Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8\ \text{N/m}^2$. Area of cross-section of upper wire is $0.008\ \text{cm}^2$ and of lower wire is $0.004\ \text{cm}^2$. The maximum mass that can be added to pan without breaking any wire is ______ kg.
Answer: (B) $38$
Concept. Each wire carries everything hanging below it. Find the largest pan load allowed by each wire; the smaller one decides. From the figure: upper wire, $30$ kg block, lower wire, $10$ kg block, then the pan (mass neglected).
Step 1. Breaking loads. Upper: $12\times10^8\times0.008\times10^{-4}=960$ N ($96$ kg). Lower: $12\times10^8\times0.004\times10^{-4}=480$ N ($48$ kg).
Step 2. Upper wire. Carries $30+10+m\le96\Rightarrow m\le56$ kg.
Step 3. Lower wire. Carries $10+m\le48\Rightarrow m\le38$ kg.
Answer. $38$ kg (Option B).
Solution by Sreeraj P, M.Sc Physics
