MCQs on physic Vectors
1. What is the vertical component of the force 5 N acting on a particle along a direction making an angle of 600?
(A) 3 N
(B) 2.5 N
(C) 10 N
(D) 4 N
Answer
Answer: (B) 2.5 N
2. What is the direction of cosines of vector (vec{A}=2 hat{i}+4 hat{j}-5 hat{k} ?)
Answer
Answer: (A) (frac{2}{sqrt{45}}, frac{4}{sqrt{45}},-frac{5}{sqrt{45}})
3. What is the minimum number of coplanar vectors with different magnitudes that can be added to get a resultant of zero?
(A) 1
(B) 2
(C) 3
(D) 4
Answer
Answer: (C) 3
4. A fly in the hall of dimensions 10 m×12 m×14 m starts to fly from one corner and ends up at the diametrically opposite corner. What is the magnitude of its flight?
(A) 17 m
(B) 20 m
(C) 26 m
(D) 36 m
Answer
Answer: (B) 20 m
5. Five equal forces of 10 N are applied at a point. If the angle between them is equal, what is the resultant force?
(A) 10 N
(B) 10√2N
(C) 20 N
(D) 0
Answer
Answer: (D) 0
6. Any vector in an arbitrary direction can be replaced by two or three vectors
(A) perpendicular to each other and have the original vector as their resultant
(B) Parallel to each other and have the original vector as their resultant
(C) Arbitrary vectors which have original vectors as their resultant
(D) It is impossible to resolve a vector
Answer
Answer: (C) Arbitrary vectors which have original vectors as their resultant
7. Angular momentum is
(A) A scalar vector
(B) An axial-vector
(C) A polar vector
(D) A displacement vector
Answer
Answer: (B) An axial-vector
8. Which of the following is a vector?
(A) Surface Tension
(B) Moment of Inertia
(C) Pressure
(D) None of the above
Answer
Answer: (D) None of the above
9. Which of the following is a scalar quantity?
(A) Acceleration
(B) Electric Field
(C) Work
(D) Displacement
Answer
Answer: (D) Displacement
10. A boy walks uniformly along the sides of a rectangular park with dimensions 400 m×300 m, starting from one corner to the other corner diagonally opposite. Which of the following statements is false?
(A) His displacement is 700 m
(B) His displacement is 500 m
(C) He has travelled a distance of 700 m
(D) His velocity is not uniform throughout the walk
Answer
Answer: (B) His displacement is 500 m
11. 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 magnitude
Answer: a
Clarification: A scalar quantity is one which only has a magnitude. Examples of scalar quantities are mass, volume, work, energy etc.
12. 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 direction
Answer: c
Clarification: 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.
13. 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 vector
Answer: a
Clarification: 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.
14. The vector obtained by addition of two vectors is termed as __
a) New vector
b) Resultant vector
c) Derived vector
d) Sum vector
Answer: b
Clarification: 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.
15. Mass is a __
a) Scalar quantity
b) Vector quantity
c) Relative quantity
d) Dependent quantity
Answer: a
Clarification: Mass represents the amount of matter in a body. It does not have any direction but only mass. Hence, it is a scalar quantity.
16. The operation used to obtain a scalar from two vectors is __
a) Cross product
b) Dot product
c) Simple product
d) Complex product
Answer: b
Clarification: 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.
17. 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 subtraction
Answer: a
Clarification: 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 vector.
18. The splitting of a vector into two component vectors is called __
a) Vector resolution
b) Vector sum
c) Vector decomposition
d) Vector difference
Answer: a
Clarification: 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.
19. 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)
Answer: a
Clarification: 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.
20. 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})
Answer: b
Clarification: 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}).
21. 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/√3
Answer: a
Clarification: 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.
22. 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/√3
Answer: a
Clarification: 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.
23. A vector is represented as 4î + 3ĵ. What is its magnitude?
a) 5
b) 10
c) 4
d) 3
Answer: a
Clarification: 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 42 + 32 = 25. Square root of 25 = 5. Hence, the answer is 5.
24. A vector can be resolved along __
a) Only one direction
b) Only two directions
c) Only three directions
d) Only in independent directions
Answer: d
Clarification: 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.
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