A steel rod of cross-sectional area `Im^(2)` is acted upon by forces as shown in the Fig. Determine the total elongation of the bar. Take `Y = 2.0xx10^(11) N//m^(2)`

Options

A. The area of right bar is `10 cm ^(2)`
B. the stresses in left and right bar are in ratio 3:2
C. The decreases in thickness of bar is more for the left
D. The decreases in thickness of bar is more for right bar.

Answer

BC

Explanation

`Deltal=(Fl_(0))/(Ay)`
`rArr (l_(0))/A=(l'_(0))/(A')`
`0.6/15=0.4(A') rArr A' =10 cm^(2)`
Stress =`F/ArArr (sigma_(1))/(sigma_(2))=(A_(2))/(A_(1))=10/15`
`(DeltaT)/r=-sigma (Deltal)/l`
`Deltar=-sigma (Deltal)/l xxr=-sigma Deltal (sqrt(A))/l`
`Delta_("left")=(sqrt(15))/0.6=sqrt(1500/0.36)`
`Deltar_("Right")=(sqrt(10))/0.4 =sqrt(1000/0.16)`