Critical load :The critical load of a column is that value of axial force that is just sufficient to keep the bar in a slightly deflected shape.
Slenderness ratio of a column : The ratio of effective length of the column (an axial compression member) to the minimum radius of gyration of the cross-sectional area is termed as slenderness ratio of the bar.
As it is a ratio so it has no units and of course it is dimensionless.
Radius of gyration is always the property of cross-section that is why the word cross-section is used with radius of gyration.
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