A carpet is rolled into the form of a cylinder (by rolling it along the length) of radius \(\frac{27}{140}\text{ m}\) and it is kept on a rough horizontal floor. The carpet is given a negligible (gentle) push and it starts to unroll without slipping. Calculate the horizontal velocity in \(\text{m}/\text{s}\) of the axis of the cylindrical part of the carpet when its radius becomes \(\frac{27}{280}\).

**Note:** Approximate \(g\) to be \(10 \text{ m}/\text{s}^2.\)

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