Question

A thin bar of mass M and length L is free to rotate about a fixed horizontal axis through a point at its end. The bar is brought to a horizontal position and then released. The angular velocity when it reaches the lowest point is :

• A. directly proportional to its length and inversely proportional to its mass.
• B. independent of mass and inversely proportional to the square root of its length
• C. dependent only upon the acceleration due to gravity.
• D. directly proportional to its length and inversely proportional to the acceleration due to gravity.

Answer 1

The correct option is B independent of mass and inversely proportional to the square root of its length

Here ,

$△v=mg\frac{l}{2}△v=K.E=\frac{1}{2}{I\omega }^2=\frac{1}{6}{ml}^2{\omega }^2=\frac{{ml}^2{\omega }^2}{6}=\frac{mgl}{2}\Rightarrow \omega =\sqrt{\frac{3g}{l}}\therefore \omega \propto \frac{1}{\sqrt{l}}$

and independent of $m$