Quick answer: C is the only option with the right units (or dimensions), so it's the answer.

(As we know, the dimensions of angular velocity are inverse time (units of which is s^{-1}); units of option C is ((m s^{-2})/m)^{1/2} = s^{-1}. It is quick to check that none of the other options have the right units for angular velocity (and so cannot be correct). The first two (A and B) are dimensionless, as they just involve the ratio of two lengths. The last option is the inverse of C, so the units are s, which is wrong.)
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