Question

A rod of mass $M$ and length $l$ is suspended freely from its end and it can oscillate in the vertical plane about the point of suspension. It is pulled to one side and then released. It passes through the equilibrium position with angular speed $\omega$. What is the kinetic energy while passing through the mean position ?

• A. $M\, l^{2}\, \omega^{2}$
• B. $M\, l^{2} \,\omega^{2} / 4$
• C. $M \,l^{2} \,\omega^{2} / 6$
• D. $M\, l^{2}\, \omega^{2} / 12$

Answer 1

Answer: (C)

Kinetic energy,
$K =\frac{1}{2} I \omega^{2}$
$\Rightarrow =\frac{1}{2} \frac{M l^{2}}{3} \times \omega^{2}$
$\Rightarrow =\frac{1}{6} M l^{2} \omega^{2}$