A wire of length L and density `rho` and Young's modulus Y is hanging from a support. Find the elongation in the length of wire at which wire will break:

Options

A. `Delta l = (rho g l^(2))/(2Y)`
B. `Delta l = (rho gl^(2))/(3Y)`
C. `Delta l = (2rho gl^(2))/(Y)`
D. `Delta l = (3 rho g l^(2))/(Y)`

Answer

A

Explanation

Now putting `rho = rho (l - x)g` in the expression `Delta l = (1)/(y) int_(0)^(1)`, We have `Delta l = (rho g)/(Y) int_(0)^(l) (l - xdx)`
this gives `Delta l = (rho g l^(2))/(2Y)`