Two blocks of masses \(3 \,{kg}\) and \(5\, {kg}\) are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \(\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}\). What is the minimum radius of the wire? (Take \(\left.g=10\, {ms}^{-2}\right)\) (in \(cm\))

Pick an option to check your answer.

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Answer & Solution

Correct Answer

(C) \(12.5\)

Step-by-step Solution

Detailed explanation

\({T}=\frac{2 {m}_{1} {m}_{2} {g}}{{m}_{1}+{m}_{2}}=\frac{2 \times 3 \times 5 \times 10}{8}\)

\(=\frac{75}{2}\)

Stress \(=\frac{{T}}{{A}}\)

\(\frac{24}{\pi} \times 10^{2}=\frac{75}{2 \times \pi {R}^{2}}\)

\({R}^{2}=\frac{75}{2 \times 24 \times 100}=\frac{3}{8 \times 24}\)

\(\Rightarrow {R}=0.125\, {m}\)

\({R}=12.5\, {cm}\)

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