Question

In the adjacent figure a uniform rod of length $L$ and mass $m$ is kept at rest in horizontal position on an elevated edge. The value of $x$ (consider the figure-3.119) is such that the rod will have maximum angular acceleration $\alpha$ as soon as it set free.

• A. $x$ is equal to $\frac{L}{2 \sqrt{3}}$
• B. $\alpha$ is equal to $\frac{g \sqrt{3}}{2 L}$
• C. $\alpha$ is equal to $\frac{g \sqrt{3}}{L}$
• D. $x$ is equal to $\frac{L}{\sqrt{3}}$

Answer 1

Answer: (A), (C)

Apply $\tau=I \alpha$ about $O$
$m g x=\left(\frac{m L^{2}}{12}+m x^{2}\right) \alpha$

For $\alpha$ to be maximum $d \alpha / d x=0$
which gives $x=\frac{L}{2 \sqrt{3}}$ and $\alpha=\frac{\sqrt{3} g}{L}$