A wire of length L and cross-sectional area A is made of material of Young's modulus Y. The work done in stretching the wire by an amount x is

Options

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

Answer

A

Explanation

If a force F is applied along the length L of wire for stretching by an amount x, then Young's modulus is given by.
`Y = ("stress")/("strain") = (FL)/(Ax)`
where , A = area of cross -sectional `rArr F =(YA)/(L)x`
The work done in stretching wire is given by
`W = underset(0)overset(x)int F.dx = underset(0)overset(x)int(YA)/(L)x =(YA)/(L)[(x^(2))/(2)]_(0)^(x) =(YAx^(2))/(2L)`