Q: A steel rod of cross-sectional area 16 cm² and two brass rods each of cross-sectional area 10 cm² together support a load of 5000 kg as shown in figure. Find the stress in the rods. Take Y for steel = 2.0 × 10^{6} kg/cm² and for brass = 1.0 × 10^{6} kg/cm².

(a) σ_{S} =161.2 kg/cm²

(b) σ_{B} =161.2 kg/cm²

(c) σ_{S} =161.3 kg/cm²

(d) σ_{B} =161.3 kg/cm²

Ans: (a)

Sol: Stress in steel rod = σ_{S}

and , Stress in brass rod = σ_{B}

A_{S} = 16 cm²

A_{B} = 10 cm²

decrease in length of steel rod = Decrease in length of brass rod

$ \displaystyle \frac{\sigma_S}{Y_S}\times L_S = \frac{\sigma_B}{Y_B}\times L_B $

$ \displaystyle \sigma_S =\frac{Y_S}{Y_B} . \frac{L_B}{L_S} \times \sigma_B $

$ \displaystyle \sigma_S =\frac{2 \times 10^6}{10^6} . \frac{20}{30} \times \sigma_B $

$ \displaystyle \sigma_S = \frac{4}{3} \times \sigma_B $ …(i)

Now , $ \displaystyle F = \sigma_S A_S + 2 \sigma_B A_B $

$ \displaystyle 50000 = \sigma_S A_S + 2 \sigma_B A_B $

On putting given values , get the ans