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(A) According to the principle of homogeneity of dimensions,the dimensions of each term in an equation must be the same.Given the force equation: $F =

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$kg\ m^{1/2}\ s^{-2}; kg\ m\ s^{-3}$

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(A) According to the principle of homogeneity of dimensions,the dimensions of each term in an equation must be the same.Given the force equation: $F = a \sqrt{x} - bt$.The dimensions of force $F$ are $[M^1 L^1 T^{-2}]$.For the first term: $[F] = [a \sqrt{x}]$$[M^1 L^1 T^{-2}] = [a] [L^{1/2}]$$[a] = [M^1 L^{1/2} T^{-2}]$Substituting the $SI$ units for mass $(kg)$,length $(m)$,and time $(s)$: Unit of $a = kg\ m^{1/2}\ s^{-2}$.For the second term: $[F] = [bt]$$[M^1 L^1 T^{-2}] = [b] [T^1]$$[b] = [M^1 L^1 T^{-3}]$Substituting the $SI$ units: Unit of $b = kg\ m\ s^{-3}$.Thus,the units of $a$ and $b$ are $kg\ m^{1/2}\ s^{-2}$ and $kg\ m\ s^{-3}$ respectively.

$A$ force $F$ acting on an object is given by $F = a \sqrt{x} - bt$,where $x$ is the distance in meters and $t$ is the time in seconds. The units of $a$ and $b$ are respectively:

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