Vectors and Equilibrium

10 free MDCAT Physics MCQs on Vectors and Equilibrium (PM&DC syllabus), each with the answer, an explanation and the textbook line it comes from. Tap to check, no sign-up.

Tap an answer to check it · 10 questions

1. Question 1

   The scalar product of two vectors obeys the:
   • AHead to tail rule
   • BAnti-commutative property
   • CRight hand rule
   • DCommutative property
   Show answer and explanation

   Answer: D) Commutative property

   A . B = AB cos theta = B . A. Source: 11 Physics Book FBISE, p. 26.

2. Question 2

   A trolley is pushed with a force of 50 N at 30 to the horizontal road. The horizontal component of the force is:
   • A43.3 N
   • B25 N
   • C50 N
   • D86.6 N
   Show answer and explanation

   Answer: A) 43.3 N

   Fx = F cos 30 = 50 x 0.866 = 43.3 N; Fy = 50 sin 30 = 25 N. Source: 11 Physics Book FBISE, p. 25.

3. Question 3

   An engine exerts a force F = (8i - 2j) N while moving with velocity v = (3i + 4j) m/s. The power delivered is:
   • A32 W
   • B16 W
   • C24 W
   • D40 W
   Show answer and explanation

   Answer: B) 16 W

   P = F . v = (8)(3) + (-2)(4) = 24 - 8 = 16 W. Source: 11 Physics Book FBISE, p. 27.

4. Question 4

   Two vectors of magnitudes 3.2 and 5.2 units make an angle of 60. The magnitude of their cross product is about:
   • A16.6 units
   • B8.3 units
   • C14.4 units
   • D9.6 units
   Show answer and explanation

   Answer: C) 14.4 units

   |A x B| = AB sin 60 = 16.64 x 0.866 = 14.4; the dot product would be 8.3. Source: 11 Physics Book FBISE, p. 29.

5. Question 5

   Which of the following is an example of a scalar product?
   • ATorque
   • BWork
   • CAngular momentum
   • DForce
   Show answer and explanation

   Answer: B) Work

   W = F . d; power and electric flux are other examples. Source: 11 Physics Book FBISE, p. 26.

6. Question 6

   Torque is the vector (cross) product of:
   • AMomentum and time
   • BForce and velocity
   • CPosition vector and force
   • DMass and acceleration
   Show answer and explanation

   Answer: C) Position vector and force

   tau = r x F; angular momentum L = r x p. Source: 11 Physics Book FBISE, p. 28.

7. Question 7

   The direction of the vector product A x B is:
   • AAlong the sum A + B
   • BParallel to vector A
   • CParallel to vector B
   • DPerpendicular to A and B
   Show answer and explanation

   Answer: D) Perpendicular to A and B

   Given by the right hand rule, rotating from A to B through the smaller angle. Source: 11 Physics Book FBISE, p. 28.

8. Question 8

   If two vectors represent adjacent sides of a parallelogram, the magnitude of their cross product gives the:
   • AArea of the parallelogram
   • BLength of a diagonal
   • CPerimeter of the figure
   • DAngle between them
   Show answer and explanation

   Answer: A) Area of the parallelogram

   The unit vector n gives the direction normal to the area. Source: 11 Physics Book FBISE, p. 29.

9. Question 9

   The cross product of a unit vector with itself (i x i) is:
   • AUnity
   • BA null vector
   • CThe unit vector k
   • DMinus one
   Show answer and explanation

   Answer: B) A null vector

   sin 0 = 0; whereas i . i = 1. Source: 11 Physics Book FBISE, p. 28.

10. Question 10

    The dot product of a unit vector with itself (i . i) is:
    • AA null vector
    • BZero
    • CUnity
    • DThe unit vector j
    Show answer and explanation

    Answer: C) Unity

    cos 0 = 1 and the magnitude of a unit vector is 1. Source: 11 Physics Book FBISE, p. 27.

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