Level 1
Vectors & Equilibrium MCQs set 2 for PMC National MDCAT Physics — 20 solved questions.
Q1. An engineer applies a force of 100 N to a structural beam at an angle of 60 degrees with the horizontal axis. What is the horizontal component?
Answer: 50.0 N
Explanation: Fx equals F cos(theta), giving 100 cos(60) which is 50N. Option C fails because it uses the sine function incorrectly for horizontal components.
Q2. A particle moves in the xy-plane with a position vector r = 3i + 4j. Calculate the magnitude of its displacement from the origin.
Answer: 5 units
Explanation: The magnitude is the square root of (3 squared plus 4 squared), totaling 5. Option B is incorrect as it simply adds the scalar components.
Q3. Two vectors are defined as A = 3i and B = 4j. What is the result of the scalar product A dot B for these vectors?
Answer: 0
Explanation: The scalar product of perpendicular unit vectors i and j is zero. Option A is tempting because it represents the product of their magnitudes.
Q4. A mechanic uses a wrench of length 50 cm to loosen a bolt by applying a perpendicular force of 20 N. Calculate the torque produced.
Answer: 10 Nm
Explanation: Torque is rF sin(90), so 0.5m times 20N equals 10 Nm. Option B fails because it ignores the 0.5m moment arm conversion.
Q5. Two forces of 3 N and 4 N act simultaneously on a point object at an angle of 90 degrees. What is the magnitude of the resultant?
Answer: 5 N
Explanation: The resultant of two perpendicular vectors is the square root of (3 squared plus 4 squared). Option A is a simple algebraic sum.
Q6. A vector is represented as A = i + j. What is the angle that this vector makes with the positive x-axis?
Answer: 45 degrees
Explanation: The angle is calculated as arctan(y/x), where arctan(1/1) equals 45 degrees. Option D is incorrect as it assumes a 90-degree orientation.
Q7. A force vector F has a magnitude of 10 N. If another vector -F is added to it, what is the magnitude of the resultant?
Answer: 0
Explanation: Subtracting a vector from itself always results in a null vector with zero magnitude. Option B is wrong because magnitudes cannot be negative.
Q8. A 5 kg block is resting on a flat horizontal table in a state of static equilibrium. Which mathematical condition must be satisfied?
Answer: Sum of forces is zero
Explanation: For the first condition of equilibrium, the vector sum of all forces must be zero. Option A describes the second condition of equilibrium.
Q9. Consider two vectors A = i + j and B = i - j. Determine the angle between these two vectors using the scalar product formula.
Answer: 90 degrees
Explanation: The dot product is (1)(1) + (1)(-1) = 0, indicating a 90-degree angle. Option A is incorrect because the vectors are not parallel.
Q10. A physicist calculates the vector product of A = 2i and B = 3j. What is the magnitude of the resulting vector A x B?
Answer: 6
Explanation: The magnitude of the cross product (2i x 3j) is 6k, which has a magnitude of 6. Option D fails by adding the magnitudes.
Q11. A 100 N weight is hung from the middle of a light string, making an angle of 30 degrees with the horizontal. Calculate the tension.
Answer: 100 N
Explanation: In vertical symmetry, 2T sin(theta) = W. Here T = 100 / (2 * sin 30) = 100 N. Option B ignores the vertical component factor.
Q12. A vector A has a magnitude of 10 units and its x-component is 6 units. Calculate the magnitude of its y-component.
Answer: 8 units
Explanation: Using the Pythagorean theorem, Ay = sqrt(10^2 - 6^2) = 8. Option B is incorrect as it is just the difference 10 - 6.
Q13. A 10 N force is applied at the end of a 2 m long lever arm at an angle of 30 degrees to the arm. Find the torque.
Answer: 10.0 Nm
Explanation: Torque is rF sin(theta), so 2m * 10N * sin(30) = 10 Nm. Option A fails because it uses cosine instead of sine.
Q14. A drone flies from point P(1, 2, 3) to point Q(4, 6, 3) in a Cartesian coordinate system. Calculate the magnitude of its displacement.
Answer: 5 units
Explanation: The displacement vector is (4-1)i + (6-2)j + (3-3)k = 3i + 4j. Magnitude is 5. Option A is the sum of coordinates.
Q15. Two forces of 10 N and 6 N act on a body. What are the maximum and minimum possible magnitudes of their resultant force?
Answer: 16 N and 4 N
Explanation: Max resultant is 10+6=16N and min is 10-6=4N. Option B is wrong as it suggests the minimum can be zero.
Q16. Given a vector A = 3i - 4j, find the unit vector in the direction of A for normalized directional analysis.
Answer: 0.6i - 0.8j
Explanation: The unit vector is A divided by its magnitude (5). This gives 0.6i - 0.8j. Option C is wrong because it uses the wrong signs.
Q17. A 10m uniform plank weighing 100N rests on two end supports. A 200N man stands 2.5m from the left support. Find the left support reaction.
Answer: 200 N
Explanation: Summing torques about one end: R(10) - 100(5) - 200(7.5) = 0, so R = 200N. Option C is wrong because it ignores the plank weight.
Q18. Calculate the area of a parallelogram formed by two vectors A = 3i and B = 4j originating from the same point.
Answer: 12
Explanation: Area equals magnitude of A x B. (3i x 4j) = 12k, magnitude 12. Option A is the result of a dot product.
Q19. A force F = 2i + 3j acts on a body, moving it from (1, 1) to (4, 5). Calculate the work done by this force.
Answer: 18 J
Explanation: Displacement d is (4-1)i + (5-1)j = 3i + 4j. Work = F dot d = (2)(3) + (3)(4) = 18 J. Option D is incorrect.
Q20. A 10 N picture frame is hung by two wires making an angle of 30 degrees with the vertical. Calculate the tension in each wire.
Answer: 10.0 N
Explanation: Using 2T cos(theta) = W where theta is 60 degrees from vertical, T = 10 / (2 * 0.5) = 10 N. Option B is incorrect.