Question

A uniform stick of length l is hinged so as to rotate about a horizontal axis perpendicular to the stick, at a distance 'x' from the centre. The value of x, for which the time period is minimum will be then

• A. $\frac{l}{2}$
• B. $\frac{l}{4}$
• C. $\frac{l}{2\sqrt{3}}$
• D. $\frac{l}{\sqrt{3}}$

Answer 1

The correct option is C $\frac{l}{2\sqrt{3}}$

$T=2r\sqrt{\frac{\frac{m{L}^2}{12}+m{x}^2}{mgx}}$
$\frac{dT}{dx}=0\Rightarrow x=\frac{L}{2\sqrt{3}}$