Answer:
When a cylinder slides without rolling, \[E=\frac{1}{2}m\upsilon
{{'}^{2}}\], \[\upsilon {{'}^{2}}=\sqrt{2E/m}\]
When the cylinder rolls without slipping
\[E=\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{2}I{{\omega
}^{2}}=\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{2}\left( \frac{1}{2}m{{r}^{2}}
\right){{\omega }^{2}}=\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{4}m{{\upsilon }^{2}}=\frac{3}{4}m{{\upsilon
}^{2}}\]
\[\therefore \] \[\upsilon
=\sqrt{\frac{4E}{3m}}\]
As \[\upsilon '>\upsilon \], therefore sliding cylinder will win the race.
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