A uniform elastic rod of cross section area A natural length L and Young's modulus Y is placed on a smooth horizontal surface. Now two horizontal forces (of magnitude F and 3F) directed along the length of rod and in opposite direction act at two of its ends as shown . After the rod has acquired steady state, the extension of the rod will be

Options

A. `(2F)/(YA)L`
B. `(4F)/(YA)L`
C. `(F)/(YA)L`
D. `(3F)/(2YA)L`

Answer

A

Explanation

Tension in rod at a distance x from right edge is
`T=F(3-2(x)/(L))`
Net extension in rod `=int_0^L(T)/(4A)dx=(2F)/(YA)L`