Free Vectors and Equilibrium MCQs with Answers
431 Vectors and Equilibrium MCQs from Physics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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Read the Vectors and Equilibrium notesFree MDCAT chapter notes with key terms431 questions · page 6 of 22
- A. Unit vector
- B. Free vector
- C. Null vector
- D. Position vector
- E. Resultant vector
Explanation: Option B is the correct answer because a free vector is one whose action is not confined or associated with a unique line in space.
Correct answer: Free vector- A. 12√3
- B. 6√3
- C. 6√12
- D. 12√6
- E. 3√6
Explanation: The vector product of two vectors, R1 and R2, is given by the formula |R1 × R2| = |R1| |R2| sin(θ2 - θ1), where θ is the angle between the…
Correct answer: 6√3- A. 1/7 (3i + 6j - 2k)
- B. (1/7) * (3i + 6j - 2k)
- C. (1/14) * (3i + 6j - 2k)
- D. 3i + 6j - 2k
- E. 7(3i + 6j - 2k)
Explanation: To find a unit vector parallel to a given vector A = 3i + 6j - 2k, first calculate the magnitude of A: |A| = √(3² + 6² + (-2)²) = √(9 + 36…
Correct answer: (1/7) * (3i + 6j - 2k)- A. 1
- B. 2
- C. 10
- D. 20
- E. 25
Explanation: The scalar product (also known as the dot product) of two vectors is calculated by multiplying their corresponding components and adding…
Correct answer: 1- A. Zero
- B. 1
- C. 2
- D. 3
Explanation: The "three" dimensions are x, y, and z. Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric…
Correct answer: 3- A. 0
- B. 10 J
- C. 45 J
- D. 20 J
Explanation: We know that work done = F x dwhere F is the force and d is the displacement in the direction of the force.The question statement says a…
Correct answer: 20 J- A. r
- B. 2πr
- C. 2r
- D. r²
Explanation: The correct answer is r. Displacement is a vector quantity that describes the shortest path between two points, taking into account…
Correct answer: r- A. Decreases
- B. Increases
- C. Remains unchanged
- D. Decreases and then increases
Explanation: The magnitude of the resultant force in vector addition is given by the formula: R = √(A² + B² + 2ABcosθ), where A and B are the…
Correct answer: Decreases- A. 8N
- B. 12.1N
- C. 9.8N
- D. 7.4N
Explanation: To solve the problem, recognize that the greatest resultant (10 N) and smallest resultant (6 N) of two forces F1 and F2 are given by the…
Correct answer: 12.1N- A. Algebraic principles
- B. Simple arithmetical rules
- C. Logical methods
- D. Vector algebra
Explanation: Addition, subtraction, and multiplication of scalars are done using the ordinary arithmetic rules of real numbers.
Correct answer: Simple arithmetical rules- A. Its magnitude
- B. Its angle
- C. Another vector
- D. Ten
Explanation: A unit vector is obtained by dividing the given vector by its magnitude or length.
Correct answer: Its magnitude- A. Left hand rule
- B. Right hand rule
- C. Head to tail rule
- D. None of the above
Explanation: When adding vectors, the head to tail rule is used in the graphical method of vector addition.
Correct answer: Head to tail rule- A. Joining the tail of the first vector with the head of the last vector
- B. Joining the head of the first vector with the tail of the last vector
- C. Joining the tail of the last vector with the head of the first vector
- D. Joining the head of the last vector with the tail of the first vector
Explanation: The head-to-tail method is used to find the resultant of vectors by sequentially connecting them so that the head of one vector is joined…
Correct answer: Joining the tail of the first vector with the head of the last vector- A. Option A
- B. Option B
- C. Option C
- D. Option D
Explanation: The correct answer is Option A, as it corresponds to the formula mentioned in the question.
Correct answer: Option A- A. 360° - θ
- B. 180° + θ
- C. 90° - θ
- D. θ
Explanation: To determine the angle subtended by the resultant vector on the x-axis, consider the signs of its components.
Correct answer: 360° - θ- A. FV sin θ
- B. FV tan θ
- C. F/V cos θ
- D. FV cos θ
Explanation: The scalar product of two vectors F and V is represented as F.V = (F) (projection of V on F) or F.V = F (magnitude of component of V in…
Correct answer: FV cos θ- A. A cos θ
- B. A sin θ
- C. A tan θ
- D. None of the above
Explanation: The scalar product of a vector A can be found by multiplying its magnitude by itself, which is the square of the magnitude of vector A.
Correct answer: None of the above- A. Perpendicular to A
- B. Parallel to B
- C. Perpendicular to B
- D. Perpendicular to the plane joining both A & B
Explanation: In the vector product of two vectors A and B, the direction of the resulting vector is perpendicular to the plane formed by the original…
Correct answer: Perpendicular to the plane joining both A & B- A. 0
- B. 1
- C. -1
- D. 1/2
Explanation: The self product of any vector is equal to the square of its magnitude.
Correct answer: 1- A. Distance
- B. Direction
- C. Speed
- D. Acceleration
Explanation: Vector quantities require both magnitude and direction to be fully described.
Correct answer: Direction