Slenderness ratio has dimensions ofa)cmb)cm-1c)dimensionless quantityd)cm2Correct answer is option 'C'. Can you explain this answer?

Question

Answer

S.r.= length/ radius of gyaration..above both in (m/m) so dimensionless

Answer

Slenderness ratio

Answer

Slenderness ratio is a dimensionless quantity.

Explanation:
Slenderness ratio is a term used in structural engineering to describe the ratio of the length of a structural member to its lateral dimensions. It is commonly used to determine the stability and buckling behavior of columns and beams.

The slenderness ratio is calculated by dividing the length of the member (in centimeters, in this case) by a characteristic dimension. The characteristic dimension can vary depending on the shape of the member. For example, for a column, it could be the radius of gyration, while for a beam, it could be the depth or width of the cross-section.

Since the slenderness ratio is calculated by dividing a length measurement (in centimeters) by a characteristic dimension (also in centimeters), the resulting value is dimensionless. This means it does not have any units associated with it.

The dimensionless nature of the slenderness ratio is important because it allows engineers to compare the stability of structural members of different sizes and shapes. By using a dimensionless quantity, engineers can focus on the relative proportions and geometries of the members rather than being influenced by the absolute measurements.

In conclusion, the slenderness ratio is a dimensionless quantity because it is obtained by dividing a length measurement (in centimeters) by a characteristic dimension (also in centimeters), resulting in a value without any units.

Answer

Slenderness ratio

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