A uniform cylindrical rod of length L and cross-sectional area A having Young's modulus Y is acted upon by forces as shown in figure. [CG PMT 2015]The elongation produced in the rod is

Elongation produced, if the  23 part of length L of rod is stretched by a force of 3F, is given byΔL1=FL1AY=3F×23LAY=2FLAYElongation produced, if the remaining (1/3) part of length L of rod is stretched by a force of 2F, is given byΔL2=F2L2AY=2F×13LAY=23FLAYTotal elongation produced in the rod,ΔL=ΔL1+ΔL2=2FLAY+23FLAY∴ ΔL=8FL3AY