Answer
$v=1.81m/s$
Work Step by Step
To keep the cylinder at rest, all forces must add up to zero. This means that the centripetal force $(\frac{mv^2}{r})$ equals the weight force $(Mg)$. This means that $$Mg=\frac{mv^2}{r}$$ Solving for $v$ yields $$v=\sqrt{\frac{rMg}{m}}$$ Substituting known values of $r=20.0cm=0.200m$, $M=2.50kg$, $m=1.50kg$, and $g=9.80m/s^2$ yields a velocity of $$v=\sqrt{\frac{(0.200m)(2.50kg)(9.80m/s^2)}{1.50kg}}$$ $$v=1.81m/s^2$$
