Properties of Matter Part 2

Given, breaking stress of wires 1 and 2 are $\sigma_{1}=\sigma_{2}=1.25 \times 10^{9} \text{ N/m}^2$Cross-sectional area of wire 1 ,$A_{1}=8 \times 10^{-7} \text{ m}^{2}$Cross-sectional area of wire 2 ,$A_{2}=4 \times 10^{-7} \text{ m}^{2}$Mass hanging from first wire, $m_{1}=20 \text{ kg}$ Mass hanging from second wire,$m_{2}=10 \text{ kg}$Acceleration due to gravity, $g=10 \text{ ms}^{-2}$Let $m$ be the maximum mass placed in pan without breaking the wire.According to free body diagram of given figure, Since, $\text{stress}(\sigma) = \frac{\;\text{Tension}\;(T)}{\text{Area}(A)}$$\therefore \;\; T_{1} = \sigma A_{1}$$= 1.25 \times 10^{9} \times 8 \times 10^{-7}$$= 10.00 \times 10^{2} = 1000 \text{ N}$and $T_{2} = \sigma A_{2}$$= 1.25 \times 10^{9} \times 4 \times 10^{-7}$$= 5.00 \times 10^{2} = 500 \text{ N}$By using concept of tension in string$T_{2} = (10 + m) g$$\Rightarrow \;\; 500 = (10 + m) 10$$\Rightarrow \;\; m = 50 - 10 = 40 \text{ kg}$