Physics · Physics of Solids

According to Hooke's Law, the extension (or increase in length) of a wire is directly proportional to the force applied to it, as long as the elastic limit is not exceeded. If a certain force increases the length of the wire by 1 mm, applying double that force (2F) will increase the length by 2 mm. The other options suggest a non-linear relationship between force and extension, which contradicts Hooke's Law. Therefore, Option A (2F) is the correct answer, while Options B (4F), C (8F), and D (16F) are all incorrect.

This option indicates that doubling the force will double the extension. According to Hooke's Law, this is the correct answer.

This option suggests that quadrupling the force would be necessary. However, Hooke's Law indicates that the relationship is linear, so this is incorrect.

This option implies that eight times the force is required. Since the extension is linear with respect to the force, this option is incorrect.

This option suggests that sixteen times the force is necessary, which is not consistent with the principles of Hooke's Law. Therefore, this option is incorrect.