A wire of length L and cross sectional area A is made of a material of Young's modulus Y. If the wire is streched by an amount x, the work done is………………

Options

A. `(Y x A)/(2L)`
B. `(Y x^(2) A)/(L)`
C. `(Y x^(2) A)/(2L)`
D. `(2Y x^(2)A)/(L)`

Answer

C

Explanation

Here, `Delta l=x, y =(F//A)/(Delta l//l)` or `F=(YA Delta L)/(L)`
For the stretching force F applied on the wire, increases in the length of wire `Delta L(=x)`. The internal force increases from 0 to F. Thus average internal force an increase in length `Delta l` of the wire is
`=(0+F)/(2)=(F)/(2)`
Work done `=(F)/(2)xxDelta L`
`=(YA Delta L)/(2L)xxDelta L=(YA(Delta L)^(2))/(2L) =(Y x^(2)A)/(2L)`