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State the principle of homogeneity. Test...

State the principle of homogeneity. Test the dimensional homogeneity of equations—
`S_(n)=u+(a)/(2)(2n-1)`

Text Solution

Verified by Experts

`S_(n)` = Distance travelled in `n^(th)` sec that is `(S_(n)-S_(n-1))`
`therefore S_(n)=uxx1+(a)/(2)(2n-1)`
`[LT^(-1)]=[LT^(-1)]+[LT^(-2)][T]`
`[LT^(-1)]=[LT^(-1)]`
L.H.S. = R.H.S.
Hence this is dimensionally correct.
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