Practice Vectors & Equilibrium MCQs for HEC USAT-M (Pre-Medical) Physics — topic-wise sets with solved answers.
Q1. A student needs to specify the direction of a force in the xy-plane without changing its magnitude. Which mathematical tool should be used?
Answer: Unit vector
Explanation: A unit vector is used only to specify direction; its magnitude is exactly one. Option C is wrong because unit vectors are dimensionless.
Q2. Two forces of equal magnitude act on a stationary block in exactly opposite directions. What is the resultant of these two vectors?
Answer: Null vector
Explanation: The null vector has zero magnitude and arbitrary direction. Option A is tempting but wrong because it implies a specific, non-zero direction.
Q3. A porter carries a heavy suitcase while walking horizontally. What is the work done by the force of gravity on the suitcase?
Answer: Zero
Explanation: The dot product is zero when vectors are perpendicular (cos 90 = 0). Option A is wrong because work is a scalar product.
Q4. When applying a force to a wrench, the resulting torque is a vector quantity. What is the orientation of this torque vector?
Answer: Perpendicular to the plane
Explanation: The cross product results in a vector perpendicular to the plane of the operands. Option B is wrong as it's only for dot products.
Q5. A mechanic applies a 100 N force at an angle of 30 degrees to a wrench of length 20 cm. What is the torque?
Answer: 10 Nm
Explanation: Torque is rF sin(theta); sin(30) is 0.5, so 0.2m * 100N * 0.5 = 10 Nm. Option C fails by using cosine.
Q6. A car moves along a straight highway at a constant velocity of 80 km/h. Which condition of equilibrium is strictly satisfied?
Answer: Sum of forces is zero
Explanation: The first condition requires the vector sum of all external forces to be zero. Option A is only for rotational equilibrium.
Q7. A uniform beam is balanced on a pivot such that it does not rotate. Which condition is being satisfied in this scenario?
Answer: Second condition of equilibrium
Explanation: The second condition ensures no net rotation by requiring the sum of torques to be zero. Option B describes translational equilibrium.
Q8. A vector of magnitude 10 units makes an angle of 60 degrees with the positive x-axis. What is the horizontal component?
Answer: 5 units
Explanation: The x-component is calculated as A cos(theta). For 10 units at 60 degrees, 10 * 0.5 = 5. Option A incorrectly uses sine.
Q9. An air traffic controller tracks a plane at coordinates (3, 4, 5) relative to the tower. What vector describes this location?
Answer: Position vector
Explanation: Position vectors start from the origin (0,0,0) to the point (x,y,z). Option C represents a displacement vector between two points.
Q10. Two forces of 6 N and 8 N act on a single point. Which of the following could possibly be their resultant magnitude?
Answer: 10 N
Explanation: The resultant range is |A-B| to |A+B|. Here, 8-6=2 and 8+6=14. Option B is wrong as it's below the minimum.
Q11. In a physics lab, a student adds three displacement vectors graphically by joining them sequentially. Which rule are they applying?
Answer: Head-to-tail rule
Explanation: Head-to-tail rule adds vectors by joining the head of the first to the tail of the second. Option B describes subtraction.
Q12. While studying vector algebra, a student notices that the product of two vectors remains unchanged when their order is reversed. Which product is this?
Answer: Scalar product
Explanation: The scalar product is commutative (A.B = B.A). Option A is wrong because cross products are anti-commutative.
Q13. When calculating the area of a parallelogram using vector products, how does reversing the order of vectors affect the result?
Answer: A x B = -(B x A)
Explanation: A x B = -(B x A), meaning it is anti-commutative. Option A is wrong because the magnitudes are equal but directions opposite.
Q14. A rigid ladder rests against a smooth wall and a rough floor. What must be true for the ladder to remain stationary?
Answer: Both first and second conditions
Explanation: Total equilibrium requires both zero net force and zero net torque. Option A only covers translational motion.
Q15. In a torque calculation, what is the term for the perpendicular distance from the axis of rotation to the force's line of action?
Answer: Moment arm
Explanation: The moment arm is the perpendicular distance from the pivot to the line of action. Option B is just the displacement.
Q16. A student has the x and y components of a force vector. Which trigonometric function determines the angle with the x-axis?
Answer: Tangent inverse ratio
Explanation: The direction theta is found using tan inverse of (Ay/Ax). Option A is wrong because it calculates magnitude.
Q17. If a vector is divided by its own magnitude, what is the magnitude of the resulting vector?
Answer: 1
Explanation: By definition, a unit vector has a magnitude of exactly 1. Option A is the magnitude of a null vector.
Q18. A picture frame is hung by two symmetric strings making an angle theta with the horizontal. What relates tension T to weight W?
Answer: 2T sin(theta) = W
Explanation: In vertical equilibrium, the sum of vertical components of tension must equal the weight. Option B ignores the angle.
Q19. A researcher uses two vectors representing the sides of a crystal face. What represents the area of this face?
Answer: Magnitude of cross product
Explanation: The magnitude of the cross product |A x B| equals the area of the parallelogram. Option D refers to a triangle.
Q20. During a vector subtraction exercise, a student subtracts a displacement vector from itself. What is the specific name of the result?
Answer: Null vector
Explanation: Subtracting a vector from itself (A - A) results in a null vector. Option A is wrong because it's a vector, not a scalar.
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