A wire of length L and area of cross-section A is stretched through a distance x metre by applying a force F along length, then the work done in this process is : (Y is Young's modulus of the material)

Options

A. `1/2 (A.L) ((Yx)/(L)) ((x)/(L))`
B. `(A.L) (YL) ((x)/(L))`
C. `2 (A.L) (YL) ((x)/(L))`
D. `4 (A.L) (YL) ((x)/(L))`

Answer

A

Explanation

Work done `= 1/2 xx` stress `xx` strain `xx` volume
or `W =1/2 Y x/L xx x/L xx AL`
`=1/2 (AL) (Y (x)/(L)) ((x)/(L))`