What are the dimensions of a and b coefficients in the relation of P=ar^-1+bsqrt (x) where Fis force, xis position and tis -3 time [b]=[M][L]^1/2[T]^2[TII]M[M]=[a] Ca 1/2[T]^-1/2[b]=[M][L]^1/2[T]^-4[L][M]=[a] (b Ma[(I)]^2[b]=[M][L][C]^2(M)=[a] 12[L][C]^2[b]=[M][L][T]M[M]=[a] II_(2)[I]^2[D]=[M][M^1/2[T]^2[L][M]=[a]-(e

The dimensions of the coefficients a and b in the relation $P=ar^{-1}+b\sqrt{x}$ can be determined by analyzing the dimensions of each term in the equation.<br /><br />In this case, the force (F) is given as a function of position (x) and time (t). The dimensions of force are [M][L][T]^{-2}, where [M] represents mass, [L] represents length, and [T] represents time. The dimensions of position (x) are [L], and the dimensions of time (t) are [T].<br /><br />Let's analyze the dimensions of each term in the equation:<br /><br />1. $ar^{-1}$: The dimensions of this term are [M][L][T]^{-2} / [L] = [M][T]^{-2}. Therefore, the dimensions of a must be [M][T]^{-2}.<br /><br />2. $b\sqrt{x}$: The dimensions of this term are [M][L][T]^{-2} / [L]^{1/2} = [M][L]^{1/2}[T]^{-2}. Therefore, the dimensions of b must be [M][L]^{1/2}[T]^{-2}.<br /><br />Therefore, the dimensions of the coefficients a and b in the relation $P=ar^{-1}+b\sqrt{x}$ are [M][T]^{-2} and [M][L]^{1/2}[T]^{-2}, respectively.