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Check The correctness of the following equation using dimensional analysis. Make a comment on it. S = ut + 1//2 "at"^(2) where s is the displacement, u is the initial velocily, t is the time and a is the acceleration produced, |
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Answer» Solution :DIMENSION for distances s = [L] Dimension or initial velocity u = `[LT^(-1)]` Dimension for TIME t = [T] Dimension for acceleration a = `[LT^(-2)]` According to the principle of homogeneity, Dimensions of LHS = Dimensions of RHS Substituting the dimensions in the given FORMULA `S = ut + 1//4 at^(2), 1/4` is a number. It has no dimensions [L] = `[LT^(-1)][T^(1)] + [LT^(-2)][T^(2)]` [L] = [L] + [L] As the dimensional formula of LHS is same as that of RHS, the equation is dimensionally correct. Comment: But actually it is a wrong equation. We know that the equation of motion is `s = ut + 1//2 at^(2)` So, a dimensionally correct equation need not be the true (or) actual equation But a true equation is always dimensionally correct. |
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