MDCAT Physics chapter 1: Physics · Vectors and equilibrium MCQs with answers
By Team Megalecture · Updated 4 Nov 2026
18 exam-style questions on Physics · Vectors and equilibrium, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.
Ten Physics · Vectors and equilibrium questions with answers
Try each one, then open the answer. These ten stay the same; the test draws new ones every time.
1. A ceiling fan turns at a constant angular velocity. Which statement about the fan is correct?
A
the net torque on it acts in the direction of rotation
B
it cannot be in equilibrium because it is rotating
C
the net torque on it is zero
D
the net force on each of its blades is zero
Show answer
Answer: C. Constant angular velocity means zero angular acceleration, so the motor's torque just balances the torque of air resistance: the fan is in rotational (dynamic) equilibrium. Each blade still needs a centripetal force, so the net force on a blade is not zero.
2. A 30 N weight hangs from a string. A horizontal force pulls the weight sideways and holds it at rest with the string at 45° to the vertical. The tension in the string is
A
30 N
B
15√2 N
C
60 N
D
30√2 N
Show answer
Answer: D. Vertical equilibrium: T cos 45° = 30 N, so T = 30√2 N ≈ 42 N. Horizontal equilibrium then gives the sideways force T sin 45° = 30 N. 15√2 N multiplies by cos 45° instead of dividing.
3. The vector product A × B of two non-parallel vectors is always
A
perpendicular to A and also to B
B
parallel to the vector A + B
C
perpendicular to A but not to B
D
in the plane that contains A and B
Show answer
Answer: A. A × B is normal to the plane containing A and B, its sense given by the right-hand rule, so it is perpendicular to each of them. Its magnitude AB sin θ equals the area of the parallelogram they form.
4. A uniform beam 3.0 m long and of weight 120 N is hinged to a wall at one end and kept horizontal by a vertical rope tied to its other end. A 60 N load hangs 1.0 m from the hinge. The tension in the rope is
A
80 N
B
180 N
C
20 N
D
140 N
Show answer
Answer: A. Take moments about the hinge, where the hinge force has no torque: T × 3.0 = 120 × 1.5 + 60 × 1.0 = 240 N m, so T = 80 N. 180 N is the total weight, and 20 N leaves out the weight of the beam.
5. For two vectors A and B, A · B = 12 and |A × B| = 16. If A has a magnitude of 4 units, the magnitude of B is
A
7 units
B
3 units
C
4 units
D
5 units
Show answer
Answer: D. (AB cos θ)2 + (AB sin θ)2 = (AB)2, so (AB)2 = 122 + 162 = 400 and AB = 20, giving B = 20/4 = 5 units. Adding 12 and 16 directly gives 7 units.
6. The angle between the vectors A = i + √3 j and B = √3 i + j is
A
60°
B
30°
C
45°
D
90°
Show answer
Answer: B. A · B = √3 + √3 = 2√3 and |A| = |B| = 2, so cos θ = 2√3/4 = √3/2 and θ = 30°. (A points at 60° and B at 30° to the x-axis.) Taking sin θ = √3/2 instead gives 60°.
7. For A = 3i + 4j and B = 3i − 4j, the angle between the vectors A + B and A − B is
A
0°
B
90°
C
106°
D
180°
Show answer
Answer: B. A + B = 6i lies along the x-axis and A − B = 8j along the y-axis, so they are at 90°. About 106° is the angle between A and B themselves.
8. An ant walks 4 m due east, then 6 m due north, then 12 m due west. The magnitude of its displacement from the starting point is
A
22 m
B
10 m
C
14 m
D
8 m
Show answer
Answer: B. Net x = 4 − 12 = −8 m and net y = 6 m, so the displacement is √(82 + 62) = 10 m. 22 m is the distance walked, and 14 m adds the two components instead of using Pythagoras.
9. Two equal and opposite forces of 5.0 N act perpendicularly at the two ends of a rod 0.40 m long, forming a couple. The torque of the couple is
A
2.0 N m
B
4.0 N m
C
1.0 N m
D
zero
Show answer
Answer: A. Torque of a couple = one force × perpendicular distance between the forces = 5.0 × 0.40 = 2.0 N m (about the centre: 5.0 × 0.20 + 5.0 × 0.20, the same). The net force is zero, but the net torque is not.
10. The greatest and least possible resultants of two forces are 17 N and 7 N. When the two forces act at right angles to each other, their resultant is
A
13 N
B
12 N
C
10 N
D
18.4 N
Show answer
Answer: A. A + B = 17 N and A − B = 7 N give A = 12 N and B = 5 N, so at right angles R = √(122 + 52) = 13 N. 18.4 N wrongly combines the greatest and least resultants by Pythagoras.
Physics · Vectors and equilibrium: questions students ask
How many Physics · Vectors and equilibrium MCQs are there?
18, each with the answer and a short explanation, across 2 topics: Vectors and components, Products of vectors and torque. Every chapter test draws ten of them, so you can take it many times.
Is the MDCAT Physics chapter 1 test free?
Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.
How is the chapter test marked?
The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.
