# The red carpets unrolls, show time

A $$\color \red{red~carpet}$$ of mass $$M$$ made of inextensible material is rolled along its length in the form of a $$cylinder$$ of Radius $$R$$ and is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it.The $$horizontal~velocity$$ of the axis of the cylindrical part of the carpet when its radius reduces to $$\dfrac{R}{2}$$ is

$$\large{\sqrt{\dfrac{a\times gR}{b}}}$$

where $$a,b$$ are $$co~ prime~integers$$ and $$g$$ is acceleration due to gravity

Find $$\large{a+b}$$

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