A body of mass \(\mathrm{m}=10\; \mathrm{kg}\) is attached to one end of a wire of length \(0.3\; \mathrm{m} .\) The maximum angular speed (in \(rad \;s^{-1}\) ) with which it can be rotated about its other end in space station is (Breaking stress of wire \(=4.8 \times 10^{7} \;\mathrm{Nm}^{-2}\) and area of cross-section of the wire \(=10^{-2}\; \mathrm{cm}^{2}\) ) is

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(D) \(4\)

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\(\mathrm{T}=\mathrm{m\omega}^{2} \ell\)

Breaking stress \(=\frac{\mathrm{T}}{\mathrm{A}}=\frac{\mathrm{mo}^{2} \ell}{\mathrm{A}}\)

\(\Rightarrow \omega^{2}=\frac{4.8 \times 10^{7} \times\left(10^{-2} \times 10^{-4}\right)}{10 \times 0.3}=16\)

\(\Rightarrow \omega=4\)

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