1. Which of the following statement is true?
a) A scalar is any physical quantity that can be completely specified by its magnitude
b) A vector is any positive or negative physical quantity that can be completely specified by its magnitude
c) A scalar is any physical quantity that requires both a magnitude and a direction for its complete description
d) A scalar is any physical quantity that can be completely specified by its direction
Explanation: A scalar is any positive or negative physical quantity that can be completely specified by its magnitude. Examples of scalar quantities include length, mass, time, etc.
2. For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents:
a) Their magnitude’s square and direction of the line of action respectively
b) Their magnitude and direction of the line of action respectively
c) Magnitude’s square root and direction of the line of action respectively
d) Magnitude’s square and the ratio of their lengths respectively
Explanation: For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents their magnitude and direction of the line of action respectively. The head/tip of the arrow indicates the sense of direction of the vector.
3. If a vector is multiplied by a scalar:
a) Then its magnitude is increased by the square root of that scalar’s magnitude
b) Then its magnitude is increased by the square of that scalar’s magnitude
c) Then its magnitude is increased by the amount of that scalar’s magnitude
d) You cannot multiply the vector with a scalar
Explanation: If a vector is multiplied by a scalar then its magnitude is increased by the amount of that scalar’s magnitude. When multiplied by a negative scalar it going to change the directional sense of the vector.
4. All the vectors quantities obey:
a) Parallelogram law of addition
b) Parallelogram law of multiplication
c) Parallelogram law of addition of square root of their magnitudes
d) Parallelogram law of addition of square of their magnitudes
Explanation: All the vectors quantities obey parallelogram law of addition. Two vectors A and B (can be called as component vectors) are added to form a resultant vector. R = A+B.
5. A force vector with magnitude R and making an angle α with the x-axis is having its component along x-axis and y-axis as:
a) Rcosine (α) and Rsine(α)
b) Rcosine (180-α) and Rsine(α)
c) Rcosine (180-α) and Rsine(180+α)
d) Rcosine (α) and Rsine(180+α)
Explanation: The component along the x-axis is the cosine component of the vector. And the y-axis component of the vector is sine component, if the angle is being made with the x-axis. And 180- α for some of the trigonometric function may change their sign.
6. Dividing the X-axis component and the Y-axis component of the of the vector making an angle with Y-axis α will give us.
a) Cot α
b) Tan α
c) Sec α
d) 1
Explanation: As the X-axis component of the vector becomes cos(90- α) and the Y-axis component becomes sin(90- α).Thus the division of both will give us Tan α.
7. Vector shown in the figure below have a length of 3m and the angles shown A and B are 60 and 30 degrees each. Calculate the X-axis and Y-axis components:
a) 2.59m and 1.50m respectively
b) 1.50m and 2.59m respectively
c) 3cos60 and 3sin30 respectively
d) 3sin60 and 3sin30 respectively
Explanation: The sine and the cosine components of the given vectors considering the angle B as the only angle of consideration comes 1.5m and 2.59m.
8. Shown as in the figure below, A=60 degree and B=30 degree. Calculate the total length obtained by adding the x-axis component of both the vectors.
a) 3.23m
b) 4.35m
c) 2.50m
d) 1.5m
Explanation: After getting the cosine components of the given vectors we obtain the total length of the x-axis components to be 3cos60 + 2cos30 = 3.23.
9. The magnitude of the resultant of the two vectors is always_____________
a) Greater than one of the vector’s magnitude
b) Smaller than one of the vector’s magnitude
c) Depends on the angle between them
d) Axis we choose to calculate the magnitude
Explanation: Yes, the magnitude of the resultant of the two vectors always depends on the angle between them. It might be greater or smaller than one of the vector’s length. For perfectly saying, it does depend upon the angle between them.
10. If two equal vector forces are mutually perpendicular then the resultant force is acting at which angle as compared to one of the vector?
a) 45 degree
b) 90 degree
c) 180 degree
d) 0 degree
Explanation: The vectors are mutually perpendicular, this means that the angle between the forces is 90 degree. Thus the resultant will form at 45 degrees to any of the vector.