Question

An elastic string of unstretched length L and force constant k is stretched by a small length x. It is further stretched by another small length y. The work done in the second stretching is

• A. \( \dfrac{1}{2} k y^2 \)
• B. \( \dfrac{1}{2} k (2x + y) y \)
• C. \( \frac{1}{2}k(x^2+y^2) \)
• D. (1)/(2)k(x+y)²

Hint:

Work done in stages equals difference of elastic potential energies.

Answer 1

The Correct Option is B

Step 1: Work done in stretching elastic string: W = (1)/(2)k(extension)²
Step 2: Work done in second stretch: W = (1)/(2)k[(x+y)² - x²]
Step 3: Simplifying, W = (1)/(2)k(2x+y)y