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51.

Unit vector along the vector 4î + 3ĵ is _____(a) (4î + 3ĵ)/5(b) 4î + 3ĵ(c) (4î + 3ĵ)/6(d) (4î + 3ĵ)/10I had been asked this question during a job interview.This is a very interesting question from Vector Addition topic in portion Motion in a Plane of Physics – Class 11

Answer» RIGHT option is (a) (4î + 3ĵ)/5

For explanation: Unit vector along 4î + 3ĵ , is obtained by dividing the PRESENT vector by its magnitude. The magnitude of the given vector is 5. HENCE, the required unit vector is (4î + 3ĵ)/5.
52.

A body moves from point A (3,6) to point B (11,12) to point C (15,15). What is the average speed of the body along the given path if the total time taken is 100s?(a) 0.15 units/s(b) 1.5 units/s(c) 15 units/s(d) 0.0015 units/sI have been asked this question in a national level competition.My question is based upon Motion in a Plane with Constant Acceleration in portion Motion in a Plane of Physics – Class 11

Answer» CORRECT option is (a) 0.15 units/s

Best explanation: The distance between A and B is 10 units. The distance between B and C is 5 units. HENCE, the total distance is 15 units. The total time taken is 100 s. Average SPEED = total distance/total time taken = 15/100 = 0.15 units/s.
53.

When two vectors in the same direction are added, the magnitude of resulting vector is equal to _______(a) Sum of magnitudes of the vectors(b) Difference of magnitudes of the vectors(c) Product of magnitudes of the vectors(d) Sum of the roots of magnitudes of the vectorsThe question was asked in homework.My question is taken from Vector Addition topic in portion Motion in a Plane of Physics – Class 11

Answer»

Right option is (a) Sum of MAGNITUDES of the vectors

Best explanation: Consider the GRAPHICAL REPRESENTATION of these two vectors. When one vector is added to the other in the same direction, the lengths will be added. The resultant vector will bear the resultant length. Length is the magnitude of the vector. HENCE the magnitudes add to give the magnitude of the resultant vector.

54.

A car travels 5m in X direction and then 7m in Y direction. What is the final vector position of the car with respect to the origin?(a) 5î + 7ĵ(b) 7î + 5ĵ(c) 7î + 7ĵ(d) 5î + 5ĵThe question was asked in an internship interview.I would like to ask this question from Motion in a Plane in section Motion in a Plane of Physics – Class 11

Answer»

The CORRECT answer is (a) 5î + 7ĵ

To EXPLAIN I would say: UNIT vector along X is î and that along Y is ĵ. Hence, when the car travels 5m in X direction and 7m in y direction, the final position BECOMES 5î + 7ĵ.

55.

A force vector (50 N) is making and angle of 30 degrees with X axis has a vertical component of magnitude ___(a) 25(b) 55(c) 50(d) 100/√3I got this question in examination.The above asked question is from Motion in a Plane in chapter Motion in a Plane of Physics – Class 11

Answer»

The correct OPTION is (a) 25

The best explanation: The vertical component of any VECTOR with magnitude a is a sin θ. Here θ = 60. sin θ = ½. HENCE the answer is 50/2 = 25 N.

56.

A vector can be resolved along ______(a) Only one direction(b) Only two directions(c) Only three directions(d) Only in independent directionsThis question was addressed to me by my college professor while I was bunking the class.Asked question is from Motion in a Plane in division Motion in a Plane of Physics – Class 11

Answer» RIGHT choice is (d) Only in INDEPENDENT DIRECTIONS

Explanation: A VECTOR can be resolved in number of components. But, the number of components has to be equal to the number of independent directions available. It can only be resolved into independent directions no MATTER how many they are.
57.

The vector obtained by addition of two vectors is termed as ______(a) New vector(b) Resultant vector(c) Derived vector(d) Sum vectorThe question was asked in class test.Question is taken from Motion in a Plane in portion Motion in a Plane of Physics – Class 11

Answer» CORRECT ANSWER is (b) Resultant vector

For explanation: The resultant vector is the vector which is obtained by the addition or SUBTRACTION of two VECTORS. The resultant vector can either be calculated by using the graphical method or the analytical method.
58.

What happens when a vector is multiplied by a scalar?(a) Its magnitude gets multiplied by that much amount(b) Its direction rotates in XY plane by that much angle(c) Its direction rotates in YZ plane by that much angle(d) Its direction rotates in ZX plane by that much angleI have been asked this question in an internship interview.I need to ask this question from Motion in a Plane in chapter Motion in a Plane of Physics – Class 11

Answer»

Correct option is (a) Its magnitude gets multiplied by that much amount

Best explanation: Any vector a, can be written as a = |a|(\(\widehat{unit vector}\)). Hence, when we MULTIPLY it by a SCALAR, the magnitude MULTIPLIES by that much amount.

59.

Which one of the following operations is valid?(a) Vector multiplied by scalar(b) Vector added to scalar(c) Vector subtracted from scalar(d) Vector divided by vectorI got this question in examination.This interesting question is from Motion in a Plane in portion Motion in a Plane of Physics – Class 11

Answer»

Correct option is (a) Vector multiplied by scalar

To elaborate: Only operations valid for vector with scalars are multiplication and DIVISION. A vector can be multiplied or DIVIDED by a scalar. Other operations like addition and SUBTRACTION are not valid for vectors with scalars.

60.

What is a vector quantity?(a) A quantity with only magnitude(b) A quantity with only direction(c) A quantity with both magnitude and direction(d) A quantity without directionThe question was posed to me during an online exam.My question is taken from Motion in a Plane topic in section Motion in a Plane of Physics – Class 11

Answer»

Right CHOICE is (c) A quantity with both magnitude and direction

To elaborate: A vector quantity is one which has both magnitude and direction. Unlike SCALARS, it can also tell the direction in which is the entity is acting. Examples of vector QUANTITIES are force, velocity, DISPLACEMENT ETC.

61.

Dividing 5î + 10ĵ by 5 gives ______(a) î + 2ĵ(b) î + 4ĵ(c) î + ĵ(d) 2î + ĵ,This question was addressed to me in semester exam.My doubt is from Motion in a Plane in section Motion in a Plane of Physics – Class 11

Answer» CORRECT CHOICE is (a) î + 2ĵ

Best explanation: When 5î + 10ĵ is DIVIDED by 5, both the components get divided by 5. Hence, the answer is î + 2ĵ.
62.

Mass is a ____(a) Scalar quantity(b) Vector quantity(c) Relative quantity(d) Dependent quantityI got this question during an interview.Query is from Motion in a Plane topic in portion Motion in a Plane of Physics – Class 11

Answer» RIGHT option is (a) Scalar quantity

For EXPLANATION: MASS REPRESENTS the amount of MATTER in a body. It does not have any direction but only mass. Hence, it is a scalar quantity.
63.

The operation used to obtain a scalar from two vectors is ______(a) Cross product(b) Dot product(c) Simple product(d) Complex productThe question was posed to me by my school teacher while I was bunking the class.This intriguing question comes from Motion in a Plane topic in division Motion in a Plane of Physics – Class 11

Answer»

Right choice is (b) Dot product

Best explanation: Dot product of TWO vectors gives a SCALAR QUANTITY as the output. Cross product gives a vector as the output. It is also known as scalar product.

64.

The operation which does not give you a vector as an output from two vector inputs is ______(a) Dot product(b) Cross product(c) Vector addition(d) Vector subtractionI got this question in semester exam.I want to ask this question from Motion in a Plane in chapter Motion in a Plane of Physics – Class 11

Answer»

The correct OPTION is (a) Dot product

For explanation I would say: Vector addition and subtraction GIVE a vector as the output. CROSS product also gives a vector as the output. Only Dot product gives a scalar after acting on two VECTORS.

65.

A unit vector has the magnitude of ___(a) 5(b) 1(c) 10(d) 0I had been asked this question by my school teacher while I was bunking the class.The query is from Motion in a Plane in portion Motion in a Plane of Physics – Class 11

Answer»

Correct option is (b) 1

To elaborate: A unit vector has the magnitude 1. It is used to represent non-unit vectors using along other unit vectors. Any vector can be REPRESENTED as a sum of unit vectors, multiplied by required SCALARS.

66.

What is a scalar?(a) A quantity with only magnitude(b) A quantity with only direction(c) A quantity with both magnitude and direction(d) A quantity without magnitudeThis question was addressed to me in an interview.Asked question is from Motion in a Plane in division Motion in a Plane of Physics – Class 11

Answer»

Correct answer is (a) A QUANTITY with only MAGNITUDE

To elaborate: A scalar quantity is one which only has a magnitude. Examples of scalar quantities are mass, volume, WORK, ENERGY etc.

67.

Multiplying 2î + 7ĵ by 5 gives ______(a) 10î + 35ĵ(b) 2î + 35ĵ(c) 10î + 7ĵ(d) 2î + 7ĵI have been asked this question in examination.I would like to ask this question from Motion in a Plane in division Motion in a Plane of Physics – Class 11

Answer»

Correct CHOICE is (a) 10î + 35Ĵ

Explanation: When 2î + 7ĵ is multiplied by 5, both the components get multiplied by 5. Hence, the answer is 10î + 35ĵ.

68.

The splitting of a vector into two component vectors is called ______(a) Vector resolution(b) Vector sum(c) Vector decomposition(d) Vector differenceI have been asked this question in exam.The doubt is from Motion in a Plane topic in portion Motion in a Plane of Physics – Class 11

Answer»

Right option is (a) Vector RESOLUTION

The explanation: The splitting of a vector into two component VECTORS is CALLED vector resolution. The vector can be resolved into as many COMPONENTS as there are independent directions.

69.

A vector is represented as 4î + 3ĵ. What is its magnitude?(a) 5(b) 10(c) 4(d) 3The question was posed to me during an interview for a job.This interesting question is from Motion in a Plane topic in chapter Motion in a Plane of Physics – Class 11

Answer»

Correct answer is (a) 5

Easiest explanation: The magnitude of any vector can be FOUND by TAKING the SQUARE root of SUM of the SQUARES of its two components. Hence, the sum of the squares of components is equal to 4^2 + 3^2 = 25. Square root of 25 = 5. Hence, the answer is 5.

70.

Eleven times unit vector along X added to 7 times unit vector along Y gives ______(a) 11î + 7ĵ(b) 7î + 11ĵ(c) 7î + 7ĵ(d) 11î + 11ĵThis question was posed to me in a job interview.Enquiry is from Motion in a Plane in section Motion in a Plane of Physics – Class 11

Answer» RIGHT option is (a) 11î + 7Ĵ

Explanation: Unit vector along X is î and that along Y is ĵ. Hence, ELEVEN times unit vector along X added to 7 times unit vector along Y will give 11î + 7ĵ.
71.

A velocity vector (5m/s) is making and angle of 60 degrees with X axis has a horizonal component of magnitude ___(a) 2.5(b) 5.5(c) 5(d) 10/√3This question was posed to me in a job interview.This intriguing question originated from Motion in a Plane topic in chapter Motion in a Plane of Physics – Class 11

Answer»

The correct answer is (a) 2.5

Easy explanation: The HORIZONTAL component of any vector with magnitude a is a COS θ. Here θ = 60. cos θ = ½. HENCE the answer is 5/2 = 2.5 m/s.

72.

What is the standard form for the resolution of a vector having magnitude ‘a’ and is inclined at an angle θ to the X axis?(a) a(cos θ î + sin θ ĵ)(b) a(sin θ î + cos θ ĵ)(c) a(sin θ î + sin θ ĵ)(d) a(cos θ î + cos θ ĵ)This question was addressed to me in an internship interview.This interesting question is from Motion in a Plane topic in portion Motion in a Plane of Physics – Class 11

Answer» CORRECT answer is (a) a(cos θ î + SIN θ ĵ)

For explanation: The correct answer is a(cos θ î + sin θ ĵ). This is obtained by CONSTRUCTING a right-angled triangle with the distance of the point from the origin with either of the axes and then finding out the CORRESPONDING VALUES for X and Y components.
73.

Subtracting 2î + 7ĵ from î + ĵ gives ______(a) -î – 6ĵ(b) 3î + 8ĵ(c) î + 6ĵ(d) 7ĵThis question was addressed to me in exam.My doubt is from Vector Addition topic in chapter Motion in a Plane of Physics – Class 11

Answer»

Right CHOICE is (a) -î – 6Ĵ

The explanation: When 2î + 7ĵ is subtracted from î + ĵ, the CORRESPONDING components get subtracted. Hence, the answer is -î – 6ĵ.

74.

Adding 2î + 7ĵ and î + ĵ gives ______(a) 3î + 8ĵ(b) î + 35ĵ(c) î + 8ĵ(d) 2î + 7ĵI have been asked this question in an interview.This key question is from Vector Addition topic in portion Motion in a Plane of Physics – Class 11

Answer»

The CORRECT choice is (a) 3î + 8Ĵ

To EXPLAIN I would say: When 2î + 7ĵ is added to î + ĵ, the corresponding components get added. Hence, the ANSWER is 3î + 8ĵ.

75.

On adding two vectors we get _____(a) A vector(b) A scalar(c) A number(d) An operationI got this question in homework.My doubt is from Vector Addition topic in section Motion in a Plane of Physics – Class 11

Answer»

The CORRECT answer is (a) A vector

The EXPLANATION is: Addition of TWO vectors gives a vector as the result. The same goes for SUBTRACTION and cross MULTIPLICATION. It is only when two vectors are operated through dot product, we get a scalar as the result.

76.

What is the resolved form for a vector which is 5 units in long and is inclined at an angle of 45 degrees to the X axis?(a) \(\frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{j}\)(b) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\)(c) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{15}{\sqrt{2}}\hat{j}\)(d) \(\frac{10}{\sqrt{2}}\hat{i} + \frac{10}{\sqrt{2}}\hat{j}\)I have been asked this question in my homework.Question is from Motion in a Plane topic in division Motion in a Plane of Physics – Class 11

Answer» RIGHT option is (B) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\)

To EXPLAIN I would SAY: The standard for is a(cos θ î + sin θ ĵ). Here, a = 5, and θ = 45 degrees. When we substitute this in the equation, we get, the resolved VECTOR as \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\).
77.

What is the result when î + 14ĵ is multiplied by √49?(a) 7î + 98ĵ(b) 98î + 14ĵ(c) 7î + 98ĵ(d) (î + 7ĵ)*√49This question was posed to me in semester exam.I would like to ask this question from Motion in a Plane topic in section Motion in a Plane of Physics – Class 11

Answer»

Right option is (a) 7î + 98Ĵ

Explanation: \(\sqrt{49}\) = 7. When î + 14ĵ is multiplied by 7, we get 7î + 98ĵ as the ANSWER. Hence, 7î + 98ĵ is the correct answer.

78.

Adding î + 77ĵ and 7î + ĵ gives ______(a) 8î + 78ĵ(b) 0î + 76ĵ(c) î + 74ĵ(d) 78î + 8ĵI had been asked this question in an interview for job.This interesting question is from Vector Addition topic in portion Motion in a Plane of Physics – Class 11

Answer»

The correct CHOICE is (a) 8î + 78ĵ

EXPLANATION: When î + 77ĵ is ADDED to 7î + ĵ, the corresponding components get added. HENCE, the ANSWER is 8î + 78ĵ.