# Book 1: Chapter No 2 Vector and Equilibrium

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## Book 1: Chapter No 2

Vector and Equilibrium

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Question 1 |

A vector is a physical quantity which has

A | magnitude |

B | Direction |

C | Both magnitude and direction |

D | either magnitude or direction |

Question 2 |

Scalar is a physical quantity which is completely described by a

A | Number only |

B | Direction only |

C | Number with proper units |

D | Number with direction |

Question 3 |

Which of! the following is a scalar quantity'

A | Velocity |

B | Speed |

C | force |

D | Momentum |

Question 4 |

The vector in space has

A | One component |

B | Two components |

C | Three components' |

D | None of these |

Question 5 |

The vector in a plane has

A | one component |

B | Two components |

C | Three components |

D | None of these |

Question 6 |

Rectangular coordinate system has

A | only one axis |

B | two axis |

C | three axes |

D | two or three axes |

Question 7 |

. If A . is unit vector in tbe direction of A, then

A | A^= A/A |

B | A^= A/{A} |

C | A^={ A}/A |

D | A=A.{A} |

Question 8 |

The positions of two aeroplanes at any instant are (2, 3, 4) and (5, 6, 7) from an origin in km, then distance between the two aeroplanes is

A | 5.2 km |

B | 4.3 km |

C | 5.8 km |

D | 6 km |

Question 9 |

0009.A force F = 2i + 3,j units, has its point of application moved from the point (1, 3)to the point (5, 7). work done is

A | 12 units |

B | 16 units |

C | 20units |

D | 22 units |

Question 10 |

Which of the following is the only scalar quantity?

A | Energy |

B | Velocity |

C | Force |

D | Torque |

Question 11 |

Name the quantity which is vector

A | Density |

B | Power |

C | Charge |

D | Impulse |

Question 12 |

An example of scalar quantity is

A | Displacement. |

B | Speed |

C | Velocity |

D | Acceleration |

Question 13 |

Name a quantity which .is vector

A | work |

B | speed |

C | Acceleration |

D | mass |

Question 14 |

Which of the following is vector quantity

A | Length |

B | Volume |

C | Mass |

D | Velocity |

Question 15 |

A vector which has magnitude one is called

A | A resultant vector |

B | A unit vector |

C | A null vector |

D | A positive vector |

Question 16 |

When a vector is multiplied by a negative number its direction

A | Remains same |

B | Changes by 180° |

C | Becomes vertical |

D | does not change |

Question 17 |

Position vector of point in xy - plane is given by

A | r = y i + z k |

B | r = y i + y k |

C | r = x i + z k |

D | None of these |

Question 18 |

Which one of the following is a scalar

A | Velocity |

B | Acceleration |

C | Force |

D | Time |

Question 19 |

Position vector of point in XZ-plane is given by

A | r = y i +z k |

B | r = x i +y k |

C | r = x i +z k |

D | r = x i + y j + z k |

Question 20 |

The sum of two or more vector is equal to a single vector which is

A | Component vector |

B | Product vector |

C | Resultant vector |

D | Position vector |

Question 21 |

Two forcees each of magnitude F act perpendicular to each other. The angle made by the resultant force with the horizontal will be

A | 30° |

B | 45° |

C | 60° |

D | 90° |

Question 22 |

The angle between two rectangular components of any 'Vector

A | 30° |

B | 50° |

C | 180° |

D | 90° |

Question 23 |

A force of 5N is acting along Y-axis. Its component along X-axis is

A | 5 N |

B | Zero |

C | IO N |

D | 2.5 |

Question 24 |

If the resultant of two vectors each of magnitude F is also of magnitude F,. the angle between them will be

A | 90° |

B | 60° |

C | 30° |

D | 120° |

Question 25 |

The Fx component of a force vector F of magnitude 30N making an angle of 60° with X-axis is

A | 7 N |

B | 15 N |

C | 5 N |

D | 10 N |

Question 26 |

The resultant of two forces 3N and 4N making an angle 90° with each other is

A | 1.0 N |

B | 7 N |

C | 5 N |

D | 3.5 N |

Question 27 |

The minimum number of unequal forces whose vector sum can be zero is

A | 1 |

B | 2 |

C | 3 |

D | 4 |

Question 28 |

Two forces act together on an object. The magnitude of their resultant is minimum when the angle between the forces is

A | 0° |

B | 45° |

C | 60° |

D | 180° |

Question 29 |

When two equal forces F and F make an angle of 180° with each other, the magnitude of their resultant is

A | F |

B | 2F |

C | 0 |

D | 3F |

Question 30 |

If a force of 10N makes an angle of 30°• with x-axis, its x-component is given By

A | 0.866 N |

B | 0.8867 N |

C | 89.2 N |

D | 8.66 N |

Question 31 |

To add vectors we add their representative lines by

A | Head to tail rule |

B | Right hand rule |

C | Left hand rule |

D | Hit and trial principle |

Question 32 |

If x-component of a vector is 3 N and y-component is -3 N, then angle of the resultant vector with x-axis will be

A | 45" |

B | 315" |

C | 135" |

D | 225" |

Question 33 |

If A = 3i + 4j, then the magnitude of A will he

A | 7 |

B | 5 |

C | 25 |

D | 1 |

Question 34 |

Two forces of same magnitude are acting on an object, the magnitude of their resultant is minimum if the angle between them is

A | 45° |

B | 60° |

C | 90° |

D | 180° |

Question 35 |

If two forces each of magnitude 5 N act along the same line on a body then the magnitude of their resultant will he

A | 5 N |

B | 10 N |

C | 20 N |

D | 30 N |

Question 36 |

If vector A = i +.i + k then its magnitude Will he.

A | 3 |

B | 3 (3^1/2) |

C | 3^1/2 |

D | (3^1/2)/3 |

Question 37 |

When two equal and opposite vectors are added, then their. resultant will have

A | Same magnitude |

B | Double magnitude |

C | Zero magnitude |

D | Half magnitude |

Question 38 |

A vector F makes an angle 8 with y-axis then its y-component is

A | F sin? |

B | F cos? |

C | F tan? |

D | F cos? |

Question 39 |

If the resultant of two forces, each of magnitude A, is also of same magnitude, then the angle between them will be

A | 30° |

B | 60° |

C | 90° |

D | 120° |

Question 40 |

A force of 20N is acting along x-axis. Its component along x-axis is.

A | 20 N |

B | 10 N |

C | 5 N |

D | Zero |

Question 41 |

Null vector is a vector having zero magnitude and

A | No direction |

B | Specific direction |

C | Arbitrary direction |

D | None of these |

Question 42 |

All the following are vectors except

A | Impulse |

B | Momentum |

C | Torque |

D | Density |

Question 43 |

A vector whose magnitude is one is called

A | Null vector |

B | Unit vector |

C | Position vector. |

D | Positive vector |

Question 44 |

Unit vector is used to specify

A | Magnitude of a vector |

B | Dimension of a vector |

C | Direction of a vector |

D | Position of vector |

Question 45 |

The unit vector of a vector A of magnitude 2 is

A | 2A |

B | A^2 |

C | A/2 |

D | A^2/2 |

Question 46 |

Vector A = Ax i + Ay j lies in

A | First quadrant |

B | Second quadrant |

C | Third quadrant |

D | Fourth quadrant |

Question 47 |

The angle of a vector A = A, i - AYJ with the x-axis will be in between

A | 0° to 90° |

B | 90° to 180° |

C | 180° to 270° |

D | 270° to 360° |

Question 48 |

A vector having magnitude equal to given vector but in opposite direction is called

A | Unit vector |

B | Positive vector |

C | Negative vector |

D | Position vector |

Question 49 |

If two equal unit vectors are inclined at an angle of 90°, then magnitude of their resultant will be

A | 2 |

B | 2*1/2 |

C | 1 |

D | 0 |

Question 50 |

The magnitude of resultant of three vectors is 3. Its x-component

A | 4 |

B | 1 |

C | 2 |

D | 0 |

Question 51 |

The y-component of a vector l00N force, making an angle of 30° with the x-axis is

A | 50 N |

B | 20 N |

C | 10 N |

D | 80 N |

Question 52 |

If B = i - 2.i + 2k, then unit vector along B will be

A | 3 |

B | 3B |

C | i-2j+2k |

D | B/3 |

Question 53 |

Two force~ of same magnitude F act on body inclined at an angle of 90 then the magnitude of their resultant is.

A | (2^1/2)F |

B | (2F)^1/2 |

C | 2F |

D | F/2 |

Question 54 |

The unit vector in the direction of vector A=

A | 2i^-2j^+k^/3 |

B | 2i^-2j^+k^/9 |

C | 2i^-2j^+k^/5 |

D | 2i^-2j^+k^ |

Question 55 |

If displacement of a body is t =3i, its only significance is

A | The displacement of 3 units is not along any axis. |

B | The displacement of 3 units along z-axis |

C | The displacement of 3 units along y-axis |

D | The displacement of 3 units along x-axis. |

Question 56 |

1ft =2i'+j+2kthen It I is

A | 0 |

B | 3 |

C | 6 |

D | 9 |

Question 57 |

The magnitude of a vector A=Axi+A)j+Azk is

A | Ax2+Ay2+Az2 |

B | (Ax+Ay+Az)^2 |

C | (Ax2+Ay2+Az2)^1/2 |

D | A/(3)^1/2 |

Question 58 |

Two vectors of magnitudes AI and A2 inclined to each other at an angle e have resultant of magnitude'

A | {(A1)^2+(A2)^2+2A1A2cos?}^1/2 |

B | {(A1)^2+(A2)^2+2A1A2}^1/2 |

C | {(A1)^2+(A2)^2+A1A2cos?}^1/2 |

D | {(A1)^2+(A2)^2+cos?}^1/2 |

Question 59 |

The second condition of equilibrium is satisfied if

A | The vector sum of all the forces is zero |

B | The vector sum of all the torques is zero |

C | Its angular acceleration is zero |

D | Its angular velocity is zero |

Question 60 |

Dot product of two non-zero vectors is zero ( a. b = 0) when angle between them is

A | 30° |

B | 45° |

C | 60° |

D | 90° |

Question 61 |

The scalar product of two vectors A and .B at an angle U with each other is

A | AB sin? |

B | AB |

C | AB cos? |

D | ABsec? |

Question 62 |

The Scalar or dot product of A A with itself i.e. A. A is equal to

A | 2A |

B | A^2 |

C | A/2 |

D | None of these |

Question 63 |

If A.B= 0 we conclude that

A | Either of two vectors is a null vector |

B | Both of the vectors are null vectors |

C | The vectors are mutually perpendicular |

D | All of the above |

Question 64 |

The scalar product of two vectors is zero (a. b) = 0 when

A | They are at right angles to each other |

B | They are equal vectors |

C | They are in the same direction |

D | They are opposite to each other |

Question 65 |

If the vectors A and B are of magnitude 4 and 3. cm making of 30° and 90° respectively with X-axis, their scalar product will be

A | 0 cm2 |

B | 18 cm2 |

C | 6.0 cm2 |

D | 21 cm2 |

Question 66 |

If A = 3i + 6j, B =.xi + k and A.B =12, then x will be equal to

A | 2 |

B | 4 |

C | 12 |

D | 3 |

Question 67 |

Two vectors of magnitudeN 20 N and 2m are acting on opposite direction. Their scalar product will be

A | 40 Nm |

B | 40 N |

C | -40 Nm |

D | 40 m |

Question 68 |

If A = Ai and B = Bj then A. B is equal to

A | AB |

B | Zero |

C | I |

D | AB K |

Question 69 |

If the dot product of two non-zero vectors vanishes, the vectors will be

A | Parallel to each other |

B | Anti-parallel to each other |

C | Perpendicular to each other |

D | None of these |

Question 70 |

The scalar product of two vectors negative when

A | They are parallel vectors |

B | They are anti-parallel vectors |

C | They are perpendicular vectors |

D | They are parallel with same magnitude |

Question 71 |

The dot product i.^ i^ =j^ j^ =k^ k^ is equal to

A | 0 |

B | 1 |

C | -1 |

D | i2 |

Question 72 |

If the dot product of two non-zero vectors A and B is zero, their cross product will be of magnitude

A | AB sin? |

B | B cos? |

C | AB sin? |

D | AB |

Question 73 |

The condition of complete equilibrium is satisfied if

A | Vector sum of all the torques is zero |

B | Vector sum of all the forces is zero |

C | Vector sum of all the forces and all torques iszero |

D | Angular acceleration is zero |

Question 74 |

Dot or scalar product oheys

A | Associative law |

B | Commutative law |

C | Distributive law |

D | All of these |

Question 75 |

The body moving with constant velocity , may be

A | at rest |

B | in equilibrium |

C | Changing in magnitude |

D | Changing in direction |

Question 76 |

If A = 2i + 2j and B = -2i + 2,i then A.Bwill he equal to

A | 6 |

B | 8 |

C | 32 |

D | 48 |

Question 77 |

When a force of HI N is acting on a body making an angle of 60° with x-axis and displaces this body through 10 m, then scalar' product of force and displacement is

A | 100 J |

B | 50 J |

C | 8.66 J |

D | 50 N |

Question 78 |

A body will be in rotational equilibrium only if the vector sum of all the external torques acting on a body is equal to

A | Maximum |

B | Unity |

C | Zero |

D | Double |

Question 79 |

What is the scalar' product of two vectors A and B making an angle 8 with each other

A | AB sin? |

B | AB |

C | AB cose? |

D | AB tan? |

Question 80 |

Scalar product of it vector A with itself is

A | A |

B | A2 |

C | 2A |

D | A/2 |

Question 81 |

If A.B = B.A, then the scalar' product is

A | Associative |

B | Additive |

C | Commutative |

D | Multiplicative |

Question 82 |

If I F1l= 3cm and I F2 l =.4cm, F1 is making an angle of 30° and F2 is making an angle of 120° with the x-axis, then their scalar product is

A | 0 cm2 |

B | 6 cm2 |

C | 10.39 cm2 |

D | 12 cm2 |

Question 83 |

If A and B are parallel then

A | A. B = 0 |

B | A. B = AB |

C | A. B = - AB |

D | A. B = I |

Question 84 |

If A. B == 0 and A -:F I) and B -:F () then

A | A,and B are parallel |

B | A and B are anti parallel |

C | A and B are perpendicular |

D | A and Bare inclined at 45° |

Question 85 |

A body is said to be in translational equilibrium provided

A | The first condition of equilibrium is satisfied |

B | The second condition of equilibrium is satisfied |

C | No torque is acting on it |

D | Its translational motion is not stopped |

Question 86 |

The vector product between two vector A and B is

A | AB sin ? |

B | AB cos ? |

C | AB sin ? n |

D | AB cos ? n |

Question 87 |

A x B for two non-zero parallel vectors will be equal to

A | AB sin |

B | AB cos |

C | AB tan |

D | 0 |

Question 88 |

If Ax B points along positive Z-axis then the vectors A and B must lie in

A | YZ-plane |

B | ZX-plane |

C | XZ-plane |

D | none of these |

Question 89 |

A metallic bob suspended by a string in the vertical plane will be in

A | Translational equilibrium |

B | complete equilibrium |

C | Rotational equilibrium |

D | none of these |

Question 90 |

The cross-product of two vector is a negative vector when

A | They are parallel vectors |

B | They are anti-parallel vectors |

C | They areperpendicular vectors |

D | They are rotated through 270° |

Question 91 |

A vector which has zero magnitude is called

A | a negative vector |

B | a null vector |

C | a unit vector |

D | a resultant vector |

Question 92 |

The reverse process of vector addition is called

A | Multiplication of a vector |

B | resolution of a vector |

C | Subtraction of vectors |

D | negative of a vector |

Question 93 |

The first condition of equilibrium of a body is satisfied if

A | Its linear velocity is zero |

B | Its linear acceleration is zero |

C | ) Its angular acceleration is zero |

D | The vector sum of all the forces is zero |

Question 94 |

A body will be in translational equilibrium only if the vector sum of all the external forces acting on a body is equal to

A | Unity |

B | Zero |

C | maximum |

D | double |

Question 95 |

Three coplanar forces acting on a body keep it in equilibrium, They should. therefore be

A | Parallel |

B | Non-Parallel |

C | Concurrent |

D | Non-Concurrent |

Question 96 |

Torque is the resultant of

A | Dot product of force and moment arm |

B | Simple product of force and moment arm |

C | Cross product between position vector and force |

D | Addition of force and moment arm |

Question 97 |

The turning effect of a force about a certain point is called

A | Momentum |

B | Angular momentum |

C | Torque |

D | Impulse |

Question 98 |

The physical quantity which produces angular acceleration' in a body is called

A | Force |

B | Centripetal force |

C | Gravitational force |

D | Torque |

Question 99 |

The vector product is

A | Commutative |

B | Associative |

C | Additive |

D | Subtractive |

Question 100 |

The magnitude of i. (i x Ii.) is

A | 1 |

B | 0 |

C | -1 |

D | j |

Question 101 |

Torque is the product between force and

A | Distance |

B | Velocity |

C | Moment arm |

D | Arm of the weight |

Question 102 |

The unit of torque in Sf units is

A | Newton-meter |

B | Dyne-meter |

C | Newton |

D | Joule |

Question 103 |

Unit of torque in SI units is

A | -m,1 |

B | N-m-2 |

C | N-kg,1 |

D | N-m |

Question 104 |

if the linc of action of thc force F passes through the axis of rotation or origin then its torque is

A | Maximum |

B | minimum |

C | zero |

D | r F sin |

Question 105 |

The point at which an applied F passes produces a linear acceleration hut not rotation is called

A | centre or the body |

B | centre of mass |

C | Centre or frame |

D | weight of the body |

Question 106 |

A force passing through the centre of gravity of a body

A | causes translational motion |

B | Causes rotational motion |

C | Produces no Illation in the body |

D | Produces both translational and rotational motion |

Question 107 |

Thc physical quantity which produces angular acceleration in a body is called

A | Angular velocity |

B | Momentum |

C | Centripetal force |

D | Torque |

Question 108 |

Torque is a

A | Scalar quantity |

B | Vector quantity |

C | Physical quantity |

D | None of these |

Question 109 |

The torque is also called as

A | Angular velocity |

B | Couple |

C | Moment or force |

D | Moment' arm |

Question 110 |

If the t1il'ection of r an Fare reversed then.

A | The magnitude 'of the torque changes but direction remain unchanged. |

B | The magnitude of the torque does not change but direction reverses. |

C | The magnitude and direction of the torque change. |

D | The magnitude and direction of the torque remain unchanged. |

Question 111 |

Conventionally, clock-wise torque is taken as

A | Negative |

B | Positive |

C | Zero |

D | None of these |

Question 112 |

Torque = Force x

A | Speed |

B | Momentum |

C | Moment arm |

D | Arm or the weight |

Question 113 |

It is easier to turn a steering wheel with both hands than with a single hand because

A | Accelerating force increases on the wheel |

B | Two forces act on the wheel |

C | Two hands provide frame grip |

D | couple acts on the wheel |

Question 114 |

Which of the following statements correctly describes the properties of two forces acting as couple

A | equal. Parallel and collinear |

B | Unequal. anti-parallel and non-collinear |

C | unequal. parallel and collinear |

D | equal. anti-parallel and non-collinear |

Question 115 |

Two equal and opposite forces acting on a body frame

A | Lincar momentum |

B | Torquc |

C | Couple |

D | None of these |

Question 116 |

In rotational motion, the torque is equal

A | Rate of change of velocity. |

B | Rate of change of angular momentum |

C | Rate of change of momentum |

D | Change or linear momentum |

Question 117 |

A couple acting on a body will only

A | Accelerate the body |

B | Vibrate the body about certain axis |

C | Rotate the body about certain axis |

D | Keep the body stationary |

Question 118 |

The perpendicular distance between the line of action of force and the axis of rotation is called

A | Displacement |

B | Distance |

C | Moment arm |

D | Angular displacement |

Question 119 |

Which is not a proper prototype?

A | int funct(char x, char y) |

B | |

C | double funct(char x) |

D | void funct() |

Question 119 Explanation:

char x()

Question 120 |

The elements of group IA and IIA are classed as

A | p-block elements |

B | f-block elements |

C | c-block elements |

D | s-block elements |

Question 121 |

while(number > 1) { factorial = factorial * number

A | number = number - 1 |

B | } cout << "The factorial is = “ << factorial |

C | Output of the program is The factorial is = ? |

D | 0 |

Question 121 Explanation:

10

Question 122 |

What is the out put of the following code segment : score = 110

A | if ( ! (score > 100) ) cout << " A century is scored" |

B | else cout << " Got to score a century" |

C | |

D | A century is scored |

Question 122 Explanation:

Nothing will display

Question 123 |

The catalytic activity of enzymes is restricted to a small portion of the enzyme known as

A | binding site |

B | |

C | active site |

D | catalytic site |

Question 123 Explanation:

2

Question 124 |

Markets are the core of the economic system

A | |

B | yes |

C | No |

D | --- |

Question 124 Explanation:

1

Question 125 |

______________provide ways to diversify risk

A | |

B | Financial intermediaries |

C | Financial interuments |

D | Financial |

Question 125 Explanation:

1

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