Question

A wire of length L and radius r is rigidly clamped from one end and the other end is pulled by force F. It is found that the wire elongates by 5 cm. Another wire of the same material but 4L length and 4r radius is pulled by 4F force under identical conditions. What will be the final elongation of the wire?

• A. 16 cm
• B. 1/16 cm
• C. 5 cm
• D. 4 cm

Hint:

- Elongation in a wire depends on force, length, cross-section, and material properties. - Thicker wires elongate less under the same force.

Answer 1

The Correct Option is D

- Using the elongation formula: \[ \Delta L = \frac{F L}{A E} \] - Since the second wire has 4 times the length and 16 times the area, the elongation is: \[ \Delta L' = \frac{F (4L)}{(16A)E} = \frac{1}{4} \times \Delta L = \frac{1}{4} \times 5 = 4 \text{ cm} \]