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Dimensions of time period = t
0 0 0
The density has dimension ML^{-3}
so take that as D 
the acceleration has dimension LT^{-2}
take it as A
the force has dimension MLT^{-2}
Take it as F
so time period has dimension as D^{ -\frac{1}{6} }A^{ -\frac{2}{3} }F^{ \frac{1}{6} }
actual dimension is T for time
1 5 1
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