The end A is subjected to a tensile force F, while force applied at end B is `Delta F` lesser than applied at the A. Total change in length of the rod will be

Options

A. `(F - Delta F) (L)/(2YA)`
B. `((2F - Delta F)L)/(2YA)`
C. `((2F - Delta F)L)/(YA)`
D. `(F - Delta F) (L)/(YA)`

Answer

B

Explanation

Tension at x
`T = F - [F - DeltaF) (x)/(L)`
`= F - DeltaF (X)/(L)` Change in length `dx Delta dx`
`= (Tdx)/(AY) = ((FL - Delta Fx) dx)/(LAY)`
Total change in length
`(F)/(AY) underset(0)overset(L)int dx - (DeltaF)/(LAY) underset(0)overset(L)int x dx`
`(L)/(2AY) [2Y - DeltaF]`