A hose of mass \(M\) and length \(L\) is made into a coiled roll of radius \(R\). The hose is then unrolled across a level ground with initial speed \(v_0\), while the free end is held at a fixed point on the ground. The hose unrolls and becomes straight.

Determine the time taken by the hose to completely unroll.

**Details and Assumptions**

\(R\ll L\).

At all instant, the hose is performing pure rolling.

The hose is arbitrarily flexible.

The work necessary for its deformation, air resistance and rolling resistance can be neglected.

\(L = 100 \text{ m}, \ v_0 = 7\text{ ms}^{-1}\).

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