VECTORS conceptual VECTORS VECTORS conceptual OBJECTIVE TYPE QUESTIONS

VECTORS - conceptual VECTORS

VECTORS - conceptual OBJECTIVE TYPE QUESTIONS

VECTORS - conceptual 1. Of the following vector – quantity is 1) Time 2) Electric current 3) Velocity of light 4) Gravitational force Solution: Here velocity of light is vector quantity. It has magnitude and direction where as other three are scalar quantities.

VECTORS - conceptual 2. Of the following the scalar quantity 1) Temperature 2) Moment of force 3) Moment of couple 4) Magnetic moment Solution: Temperature is scalar it has no specified direction where as other three are vectors

VECTORS - conceptual 3. The pair containing a scalar quantity and vector quantity is 1) Impulse and Angular momentum 2) Work and Frequency 3) Electromotive force and force 4) Electronic power and Energy Solution: Electromotive force (voltage) is a scalar and force is a vector

VECTORS - conceptual 4. The set containing only scalar quantities is 1) Temperature gradient, specific heat and latent heat 2) Electric intensity, Electric potential and Electric capacity 3) Polestrength, permeability and permittivity 4) Torque, Angular acceleration and linear momentum Solution: Pole strength in permeability and permittivity are scalar quantities

VECTORS - conceptual 5. The set containing only vector quantities is 1) Thermal capacity, Magnetic susceptibility and Electric charge 2) Magnetic moment, Electric intensity and Torque 3) Magnetic flux, Electric potential and Force 4) Magnetic induction, Electric capacity and Impulse Solution: Magnetic moment and electric intensity are vector quantities

VECTORS - conceptual 6. Intensity of magnetisation is 1) Scalar 2) Vector 3) both 4) none Solution: Intensity is vector quantity

VECTORS - conceptual 7. Electric potential gradient 2) Vector 1) Scalar 3) both 4) none Solution: Potential gradient means=

VECTORS - conceptual 8. Which of the following units could be associated with a vector quantity? 1) newton/ metre 2) newton metre / second 3) Kg m 2 s-2 4) newton second Solution: Newton – second is impulse. It is vector

VECTORS - conceptual 9. A vector is not changed if 1) It is rotated through an arbitary angle 2) It is multiplied by an arbitary scalar 3) It is cross multiplied by a unit vector 4) It is slid parallel to itself Solution: If a vector slide parallel to itself its direction remains constant

VECTORS - conceptual 10. Choose the correct statement 1) Temperature is a scalar but temperature gradient is a vector 2) Velocity of a body is a vector but velocity of light is a scalar 3) Electric intensity and Electric current density are vectors 4) All the above Solution: All the respected quantities given correct

VECTORS - conceptual 11. Choose the false statement: 1) Electric current is a vector because it has both magnitude and direction 2) Time is a vector which has direction always in the forward direction 3) All quantities having magnitude and direction are vector quantities 4) All the above Solution: Electric current is not a vector. Time is a scalar. Quantities have magnitude and direction may not be vectors because they may not obey vector laws

VECTORS - conceptual 12. Angular velocity is 1) a scalar 3) an axial vector 2) a polar vector 4) none of the above Solution: Angular velocity direction along the axis of rotation.

VECTORS - conceptual 13. The resultant of two forces cannot exceed 1) Average of the forces 2) Algebraic sum of the two forces 3) Difference of the two forces 4) none Solution: Resultant of two vectors cannot exceed sum of the two vectors from parallelogram law. Rmax = P + Q

VECTORS - conceptual 1) Parallel to each other 3) Perpendicular to each other Solution: R A P Q B P A R B -Q

VECTORS - conceptual 15. Choose the correct statement. 3) Both of the above 4) None of the above Solution: Since A 2 + B 2 + 2 AB cos = A 2 + B 2 - 2 AB cos i. e cos 00, = 900

VECTORS - conceptual 1) R is always greater than P 2) R is always equal to P + Q 3) R is never equal to P + Q 4) R may be less than P or Q Solution: R may be less than P or Q. From parallelogram =1800 then R = P-Q. Example: Q=6 P = 10 = R=4

VECTORS - conceptual 17. The minimum number of equal forces in a plane that can keep a particle in equilibrium is 1) 4 2) 2 3) 3 4) 5 Solution: Two minimum no. of equal vectors in a plane can keep a particle in equilibrium Ex: Two equal forces acting in a particle in opposite direction

VECTORS - conceptual 18. The minimum number of unequal forces in a plane that can keep a particle in equilibrium is 1) 4 2) 2 3) 3 Solution: Three minimum No. of unequal vectors in a can keep a particle in equilibrium Ex: Triangle law of vectors 4) 6

VECTORS - conceptual 19. The minimum number of non coplanar forces in a plane that can keep a particle in equilibrium is 1) 1 2) 2 3) 3 4) 4 Solution: Minimum number of non coplanar vectors that can keep a particle in equilibrium is four.

VECTORS - conceptual 20. The component of vector is 1) Always less than its magnitude 2) Always greater than its magnitude 3) Always equal to its magnitude 4) Less than or equal to its magnitude Solution: Y B C R Ry O Rx A The component of a vector is less than (when it makes some angle to the axis) or equal (in the same axis) to its magnitude. X

VECTORS - conceptual 21. The horizontal component of the weight of a body of mas m is 1) mg 3) zero Solution: Horizontal component of weight of body of mass is zero W = mg = m(0) = 0 4) Infinity

VECTORS - conceptual 22. A body of mass m is pulled with a horizontal force so that it moves with acceleration. Then the vertical component of the pulling force is 2) mg 1) ma 3) infinity 4) Zero Solution:

VECTORS - conceptual 23. Choose the correct statement: 1) The dot product of two vectors is a vector 2) The cross product of two vectors is a scalar 3) The cross product of two vectors is a vector 4) The dot product of two vectors may be scalar or vector. Solution: The cross product of two vectors is a vector. This is pseudo vector

VECTORS - conceptual 1) Parallel to the conductor 2) Parallel to the magnetic field 3) Perpendicular to both the conductor and the magnetic field 4) None of these Solution: Cross product

VECTORS - conceptual Solution: Direction of C is shown in figure

VECTORS - conceptual Solution:

VECTORS - conceptual 1) /2 2) 3) /4 4) None Solution: Angle between A×B and B × A is radian because from cross product direction will change.

VECTORS - conceptual 28. Choose the false statement 1) A vector having zero magnitude can have a particular direction 3) The component of a vector is a vector 4) All the above Solution: All above three are wrong concepts

VECTORS - conceptual 4) All the above are true Solution:

VECTORS - conceptual 1) Long west 3) Along north Solution: It is right hand principle 2) Along east 4) Vertically downward

VECTORS - conceptual 1) Equal to PQ 3) Equal to zero 2) Less than PQ 4) All the above Solution: P x Q = PQ sin If = 900 P x Q = PQ If = 00 Px. Q=0 If lies between 00 and 900 P x Q < PQ

VECTORS - conceptual 1) 0 Solution: 2) /4 3) /2 4)

VECTORS - conceptual 33. i x (j x k) is 1) Unit vector Solution: i x (j x k) = i x i = i i sin 00 =0 2) Null vector 3) i + j + k 4) i + j - k

VECTORS - conceptual 1) P>Q 2) P<Q Solution: If < then P > Q 4) All the above 3) P = Q D Q A C R α P B

VECTORS - conceptual 35. The forces, which meet at one point but their lines of action do not lie in one plane, are called: 1) non- coplanar non- concurrent forces 2) non- coplanar concurrent forces 3) Coplanar concurrent forces 4) Coplanar non – concurrent forces Solution: Non coplanar concurrent forces meet at one point but their lines of action do not lie in one plane

VECTORS - conceptual Force system None-coplanar Concurrent Collinear Coplanar Parallel Concurrent KEY: 2 Non-Concurrent & Non parallel Parallel Non-Concurrent & Non parallel

VECTORS - conceptual Solution:

VECTORS - conceptual 37. A particle P moves with speed ‘v’ along AB and BC sides of a square ABCD. Another particle Q also starts at A and moves with the same speed but along AD and DC of the same square ABCD. Then their respective changes in velocities are 2) Different in magnitude but same in directions 3) Different both in magnitude and direction 4) Same both in magnitude and direction

VECTORS - conceptual Solution: D C A B Now P, Q velocity magnitudes are equal and their directions are not same KEY: 1

VECTORS - conceptual 38. A ball moving with speed v strikes a wall making an angle with the wall and rebounds with the same speed making the same angle . Then change in its velocity 1) Parallel to the wall is zero but perpendicular to the wall is 2 v sin 2) Parallel to the wall is 2 v and cos but perpendicular to the wall is 2 v sin 3) Parallel to the wall is 2 v and cos but perpendicular to the wall is zero 4) Parallel to the wall is zero and perpendicular to the wall is also zero

VECTORS - conceptual Solution: Vsin Vcos Normal Vsin Vcos wall In parallel direction to the wall is Vcos will cancel and in perpendicular direction to the wall VSin - (-Vsin ) = 2 V sin KEY: 1

VECTORS - conceptual 39. A train is moving due east and a car is moving due north with equal speeds. A passenger in the train finds that the car is moving towards 1) North- East 2) North - West 3) South - West 4) South - East Solution: N Velocity of the car with respect to the train = Vct = Vc - Vt N E NE E

VECTORS - conceptual 40. A vector of length l is turned through the angle about its tail. What is the change in the position vector of its head? Solution:

VECTORS - conceptual 41. A river is flowing from west to east at a speed of 5 m / minute. A man on the south bank of the river capable of swimming at 10 m. Minute in still water wants to swim across the river in short time. In which direction he should swim 1) Due north 3) Due east 2) Due south 4) North east N Solution: Shortest path means he has to cross in straight path W 5 m/min E S 10 m/min

VECTORS - conceptual 1) Equal to AB 2) Less than AB 3) More than AB 4) Equal to AB Solution: Conceptual

VECTORS - conceptual 43. The volume of a parallelopiped bounded by vectors and can be obtained from the expression Solution: Only 2 nd option. It is only scalar quantity

VECTORS - conceptual Solution:

VECTORS - conceptual KEY: 3

VECTORS - conceptual 45. Which of the following expression is meaningless Solution: Dot product of scalar and vector is meaningless

VECTORS - conceptual Solution:

VECTORS - conceptual a KEY: 3 c b

VECTORS - conceptual Solution:

VECTORS - conceptual 48. The correct expression in the following is : Solution:

VECTORS - conceptual 49. Mark correct statement 4) All of these Solution:

VECTORS - conceptual 50. Which of the following vector identities is / are false 1) Both b & c 2) Only a 3) Both c & d 4) Both a & b Solution:

VECTORS - conceptual 51. Two vectors of same physical quantity are unequal if a) They have the same magnitude and direction b) They have different magnitudes but same direction c) They have same magnitude but different directions d) They have different magnitudes and different directions 1) a & b are true 2) b, c & d are true 3) Only c and d are true 4) a, b, c & d are true

VECTORS - conceptual Solution: Equal vectors means if two vectors are equal in magnitude and equal in direction if not equal vectors. KEY: 2

VECTORS - conceptual 52. Which of the following is a null vector a) Velocity vector of a body moving in a circle with a uniform speed b) Velocity vector of a body moving in a straight line with a uniform speed c) Position vector of the origin of the rectangular co-ordinate system d) Displacement vector of a stationary object 1) Both a & b 2) Both b & c 3) a, b & c 4) Both c & d

VECTORS - conceptual Solution: Position vector of the origin of the rectangular coordinate system is a null vector. Displacement vector of a stationary orbit is null vector KEY: 4

VECTORS - conceptual 53. Which of the following physical quantities can be obtained from dot product of two vectors a) Work b) torque 1) a, b 2) a, c & d 3) Only b 4) a & d c) power d) Magnetic flux Solution: Work, power magnetic flux are obtained from dot product W = F. S

VECTORS - conceptual P = F. V KEY: 2

VECTORS - conceptual 1) c & d are correct 2) a, b & c are correct 3) Only a is correct 4) Only d is correct

VECTORS - conceptual Solution: Here P, Q and R are mutually perpendicular P + Q + R cannot be equal to zero KEY: 1

VECTORS - conceptual 55. A boat moves relative to water with a velocity which is ‘n’ times the river flow velocity a) If n<1 boat can not cross the river b) If n = 1 boat can not cross the river without drifting c) If n > 1 boat can cross the river along shortest of n excluding zero value d) Bot can cross the river what ever is the value of n excluding zero value 1) Only a is correct 2) a, b are correct 3) c, d are correct 4) b, c & d are correct

VECTORS - conceptual Solution: Even n < 1 boat cross the river KEY: 4

VECTORS - conceptual 56. Statement I: Electric current density is a vector Statement II: physical quantity having magnitude and direction should be a vector 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true. Solution: Though a vector have magnitude and direction, it need not be a vector

VECTORS - conceptual 57. Statement I: The direction of velocity vector remains unchanged though the coordinate system is changed Statement II: The direction of real vector is independent of coordinate system 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 58. Statement I: Two forces 7 N and 5 N are acting at a point and their resultant can be 3 N Statement II: If two vectors P and Q are acting at a point their resultant can have a value is between P – Q to P + Q 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: The cross product of two vectors does not obey commutative property 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 60. Statement I: Every component of a null vector is zero Statement II: Origin and terminus of null vector are the same point 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true. Solution: Every component of null vector need not be zero

VECTORS - conceptual Statement II: Direction of cross product obeys right and thumb rule 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: Direction of cross product obeys right and thumb rule 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 62. Statement I: Vector sum of three forces can be zero Statement II: Minimum number of unequal coplanar vectors required to keep a point in equilibrium is three. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 63. Statement I: Two vectors of equal magnitude cannot keep the point of action in the state of equilibrium. Statement II: Two vectors may keep the point of action in the sate of equilibrium. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Solution: Two vectors of equal magnitude and in opposite direction may keep the point of action in the state of equilibrium KEY: 2

VECTORS - conceptual Statement II: The projection of a vector is a scalar 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: The dot product of two vectors is a scalar 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: A scalar and a vector cannot have a dot (or) cross products. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: Resultant is always closer to the vector of larger magnitude 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: The component vectors of a unit vector need not be unit vectors 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: The addition of unit vectors never gives unit vector 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true. Solution: The addition of unit vector can give unit vector

VECTORS - conceptual 70. Statement I: Torque is a pseudo vector Statement II: The cross product of two polar vectors is a pseudo vector 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 71. Statement I: when a vector is rotated, its magnitude remains constant. Statement II: The magnitude of a vector is independent of the coordinate system. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: The vector sum of three vectors can never be zero 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Solution: Vector sum of three vectors can be zero Example: Triangle law of vectors KEY: 3

VECTORS - conceptual Statement II: The magnitude of the cross product of two vectors depends upon the angle between them. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual Statement II: To find resultant of two vectors, we use parallelogram law. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 76. Statement I: The division of a vector by another vector is not defined. Statement II: The division of a vector by a direction is not possible. 1) Statement I is true, Statement II true Statement II is the correct explanation for Statement I 2) Statement I is true, Statement II is not the correct explanation for statement I 3) Statement I is true, Statement II is false 4) Statement I is false, Statement II is true.

VECTORS - conceptual 77. Match the following List - II 1) a – e 2) a – g 3) a – g 4) a – e b–f b–g c–h c–e c–h d-f d-h d-f

VECTORS - conceptual Solution: A 2 + B 2 + 2 AB Cos AB sin = A 2 + B 2 - 2 AB Cos =AB Cos tan = 1 KEY: 2

VECTORS - conceptual 78. Match the following List - II e) 0 f) 1 g) 3 h) 2 1) a – e 2) a – g 3) a – g b–f c–g b–h c–f b–f c–e d-h d-e d-h 4) a – e b–g d-e c–h

VECTORS - conceptual Solution: 1+1+1 = 3 1+0=1 KEY: 3

VECTORS - conceptual 79. Match the following List - II e) f) 2 /3 g) 0 h) /2 1) a – g 2) a – h 3) a – f 4) a – g b–h b–e b–e c–f c–h d-e d-g d-f Solution: Basic statement

VECTORS - conceptual 80. Match the following List - I a) Work List - II b) Power c) Linear velocity d) Torque 1) a – g 2) a – f 3) a – f 4) a – g b–h b–g b–f c–e c–h c–e d-h d-e d-h

VECTORS - conceptual Solution: KEY: 3

VECTORS - conceptual Thank you…