A uniform rod of length `L` and mass `M` is pulled horizontally on a smooth surface with a force `F`. Determine the elongation of rod if Young's modulus of the material is `Y`.

Explanation

Let a small element `dx` from the free end of the rod, the magnitude of force at this section is
`F^(1) = (F)/(L) (x)`,
Elonagation on this differential element is
`de = (F)/(YAL) xx x xx dx `, Total elongation, `e = int de`
`e = int_(0)^(L) (F)/(YAL) xdx = (F)/(YAL) [(x^(2))/(2)]_(0)^(L) rArr e = (1)/(2) (FL)/(YA)`