(a) The same

(b) **Zero**

(c) Half magnitude

(d) None of these

*37. Choose one among the A force of 10 N is acting along z-axis, its component along x-axis and y-axis is choose which one is correct:*

(a) 5N, 8 N

(c) 5 N each

(d) **Zero**

*38. If two vectors of magnitude Fl and F2 act on a body at an angle O, the magnitude of their resultant is choose which one is correct:*

(a)

(b)

**(c)**

(d)

*39. The magnitude of a vector A = A*_{x}* + A*_{y}* + A*_{z}* is given by choose which one is correct:*

(a) A_{x }+ A_{y} + A_{z}

(b) A_{x }cos

**(c)**

(d) None of these

*40. If a vector A makes an angle with x-axis, the magnitude of its, x-component is choose which one is correct:*

**(a) A _{y} = A sin**

(b) A_{x} = A cos

(c) Both (a) and (b)

(d) None of these

*41. Choose one If a vector A makes an angle with x-axis, the magnitude of its y-component is choose which one is correct:*

**(a) A _{y} = A sin**

(b) A_{x} = A cos

(c) Both (a) and (b)

(d) None of these

*42. The reverse process of vector addition is called choose which one is correct:*

(a) Subtraction of a vector

(b) Addition of a vector

(c) Negative of a vector

**(d) Resolution of a vector**

*43. The expression r = a + b is for choose which one is correct: *

(a) Unit vector

**(b) Position vector**

(c) Null vector

(d) Negative vector

*44 The direction of a resultant vector R is given by choose which one is correct:*

(a) = tan^{-1}

**(b) = tan ^{-1}**

(c) = sin^{-1}

(d) None of these

*45. If both the components of a vector are negative then vector is in choose which one is correct:*

(a) 1st quadrant

(b) 2nd quadrant

**(C) 3rd quadrant **

(d) 4th quadrant

*46. The scalar product is also known as choose which one is correct: *

(a) Vector product

**(b) Dot product**

(c) Vector sum

(d) Scalar sum

*47. The scalar product of A and B is given by choose which one is correct:*

(a) A x B

**(b) A . B **

(c) A – B

(d) AB

*48. The projection of vector A on B is given by choose which one is correct: *

**(a)**

(b)

(c) AB cos ~~0~~

(d)

*49. The self scalar product of A is given by choose which one is correct:*

(a)

(b) A^{3}

**(c) A ^{2}**

(d) A

*50. If A and B are anti-parallel then their scalar product is choose which one is correct:*

(a) AB cos ~~0~~

**(b) -AB**

(c) -AB cos ~~0~~

(d) Zero

*51. The scalar product of two similar unit vector is choose which one is correct:*

**(a) One **

(b) Zero

(c) Twice

(d) Negative

*52. If A . B = B . A this is called choose which one is correct: *

**(a) Commutative law**

(b) Associative law

(c) Distributive law

(d) None of these

*53. If the multiplication of two vectors results into a vector quantity then the product is called choose which one is correct:*

(a) Dot product

**(b) Vector product**

(c) Scalar product

(d) None of these

*54. If the multiplication of two vectors result into a scalar quantity then the product is called choose which one is correct:*

(a) Vector product

(b) Cross product

**(c) Scalar product **

(d) None of these

*55. If A x B points along positive z-axis, then vector A and B will lie in choose which one is correct:*

(a) zx-plane

**(b) xy-plane**

(c) yz-plane

(d) None Of these

*56. If two vectors A and B are non-parallel vectors then the direction of A x B is along choose which one is correct:*

(a) y-axis

**(b) z-axis**

(c) x-axis

(d) None of these

*57. Select the correct answer choose which one is correct:*

(a) . =

**(b) . = 0**

(c) . =

(d) . = 1

*58. Select the correct one choose which one is correct: *

(a) A . B = – B . A

(b) A . B = ½ B . A

**(c) A . B = B . A **

(d) None of these

*59. Which of the following unit vectors represent the direction of normal drawn on a specific surface choose which one is correct:*

(a)

(b)

**(c)**

(d)

*60. If A= 2 +4 + 5 and B = 2 +2 + ,What will be the value of A . B choose which one is correct:*

(a)** 9**

(b) -9

(c) 5

(d) 10

*61 If A= 2 +4 + 5 then What will be the value of choose which one is correct:*

(a)

(b)

**(c)**

(d) None of these

*62. The scalar product of two vectors is zero when choose which one is correct: *

(a) They are equal vectors

(b) They are in the same direction

**(c) They are at right angle **

(d) None of these

*63. If the vectors A and B are parallel to each other then choose which one is correct:*

**(a) A . B = AB**

(b) A . B AB

(c) A . B = 0

(d) A . B = AB cos ~~0~~

*64. If A = A*_{x}* + A*_{y}* + A*_{z}* and B = B*_{x}* + B*_{y}* + B*_{z}* then the value of A . B is choose which one is correct:*

(a) A_{x}B_{x} + A_{,y}B_{y }+ A_{z}B_{z}

**(b) A _{x}B_{x}+ A_{y}B_{z} +A_{z}B_{z}**

(d) None of these

*65. The scalar product of two vectors will be negative if choose which one is correct:*

(a) They are at right angle to each other

(b) They are parallel

**(c) They are anti-parallel **

(d) None of these

*66. The dot product of . = . = . is equal to choose which one is correct:*

(a) 0

**(b) 1**

(c) -1

(d) 2

*67. The dot product of . = . = . is equal to choose which one is correct:*

**(a) 0**

(b) 1

(c) -1

(d) 2

*68. The vector product of two vectors A and B is given by choose which one is correct:*

(a) AB sin ~~0~~

**(b) AB sin 0**

(c) AB sin ~~0 ~~

(d) none

*69. Vector product does not hold choose which one is correct: *

**(a) Commutative law**

(b) Associative law

(c) Distributive law

(d) None of these

*70. The direction of vector product is choose which one is correct: *

(a) Parallel to plane

**(b) Perpendicular to plane**

(c) Anti-parallel

Along the plane

*71. Self cross-product of a vector is equal to choose which one is correct:*

**(a) Zero **

(b) One

(c) Double

(d) Negative

*72. The cross product of unit vectors . = . = .*

(a) One

(b)

(c)

**(d) Zero**

*73. If A x B = 0 then the angle between the vectors is choose which one is correct:*

(a) 600

(b) 900

(c) 270 0

**(d) 1800**

*74. The magnitude of A x B is equal to area of choose which one is correct:*

(a) Triangle

(b) Circle

**(c) Parallelogram **

(d) Rectangle

*75. The cross product of two vectors will be negative when choose which one is correct:*

(a) They are anti-parallel

**(b) They are parallel**

(c) They are rotated through an angle of 270^{0}

(d) None of these

*76. The cross product of two parallel vectors A and B is equal to choose which one is correct:*

(a) AB sin ~~0~~

(b) AB sin ~~0~~

(c) AB

**(d) Zero**

*77. Select the correct one choose which one is correct: *

(a) A . B = A . B

**(b) A x B A x B**

(c) ** **A x B = A x B

(d) None of these

*78. The cross product of i x j is equal to choose which one is correct: *

**(a)**

(b)

(c) 0

(d)

*79. The cross product of x is equal to choose which one is correct:*

(a)

**(b)**

(c) 0

(d)

*80. Select the correct one choose which one is correct:*

**(a) x = **

(b) x =

(c) x =

(d) x =

*81. The turning effect of a force is called its moment or choose which one is correct:*

(a) Momentum

(b) Inertia

**(c) Torque **

(d) Impulse

*82. The perpendicular distance from the line of action to the pivot is called choose which one is correct:*

(a) Displacement

(b) Momentum

(c) Moment distance

**(d) Moment arm**

*83. The SI unit of torque is choose which one is correct:*

(a) N , m^{2}

**(b) N , m**

(c) N/m^{2}

(d) N^{2}m

*84. The expression for torque is given by choose which one is correct: *

(a) rF cos ~~0~~

**(b) rF sin **~~0~~

(c) rF sin ~~0~~

(d) rF cos ~~0~~

*85. Torque acting on a body determines its choose which one is correct: *

(a) Velocity

**(b) Momentum**

(c) Force

(d) Angular momentum

*86. When line of action of applied force passes through the pivot point then torque will be choose which one is correct:*

(a) Maximum

(b) Constant

(c) Negative

**(d) Zero**

*87. The direction of torque t = r x F is determined by choose which one is correct:*

(a) Head to tail rule

**(b) Right hand rule**

(c) Left hand rule

(d) None of these

*88. Conventionally anti-clock wise torque is taken as choose which one is correct:*

(a) Zero

(b) Negative

**(c) Positive **

(d) None of these

*89. Conventionally clockwise torque is taken as choose which one is correct: *

(a) Zero

**(b) Negative**

(c) Positive

(d) None of these

*90. Torque is also called as choose which one is correct: *

(a) Moment of inertia

(b) Moment arm

**(c) Moment of force **

(d) Angular velocity

*91. The dimension of torque are choose which one is correct: *

**(a) [ML ^{2}T^{2}]**

(b) [MLT^{-I}]

(c) [MOT]

(d) [M^{2}LT-^{2}]

*92. Torque = *__ __* x Force choose which one is correct: *

(a) Velocity

(b) Momentum

(c) Arm of the weight

**(d) Moment arm**

*93. Let torque r= r x F then direction of torque is choose which one is correct:*

(a) In the direction F

(b) In the direction of r

**(c) Normal to the plane**

(d) None of these

*94. Two equal and opposite forces acting on a body form a choose which one is correct:*

(a) Momentum

(b) Torque

**(c) Couple **

(d) None of these

*95. Indicate The point at which the whole weight of the body acts is called choose which one is correct:*

(a) Torque

**(b) Centre of gravity**

(c) Centre of mass

(d) Centre of the body

*96. The centre of gravity of a uniform body is choose which one is correct: *

(a) At the axis of rotation of the body

**(b) At its centre**

(c) At its one end

(d) None of these

*97. The centre of gravity of a triangular plate is choose which one is correct: *

(a) At the axis of rotation of the body

(b) At its centre

**(c) At the intersections of medians **

(d) None of these

*98. If a body is at rest or moving with uniform velocity then it is said to be in choose which one is correct:*

(a) Torque

**(b) Equilibrium**

(c) Both (a) and (b)

(d) None of these

*99. Torque has zero value if angle between r and F choose which one is correct:*

(a) 60^{0}

(b) 45^{0}

(c) 90^{0}

**(d) 0 ^{0}**

*100. The torque has maximum value if angle between r and F is choose which one is correct:*

(a) 60^{0}

(b) 45^{0}

**(c) 90 ^{0}**

(d) 0^{0}