Force and Motion

Sample questions

Showing 20 of 70 questions from this chapter. The full bank is in the chapter test below.

1. 1

   Which of the following is a vector quantity?

   • A.Speed
   • B.✓ Displacement (correct answer)
   • C.Energy
   • D.Work

   Why: Displacement is completely specified only when a direction is given along with its magnitude. Speed, energy and work are scalars, each fixed by a magnitude alone.
2. 2

   Which of the following is a scalar quantity?

   • A.Momentum
   • B.Force
   • C.Acceleration
   • D.✓ Temperature (correct answer)

   Why: Temperature is fully described by its magnitude and unit, for example $20^\circ\mathrm{C}$, and has no direction. Momentum, force and acceleration are all vectors.
3. 3

   The length of the arrow used to represent a vector in a vector diagram indicates the

   • A.✓ magnitude of the vector (correct answer)
   • B.direction of the vector
   • C.unit of the vector
   • D.angle the vector makes with the x-axis

   Why: The arrow is drawn with a length proportional to the magnitude, while the head of the arrow shows the direction.
4. 4

   Which one of the following pairs contains a scalar quantity and a vector quantity?

   • A.distance and speed
   • B.force and momentum
   • C.✓ mass and displacement (correct answer)
   • D.work and energy

   Why: Mass is a scalar and displacement is a vector. The members of each of the other pairs are either both scalars or both vectors.
5. 5

   A vector of magnitude $A$ makes an angle $\theta$ with the x-axis. Its x-component is

   • A.✓ $A\cos\theta$ (correct answer)
   • B.$A\sin\theta$
   • C.$A\tan\theta$
   • D.$A\sec\theta$

   Why: The component along the x-axis is $A\cos\theta$, while the component along the y-axis is $A\sin\theta$.
6. 6

   A force of $50\ \mathrm{N}$ acts at an angle of $60^\circ$ to the x-axis. Its x-component is

   • A.$43\ \mathrm{N}$
   • B.✓ $25\ \mathrm{N}$ (correct answer)
   • C.$50\ \mathrm{N}$
   • D.$87\ \mathrm{N}$

   Why: $F_x = 50\cos 60^\circ = 25\ \mathrm{N}$. The value $43\ \mathrm{N}$ is the y-component, $50\sin 60^\circ$.
7. 7

   A force of $100\ \mathrm{N}$ is applied at $30^\circ$ above the horizontal. Its vertical component is

   • A.$100\ \mathrm{N}$
   • B.$86.6\ \mathrm{N}$
   • C.$70.7\ \mathrm{N}$
   • D.✓ $50\ \mathrm{N}$ (correct answer)

   Why: The vertical component is $100\sin 30^\circ = 50\ \mathrm{N}$. The value $86.6\ \mathrm{N}$ is the horizontal component, $100\cos 30^\circ$.
8. 8

   A vector has rectangular components $A_x = 3$ and $A_y = 4$. Its magnitude is

   • A.$7$
   • B.$12$
   • C.✓ $5$ (correct answer)
   • D.$25$

   Why: $A = \sqrt{A_x^2 + A_y^2} = \sqrt{9 + 16} = 5$. Simply adding the components to get 7 is a common error.
9. 9

   The x-component and the y-component of a vector are equal in magnitude. The angle the vector makes with the x-axis is

   • A.$30^\circ$
   • B.$60^\circ$
   • C.$90^\circ$
   • D.✓ $45^\circ$ (correct answer)

   Why: $\tan\theta = A_y/A_x = 1$, so $\theta = 45^\circ$.
10. 10

    The direction of a vector, measured from the x-axis, is found from its rectangular components by using

    • A.$\theta = \tan^{-1}(A_x/A_y)$
    • B.✓ $\theta = \tan^{-1}(A_y/A_x)$ (correct answer)
    • C.$\theta = \sin^{-1}(A_y/A_x)$
    • D.$\theta = \cos^{-1}(A_y/A_x)$

    Why: $\tan\theta = A_y/A_x$, so $\theta = \tan^{-1}(A_y/A_x)$. Inverting the ratio would give the angle measured from the y-axis.
11. 11

    The scalar product of two vectors $\mathbf{A}$ and $\mathbf{B}$ with an angle $\theta$ between them is

    • A.✓ $AB\cos\theta$ (correct answer)
    • B.$AB\sin\theta$
    • C.$AB\tan\theta$
    • D.$AB$

    Why: The scalar or dot product is defined as $AB\cos\theta$; the $AB\sin\theta$ form belongs to the vector product.
12. 12

    The scalar product of two vectors is maximum when the vectors are

    • A.perpendicular to each other
    • B.anti-parallel to each other
    • C.✓ parallel to each other (correct answer)
    • D.at $45^\circ$ to each other

    Why: $\mathbf{A}\cdot\mathbf{B} = AB\cos\theta$ is largest when $\cos\theta = 1$, which happens when the vectors are parallel.
13. 13

    The scalar product of two mutually perpendicular non-zero vectors is

    • A.$AB$
    • B.$-AB$
    • C.$AB/2$
    • D.✓ zero (correct answer)

    Why: The angle is $90^\circ$ and $\cos 90^\circ = 0$, so the scalar product of perpendicular vectors vanishes. For anti-parallel vectors the angle is $180^\circ$ and the product would instead be $-AB$.
14. 14

    The direction of the vector product $\mathbf{A}\times\mathbf{B}$ is determined by

    • A.✓ the right hand rule, the product being perpendicular to the plane of $\mathbf{A}$ and $\mathbf{B}$ (correct answer)
    • B.the head-to-tail rule, the product lying in the plane of $\mathbf{A}$ and $\mathbf{B}$
    • C.the rule that the product points along the larger of the two vectors
    • D.the rule that the product bisects the angle between $\mathbf{A}$ and $\mathbf{B}$

    Why: Curl the fingers of the right hand from $\mathbf{A}$ towards $\mathbf{B}$ through the smaller angle and keep the thumb erect; the thumb then gives the direction of $\mathbf{A}\times\mathbf{B}$, which is perpendicular to the plane containing the two vectors.
15. 15

    The scalar product of two vectors becomes equal in magnitude to their vector product when the angle between them is

    • A.$30^\circ$
    • B.$60^\circ$
    • C.✓ $45^\circ$ (correct answer)
    • D.$90^\circ$

    Why: $AB\cos\theta = AB\sin\theta$ requires $\tan\theta = 1$, which gives $\theta = 45^\circ$.
16. 16

    A force of $20\ \mathrm{N}$ acts at $60^\circ$ to the direction of a displacement of $5\ \mathrm{m}$. The work done by the force is

    • A.$100\ \mathrm{J}$
    • B.✓ $50\ \mathrm{J}$ (correct answer)
    • C.$86.6\ \mathrm{J}$
    • D.$25\ \mathrm{J}$

    Why: $W = Fd\cos\theta = (20)(5)\cos 60^\circ = 50\ \mathrm{J}$. Using $Fd$ alone gives $100\ \mathrm{J}$, which ignores the angle.
17. 17

    The magnitude of the vector product of two vectors is

    • A.$AB\cos\theta$
    • B.$AB\tan\theta$
    • C.✓ $AB\sin\theta$ (correct answer)
    • D.$A^2B^2\sin\theta$

    Why: The vector or cross product has magnitude $AB\sin\theta$ and is directed perpendicular to the plane containing the two vectors.
18. 18

    The vector product of two parallel vectors is

    • A.a vector of magnitude $AB$
    • B.a vector of magnitude $2AB$
    • C.a unit vector along their common direction
    • D.✓ a null vector (correct answer)

    Why: For parallel vectors $\theta = 0^\circ$ and $\sin 0^\circ = 0$, so $\mathbf{A}\times\mathbf{B} = 0$.
19. 19

    The magnitude of $\mathbf{A}\times\mathbf{B}$ is maximum when the angle between $\mathbf{A}$ and $\mathbf{B}$ is

    • A.✓ $90^\circ$ (correct answer)
    • B.$45^\circ$
    • C.$0^\circ$
    • D.$180^\circ$

    Why: The magnitude $AB\sin\theta$ is greatest when $\sin\theta = 1$, that is at $90^\circ$; at $0^\circ$ or $180^\circ$ it is zero.
20. 20

    For two vectors $\mathbf{A}$ and $\mathbf{B}$, which relation is correct?

    • A.$\mathbf{A}\times\mathbf{B} = \mathbf{B}\times\mathbf{A}$
    • B.✓ $\mathbf{A}\times\mathbf{B} = -\mathbf{B}\times\mathbf{A}$ (correct answer)
    • C.$\mathbf{A}\times\mathbf{B} = 2\,\mathbf{B}\times\mathbf{A}$
    • D.$\mathbf{A}\times\mathbf{B} = \mathbf{A}\cdot\mathbf{B}$

    Why: Reversing the order of a cross product reverses its direction, so the vector product is not commutative.