Question

If the length of a column is doubled, the critical load becomes

• A. 1/2 of the original value
• B. 1/4 of the original value
• C. 1/8 of the original value
• D. 1/16 of the original value

Answer 1

The correct option is B 1/4 of the original value

$P=\frac{{\pi }^{2}EI}{l^2}\Rightarrow P\propto \frac{1}{l^2}$
if $l^{\prime }=2l$
$P^{\prime }=\frac{1}{4}\times P$