A long thin metallic rod of length l, cross sectional area S and Young's modulus γ rests on a smooth horizontal surface. A horizontal force P is applied at one end of the rod. Then the elongation produced in the rod is

(4)a = Acceleration of the rod, a = P/m. If we observe the rod from its frame, then pseudo force ma acts at the COM C of the rod. So under the action of P and ma, elongation produced in the rod is δ=P×  ACSγ =   P.  l2Sγ=Pl2Sγ.