A wire of length L and area of cross section A is made of a material of Young's modulus Y. If it is stretched by an amount x, the work done is given by

Options

A. `(2Y A x^(2))/(L)`
B. `(Y Ax^(2))/(L)`
C. `(1)/(2) (Y A x^(2))/(L)`
D. `(1)/(2) (Y A x)/(L)`

Answer

C

Explanation

Work done `= (1)/(2) "load" xx "extension"`
`because Y = (MgL)/(Ax) :. Load = Mg = (YAx)/(L)`
`:. W = (1)/(2) xx (Yax)/(L) xx x = (1)/(2) (YAx^(2))/(L)`