Physics - Rotation Question with Solution | TestHub

By the principle of conservation of mechanical energy, the maximum rotational kinetic energy of the rod is converted into the gravitational potential energy at the highest point.

The moment of inertia of a uniform rod of mass $M$ and length $L$ about an axis passing through one of its ends is $I=\frac{M{L}^2}{3}$.

The maximum kinetic energy is given by:

$K=\frac{1}{2}I{\omega }^2=\frac{1}{2}\left(\frac{M{L}^2}{3}\right){\omega }^2=\frac{M{L}^2{\omega }^2}{6}$

Let $h$ be the maximum height to which the centre of mass rises. The increase in potential energy is:

$U=Mgh$

Equating the maximum kinetic energy to the maximum potential energy:

$Mgh=\frac{M{L}^2{\omega }^2}{6}$

$h=\frac{{\omega }^2{L}^2}{6g}$

Answer: $\frac{{\omega }^2{L}^2}{6g}$