Which of the following pairs of items will be attracted by one another due to gravitational or electromagnetic forces?$F=\frac{Gm\mathrm{\_1}m\mathrm{\_2}}{r^2}$ or $F=\frac{kq\mathrm{\_1}q\mathrm{\_2}}{r^2}$

• A. A plastic comb and small pieces of paper after the comb has been rubbed on wool
• B. A book and a pencil lying side by side on a desk
• C. Two wooden blocks placed next to each other on a table
• D. A glass rod and a plastic ruler, both uncharged

Answer: (A)

Verified step by step guidance

1. Identify the two fundamental forces mentioned: gravitational force and electromagnetic force. The gravitational force between two masses is given by the formula \(F = \frac{G m_1 m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses, and \(r\) is the distance between them.
2. The electromagnetic force between two charges is given by Coulomb's law: \(F = \frac{k q_1 q_2}{r^2}\), where \(k\) is Coulomb's constant, \(q_1\) and \(q_2\) are the electric charges, and \(r\) is the distance between the charges.
3. Analyze each pair of items to determine if they have significant mass or charge that would cause attraction. For example, a plastic comb rubbed on wool becomes electrically charged, and small pieces of paper can be attracted due to induced charges, so electromagnetic attraction occurs.
4. Consider that objects like a book and pencil or wooden blocks have mass and thus gravitational attraction, but this force is extremely weak and not noticeable at everyday scales. Also, if they are uncharged, there is no electromagnetic attraction.
5. Conclude that the pair involving the plastic comb and small pieces of paper after rubbing exhibits noticeable electromagnetic attraction, while the other pairs do not show significant attraction due to either force under normal conditions.