Question

A rigid body is made of three identical thin rods, each of length L fastened together in the form of letter H. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body is allowed to fall from rest from a position in which the plane of H is horizontal. What is the angular speed of the body when the plane of H is vertical ?

• A. $\sqrt{\frac{g}{L}}$
• B. $\frac{1}{2}\sqrt{\frac{g}{L}}$
• C. $\frac{3}{2}\sqrt{\frac{g}{L}}$
• D. $2\sqrt{\frac{g}{L}}$

Answer 1

Answer: (C)

$I=0+\left[\frac{M{L}^2}{12}+M{\left(\frac{L}{2}\right)}^2\right]+\left[0+M{L}^2\right]=\frac{4}{3}M{L}^2$
( using parallel axis theorem )


$\because \frac{1}{2}I{\omega }^2=mg{h}_{cm}$
$\therefore \frac{1}{2}\left(\frac{4}{3}M{L}^2\right){\left(\omega \right)}^2=3Mg\left(\frac{L}{2}\right)$
$\Rightarrow \omega =\frac{3}{2}\sqrt{\frac{g}{L}}$