What are the dimensions of a and b coefficients in the relation of F=at^-1+bsqrt (x) where Fis force, xis position and tis -3 time [b]=[M][L]^1/2[T]^-2[T][L][M]=[a] (a 1/2[T]^-1/2[b]=[M][L]^1/2[T]^-4[L][M]=[a] 1/2[L][m]^-2[b]=[M][L][m]^-2[M]=[a] (c 1/2[L][T]^-2[b]=[M][L][T][M]=[a] (d 1/2[T]^-2[b]=[M][L]^1/2[T]^-3[L][M]=[a]

The correct answer is:<br /><br />$1/2[L][T]^{-2}[b]=[M][L]^{1/2}[T]^{-3}[L][M]=[a]$ (d)<br /><br />Explanation:<br />In the given relation $F=at^{-1}+b\sqrt{x}$, the dimensions of the coefficients a and b can be determined by analyzing the dimensions of the variables involved.<br /><br />The force F has the dimension [M][L][T]^{-2}, where [M] represents mass, [L] represents length, and [T] represents time. The position x has the dimension [L], and the time t has the dimension [T].<br /><br />To find the dimensions of a, we look at the term $at^{-1}$. Since the dimension of force is [M][L][T]^{-2} and the dimension of time is [T], the dimension of a must be [M][L][T]^{-3} to ensure the dimensions are balanced.<br /><br />To find the dimensions of b, we look at the term $b\sqrt{x}$. Since the dimension of force is [M][L][T]^{-2} and the dimension of position is [L], the dimension of b must be [M][L]^{1/2}[T]^{-3} to ensure the dimensions are balanced.<br /><br />Therefore, the correct answer is option (d), which states that the dimensions of a and b are [M][L][T]^{-3} and [M][L]^{1/2}[T]^{-3}, respectively.