Write the dimensions of a/b in the relation P | vedclass

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(B) Given the relation: $P = \frac{a - t^2}{bx}$.According to the principle of homogeneity of dimensions,quantities added or subtracted must have the

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${M^1}{L^0}{T^{-2}}$

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(B) Given the relation: $P = \frac{a - t^2}{bx}$.According to the principle of homogeneity of dimensions,quantities added or subtracted must have the same dimensions. Therefore,the dimension of $a$ must be equal to the dimension of $t^2$.$[a] = [T^2]$.Now,consider the dimension of the entire expression:$[P] = \frac{[a - t^2]}{[b][x]} = \frac{[T^2]}{[b][L]}$.We know that pressure $P$ has dimensions $[M L^{-1} T^{-2}]$.Substituting this into the equation:$[M L^{-1} T^{-2}] = \frac{[T^2]}{[b][L]}$.Solving for $[b]$:$[b] = \frac{[T^2]}{[M L^{-1} T^{-2}][L]} = \frac{[T^2]}{[M T^{-2}]} = [M^{-1} T^4]$.Now,find the dimensions of $a/b$:$[a/b] = \frac{[T^2]}{[M^{-1} T^4]} = [M^1 L^0 T^{-2}]$.Thus,the correct option is $B$.

Write the dimensions of $a/b$ in the relation $P = \frac{a - t^2}{bx}$,where $P$ is pressure,$x$ is distance,and $t$ is time.

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