The expression given below shows the variatio | vedclass

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(A) Given the equation $v = At^2 + \frac{Bt}{C+t}$.According to the principle of homogeneity of dimensions,the dimensions of each term added must be t

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$[M^0 L^2 T^{-3}]$

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(A) Given the equation $v = At^2 + \frac{Bt}{C+t}$.According to the principle of homogeneity of dimensions,the dimensions of each term added must be the same as the dimension of velocity $[LT^{-1}]$.For the term $\frac{Bt}{C+t}$,the dimension of $C$ must be equal to the dimension of $t$,so $[C] = [T]$.Now,for the term $\frac{Bt}{C+t}$,the dimension is $\frac{[B][T]}{[T]} = [B]$. Since this must equal $[LT^{-1}]$,we get $[B] = [LT^{-1}]$.For the term $At^2$,the dimension is $[A][T^2]$. Since this must equal $[LT^{-1}]$,we get $[A] = [LT^{-3}]$.Finally,the dimension of $ABC$ is $[A][B][C] = [LT^{-3}] \cdot [LT^{-1}] \cdot [T] = [L^2 T^{-3}]$.

The expression given below shows the variation of velocity $(v)$ with time $(t)$,$v=At^2+\frac{Bt}{C+t}$. The dimension of $ABC$ is

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