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Question

Let x and a stand for distance. Show that dxa2x2=1asin1ax dimensionally correct.

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Solution

As x and a stand for distance so dimension on left side =[L]/[L2]=1, so left side dimensionless .
On right side, 1/[L]=L1 (as any trigonometric funtions are the ratio of lengths so they are dimensionless )
Hence, dimensions on both sides are not same. So the given equation is not dimensionally correct.

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