Question

A wire fixed at the upper end stretches by length $\mathrm{l}$ by applying a force $\mathrm{F}$. The work done in stretching is:

• A. $\frac{\mathrm{F}}{2\mathrm{l}}$
• B. $\mathrm{Fl}$
• C. $\frac{2\mathrm{F}}{\mathrm{l}}$
• D. $\frac{\mathrm{Fl}}{2}$

Answer 1

The correct option is D

$\frac{\mathrm{Fl}}{2}$

Step 1: Given data and formula used

Let, The area be $\mathrm{A}$.

Stretch length = $\mathrm{l}$

The work done by the force $\mathrm{F}$ is

$\mathrm{Work}\mathrm{done}=\frac{1}{2}\times \mathrm{stretching}\mathrm{force}\times \mathrm{extension}\mathrm{in}\mathrm{length}$

Step 2: Determine the work done

The work done in stretching is equal to half of the product of stretching force and the increase in length.

By substituting the values in the above formula,

Work done $=\frac{1}{2}\times \mathrm{F}\times \mathrm{l}$

$=\frac{\mathrm{Fl}}{2}$

Therefore, the work done in stretching is $\frac{\mathrm{Fl}}{2}$.

Hence, option (D) is the correct answer.