Question

A wire fixed at the upper end streched by length l by applying a force the work done in streching is​

Answer 1

Answer:

Work done = Fl/ 2

Explanation:

As per given question statement; a force F is applied to stretch a wire of length l

We need to find the work done in this case;

Formula for the work done is:

Work done =1/ 2 × stress × strain × volume

Putting the formulas of stress, strain and volume, we have;

Work done = 1/2× F/A × l/ L × A L

Work done = Fl/ 2

Answer 2

The work done in stretching is Fl/2

Explanation:

The young's modulus of the wire is given by the formula:

Y = FL/Al

Now, the force from the young's modulus is:

F = YAl/L ⇒ (equation 1)

The work done is given by the formula:

Work done = Force × Length

Now, the work done acting on the small area of the wire is derived as:

dW = F × dl

Now, on substituting force formula, we get,

$dW=\frac{Y A l(d l)}{L}$

Now, on integrating the work done for a large area, we get,

$\int d W=\frac{Y A}{L} \int_{0}^{l} l d l$

Now, the work done is:

$W=\frac{Y A l^{2}}{2 L}$

Now, from equation (1),  we get,

W = Fl/2