Step 1: Understanding the Question:
We need to identify the logically false statement among the given options regarding the fundamental properties of electric charges.
Step 2: Detailed Explanation:
Let's evaluate each option:
(A) Static charges are produced by rubbing: This is true. Frictional electricity (triboelectric effect) is generated by rubbing two suitable materials together.
(B) An electroscope can detect whether a body is charged or not: This is true. A gold-leaf electroscope diverges its leaves when brought near or in contact with a charged body.
(C) Like charges repel each other: This is a fundamental law of electrostatics and is entirely true.
(D) A glass rod becomes negative charged when it is rubbed with silk: This statement is mathematically and physically incorrect. When a glass rod is rubbed with silk, electrons are transferred from the glass rod to the silk. Because it loses electrons, the glass rod acquires a positive charge, while the silk acquires a negative charge.
Step 3: Final Answer:
The incorrect statement is that a glass rod becomes negatively charged when rubbed with silk.