Question

The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?

Answer 1

As we know that the Young’s modulus is given by,

Young's modulus,

$\left(Y\right)=\frac{TensileStress}{Longitudinalstrain}$

For same longitudinal strain, Young's modulus is proportional to tensile stress,

i.e., $Y\alpha stress$

$Y_s\left(steel\right)>Y_r\left(rubber\right)$

$\therefore \frac{Y_{Steel}}{Y_{rubber}}=\frac{(Stress{)}_{Steel}}{(Stress{)}_{rubber}}$ …..(i)

$\because \frac{Y_{steel}}{Y_{rubber}}>1$

Therefore, from Eq. (i),

$\frac{(Stress{)}_{steel}}{(Stress{)}_{rubber}}>1$

$\to (Stress{)}_{steel}>(Stress{)}_{rubber}$

Hence, for same longitudinal strain, steel will have greater tensile stress than that of rubber.

Final Answer: Steel