A rail tack made of steel having length l0 m is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by 20°C. It is deformed as shown in figure. Find x (displacement of the centre) if                       αsteel= 1.2 ×10-5/ 0C

Consider the diagram.Applying Pythagoras theorem in right angled triangle in figure(L+∆L2)2 = (L2)2 +x2⇒x = (L+∆L2)2-(L2)2   = 12(L+∆L)2-L2⇒12(∆L2+2L∆L)As increase in length ∆L is very small, therefore, neglecting ((∆L)2), we getx = 12×2L∆L    ---------(i)But ∆L = L α∆t------(ii)Substituting value of ∆L in Eq.(i) from Eq.(ii)x= 122L×Lα∆t = 12L2α∆t    = 102×2×1.2×10-5×20    = 5×4×1.2×10-4 = 2030 ×10-3 cm