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(A) The dimensions of kinetic energy $(K.E.)$ are $[M L^2 T^{-2}]$.The dimensions of surface tension $(S)$ are $[M T^{-2}]$.Let the required quantity

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distance

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(A) The dimensions of kinetic energy $(K.E.)$ are $[M L^2 T^{-2}]$.The dimensions of surface tension $(S)$ are $[M T^{-2}]$.Let the required quantity be $X = \sqrt{\frac{K.E.}{S}}$.Substituting the dimensions: $X = \sqrt{\frac{[M L^2 T^{-2}]}{[M T^{-2}]}}$.Simplifying the expression: $X = \sqrt{[L^2]} = [L]$.The dimension $[L]$ corresponds to length or distance.Therefore,the correct option is $A$.

The physical quantity having the dimensions of the square root of the ratio of the kinetic energy and surface tension is

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