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 1 of 22
- A. 1 N
- B. 5 N
- C. 7 N
- D. 12 N
Explanation: For perpendicular vectors the resultant is the square root of (3 squared plus 4 squared), which is the square root of 25, giving 5 N.
Correct answer: 5 N- A. 2F
- B. F times the square root of 3
- C. F
- D. zero
Explanation: Using the parallelogram rule, the resultant is the square root of (F squared plus F squared plus 2F squared cos 120), and since cos 120 is…
Correct answer: F- A. one
- B. two
- C. three
- D. four
Explanation: Two unequal forces can never cancel, since cancelling requires equal magnitudes in opposite directions.
Correct answer: three- A. 10 N
- B. 20 N
- C. 17.3 N
- D. 11.5 N
Explanation: The horizontal component is 20 cos 30, and cos 30 is 0.866, so the component is 17.3 N.
Correct answer: 17.3 N- A. 30 degrees
- B. 45 degrees
- C. 60 degrees
- D. 90 degrees
Explanation: The angle is given by the inverse tangent of the ratio of the y component to the x component, and when the two are equal that ratio is 1…
Correct answer: 45 degrees- A. AB sin theta, and the result is a vector
- B. AB cos theta, and the result is a scalar
- C. AB tan theta, and the result is a scalar
- D. AB, independent of the angle between them
Explanation: The dot product multiplies the magnitudes by the cosine of the angle between the vectors and gives a scalar, which is why work, the dot…
Correct answer: AB cos theta, and the result is a scalar- A. maximum
- B. equal to their magnitudes multiplied
- C. zero
- D. negative
Explanation: Cos 90 is zero, so the dot product vanishes whenever the vectors are at right angles, and this is the standard test for perpendicularity.
Correct answer: zero- A. zero
- B. maximum and equal to AB
- C. equal to AB cos theta
- D. a scalar
Explanation: The cross product has magnitude AB sin theta, and sin 0 is zero, so parallel vectors give a null vector.
Correct answer: zero- A. the direction of A
- B. the direction of B
- C. the bisector of the angle between A and B
- D. the right hand rule, perpendicular to the plane containing A and B
Explanation: Curling the fingers of the right hand from A to B points the thumb along A cross B, which is perpendicular to both vectors.
Correct answer: the right hand rule, perpendicular to the plane containing A and B- A. the vector sum of all forces acting on the body is zero
- B. the sum of all torques about any point is zero
- C. the body is at rest
- D. no force acts on the body at all
Explanation: With zero net force there is no acceleration of the centre of mass, which is translational equilibrium.
Correct answer: the vector sum of all forces acting on the body is zero- A. its mass is very small
- B. the net force is zero but the net torque is not
- C. the forces are all vertical
- D. it is moving at constant speed
Explanation: Two equal and opposite forces acting along different lines form a couple: they cancel as vectors, so there is no acceleration, but they…
Correct answer: the net force is zero but the net torque is not- A. force divided by distance
- B. the scalar product of force and distance
- C. the product of force and the perpendicular distance from the axis to the line of action
- D. force multiplied by time
Explanation: Only the perpendicular distance, the moment arm, counts, which is why pushing a door near its hinge is so ineffective.
Correct answer: the product of force and the perpendicular distance from the axis to the line of action- A. 90 degrees
- B. 180 degrees
- C. 120 degrees
- D. 0 degrees
Explanation: Parallel vectors add directly, so the resultant equals the sum of the magnitudes, which is the largest value achievable.
Correct answer: 0 degrees- A. magnitude one and specifies direction only
- B. zero magnitude
- C. magnitude equal to the vector it came from
- D. no direction
Explanation: Dividing any vector by its own magnitude gives a unit vector along the same line, which carries the direction information with the size…
Correct answer: magnitude one and specifies direction only- A. 7
- B. 5
- C. 12
- D. 25
Explanation: The magnitude is the square root of the sum of the squares of the components, so the square root of (9 plus 16), which is the square root…
Correct answer: 5- A. 11
- B. 5
- C. 8
- D. minus 3
Explanation: In component form the dot product is the sum of the products of like components, so (2)(4) plus (3)(minus 1) gives 8 minus 3, which is 5.
Correct answer: 5- A. Force and acceleration
- B. Velocity and momentum
- C. Work and power
- D. Torque and displacement
Explanation: Work and power have magnitude only, with work being a dot product and power its rate of change with time.
Correct answer: Work and power- A. along the ladder
- B. vertically upwards
- C. perpendicular to the wall
- D. parallel to the wall
Explanation: A smooth surface can exert no friction, so the only force it can apply is the normal reaction, which by definition acts at right angles to…
Correct answer: perpendicular to the wall- A. lie along one straight line
- B. form a closed triangle
- C. all be equal in magnitude
- D. be mutually perpendicular
Explanation: A zero resultant means the head of the last vector coincides with the tail of the first, so the three vectors close a triangle.
Correct answer: form a closed triangle- A. 90°
- B. 180°
- C. 270°
- D. None of these
Explanation: Anti-parallel vectors lie along the same line but point in opposite directions, so the angle between them is 180°.
Correct answer: 180°Vectors and Equilibrium MCQs: common questions
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