A lift of mass $1600$ kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^8\ \text{N/m}^2$ and its radius is $4$ mm, then maximum acceleration the lift can take is ______ $\text{m/s}^2$. (take $g = 10\ \text{m/s}^2$ and $\pi = 3.14$)
Answer: (A) $2.56$
Concept. The wire breaks if its stress exceeds the maximum stress, so the largest tension it can take is $T_{\max}=\sigma_{\max}A$. When the lift accelerates upward, Newton's law gives $T-mg=ma$, so the tension is largest then.
Step 1. Largest tension.
$$T_{\max}=4\times10^8\times\pi(4\times10^{-3})^2=4\times10^8\times3.14\times16\times10^{-6}=20\,096\ \text{N}$$
Step 2. Newton's law for the lift (upward acceleration $a$):
$$T_{\max}=m(g+a)\ \Rightarrow\ g+a=\frac{20\,096}{1600}=12.56$$
Step 3. Acceleration. $a=12.56-10=2.56$ m s$^{-2}$.
Answer. Option A.
Solution by Sreeraj P, M.Sc Physics
