Which of the following is dimensionally incor | vedclass

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Question

(A) According to the principle of homogeneity of dimensions,an equation is dimensionally correct only if the dimensions of each term on both sides are

Vedclass · Accepted Answer

$u^2 = 2a(gt - 1)$

Vedclass · Answer

(A) According to the principle of homogeneity of dimensions,an equation is dimensionally correct only if the dimensions of each term on both sides are the same.For option $A$: $u^2 = 2a(gt - 1)$. The term $gt$ has dimensions $[LT^{-2}][T] = [LT^{-1}]$,which is the dimension of velocity. However,the number $1$ is dimensionless. We cannot subtract a dimensionless quantity from a quantity with dimensions $[LT^{-1}]$. Thus,this equation is dimensionally incorrect.For option $B$: $s - ut = \frac{1}{2}at^2$. Dimensions of $s$ are $[L]$,$ut$ are $[LT^{-1}][T] = [L]$,and $\frac{1}{2}at^2$ are $[LT^{-2}][T^2] = [L]$. All terms have the same dimensions.For option $C$: $u = v - at$. Dimensions of $u$ are $[LT^{-1}]$,$v$ are $[LT^{-1}]$,and $at$ are $[LT^{-2}][T] = [LT^{-1}]$. All terms have the same dimensions.For option $D$: $v^2 - u^2 = 2as$. Dimensions of $v^2$ are $[L^2T^{-2}]$,$u^2$ are $[L^2T^{-2}]$,and $2as$ are $[LT^{-2}][L] = [L^2T^{-2}]$. All terms have the same dimensions.Therefore,option $A$ is dimensionally incorrect.

Which of the following is dimensionally incorrect?

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