Question

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is

• A. $\sqrt{\frac{3}{8}}l$
• B. $\frac{l}{8}$
• C. $\sqrt{\frac{7}{48}}l$
• D. $\frac{l}{4}$

Answer 1

The correct option is C $\sqrt{\frac{7}{48}}l$


From parallel axis theorem
$I=I_C+m{d}^2$
$I=\frac{m{l}^2}{12}+m{\left(\frac{l}{4}\right)}^2$
$I=m{l}^2[\frac{1}{12}+\frac{1}{16}]$
$m{k}^2=\frac{7m{l}^2}{48}(\because I=m{k}^2)$
$\Rightarrow k=\sqrt{\frac{7}{48}}l.$