The table shows some physical quantities.
Which row correctly identifies the quantities as scalars or vectors?
| acceleration | charge | kinetic energy | wavelength | |
|---|---|---|---|---|
| A | scalar | vector | vector | scalar |
| B | vector | vector | scalar | scalar |
| C | scalar | scalar | scalar | vector |
| D | vector | scalar | scalar | scalar |
Correct Answer: \( \boxed{\mathrm{D}} \)
Acceleration is a vector quantity because it has both magnitude and direction.
Charge, kinetic energy and wavelength are scalar quantities because they have magnitude only.
Therefore, the correct answer is (D).
The diagram shows two forces of \( 6.0\,\mathrm{N} \) acting on an object. The angle between the lines of action of the two forces is \( 60^\circ \).
What is the magnitude of the resultant force?
Correct Answer: \( \boxed{\mathrm{C}} \)
Using the cosine rule for vector addition,
\( R=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\theta} \).
Substituting \( F_1=F_2=6.0\,\mathrm{N} \) and \( \theta=60^\circ \),
\( R=\sqrt{6^2+6^2+2(6)(6)\cos60^\circ}=\sqrt{36+36+36}=\sqrt{108}\approx10.4\,\mathrm{N} \).
To two significant figures, the resultant force is \( 10\,\mathrm{N} \).
Therefore, the correct answer is (C).
Two vectors, X and Y, are shown.
What are the directions of \(X+Y\) and \(X-Y\)?
Correct Answer: \( \boxed{\mathrm{B}} \)
Vector X is directed up and to the right, while vector Y is directed down and to the right.
For \(X+Y\), the vertical components cancel because they are equal and opposite, while the horizontal components add together. Hence, \(X+Y\) points horizontally to the right.
For \(X-Y=X+(-Y)\), reversing \(Y\) gives a vector directed up and to the left. Adding this to \(X\) causes the horizontal components to cancel while the vertical components add, giving a vector directed upward.
Therefore, the correct answer is (B).
