Wires W1 and W2 are made of same material having the breaking stress… | JEE Main 2021 (27 Aug, Shift 2)

Q11JEE Main 2021 · 27 AUG · SHIFT 2Medium

Thermal Stress & Breaking Stress

Wires W1 and W2 are made of same material having the breaking stress of 1.25 $\times$ 109 N/m2. W1 and W2 have cross-sectional area of 8 $\times$ 10−7 m2 and 4 $\times$ 10−7 m2, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ____________ kg. (Use g = 10 m/s2)

Numerical answer type. Work it out, then open the answer.

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Answer: 40

W1 holds $(20 + 10 + m)g$ : $(30 + m) \times 10 \le 1.25 \times 10^9 \times 8 \times 10^{-7} = 1000\text{ N} \Rightarrow m \le 70\text{ kg}$ .
W2 holds $(10 + m)g$ : $(10 + m) \times 10 \le 1.25 \times 10^9 \times 4 \times 10^{-7} = 500\text{ N} \Rightarrow m \le 40\text{ kg}$ .
Both wires must survive, so take the smaller value.
So the answer is 40 kg.

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Thermal Stress & Breaking Stress question from JEE Main 2021 (27 Aug, Shift 2)

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