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What are the applications of dimensional...

What are the applications of dimensional analysis? Verify `s= ut + 1/2 at^2` by dimensional analysis

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Given equation is dimensionally correct as the dimensions on the both side are same. Applications of dimensional analysis
(i) Convert a physical quantity from one system of units to another. (ii) Check the dimensional correctness of a given physical equation. (iii) Establish relations among various physical quantities.
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