A steel bar `ABCD` `40 cm` long is made up of three parts `AB, BC` and `CD`, as shown in figure. The rod is subjected to a pull of `25 kN`. Determine the stress in the the parts and the total extension of the rod. Young's modulus for steel`=2xx10^(11)Nm^(-2)`.

Options

A. 0.0637 mm
B. 0.0647 mm
C. 0.0657 mm
D. 0.0667 mm

Answer

A

Explanation

The axial froce 25 kN is transmitted to each of the three bars.
Stress in part AB is `(25000N)/((pi)/(4)(50)^(2) mm^(2)) = (40)/(pi) = 12.73 N//mm^(2)`
Stress in part `BC=(25000)/((pi)/(4)(25)^(2)) = 50.93 N/mm^(2)`
Stress in part CD `= 12.73 N//mm^(2)`
Therefore, total extension of the rod == extension in the parts AB + BC + CA.
`= ((12.73 N//mm^(2))/(2xx10^(5)N//mm^(2))xx 100mm )xx2+ (50.93 N//mm^(2))/(2xx10^(5)N//mm^(2)) xx200 mm = (12732)/(2xx10^(5)) mm = 0.0637 mm`