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A sphere of mass $4 \mathrm{~kg}$ is attached to one end of a steel wire of length $1 \mathrm{~m}$ and radius $1 \mathrm{~mm}$. It is whirled in a vertical circle with an angular velocity $10 \mathrm{rad} \mathrm{s}^{-1}$. If the sphere is at the lowest point of its path, the elongation in the wire is ____
$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}, \mathrm{Y}_{\text {steel }}=20 \times 10^{10} \mathrm{Nm}^{-2}\right)$
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$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}, \mathrm{Y}_{\text {steel }}=20 \times 10^{10} \mathrm{Nm}^{-2}\right)$
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The correct answer is:
$0.7 \mathrm{~mm}$
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