Mechanical Properties of Solids

JEE Main level, numerical answer, medium

55 of 118

Question 55 of 118

Wires W1{W}_{1} and W2{W}_{2} are made of same material having the breaking stress of 1.25×109Nm−2.W11.25\times {10}^{9}N{m}^{-2}.{W}_{1} and W2{W}_{2} have cross-sectional area of 8×10−7m28\times {10}^{-7}{m}^{2} and 4×10−7m24\times {10}^{-7}{m}^{2}, respectively. Masses of 20kg20kg and 10kg10kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _____kgkg (Use g=10ms−2)\left.g=10m{s}^{-2}\right)

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Answer: 40

(F1)max=stress×area{\left({F}_{1}\right)}_{\text{max}}=stress\times area
=1.25×8×102=1000N=1.25\times 8\times {10}^{2}=1000N
(F2)max=500N{\left({F}_{2}\right)}_{\text{max}}=500N
(F2)max=(10+M)g=500N{\left({F}_{2}\right)}_{\text{max}}=(10+M)g=500N
M=40kgM=40kg

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