This question was previously asked in

UP Jal Nigam Civil 2016 Official Paper

Option 4 : 416

__Concept:__

Slenderness Ratio:

- It is defined as the ratio of Effective length to the radius of gyration.

\(\rm S.R = \;\dfrac{{L_e\;}}{{Radius\;of\;gyration}}\)

Calculation:

We know that,

Slenderness Ratio:

\(\rm S.R = \;\dfrac{{L_e\;}}{{Radius\;of\;gyration}}\)

Where,

Effective length = L_{e}

The radius of gyration = \(\rm K = \sqrt {\dfrac{{{I_{minimum\;}}}}{A}} \;\;\)

__Calculation:__

Given, Side = 2.5 cm, Le = 300 cm

\(\rm I = \;\dfrac{{{b^4}}}{{12}} = \dfrac{{ {{2.5}^4}}}{{12}} = 3.255 \ c{m^4}\)

\(\rm A = b^2 = 2.5 \times 2.5 = 6.25 \ c{m^2}\)

\(\rm K = \sqrt {\dfrac{{3.255}}{{6.25}}} = 0.721\)

\(\rm S.R = \;\dfrac{{300}}{{0.721}} = 416\;\)