Question

A uniform rod of mass $m$ and length $L$ is free to rotate in the vertical plane about a horizontal axis passing through its end.The rod is released from rest in the position shown by slightly displacing it clockwise.Find the hinge reaction at the axis of rotation at the instant the rod tums through

• A. ${90}^{\circ }$
• B. ${180}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A ${90}^{\circ }$

I have conserved energy as shown in the following equation:

$\frac{mgL}{2}=\frac{m{v}^2}{2}+\frac{I{\omega }^2}{2}$

and also $\omega =\frac{2v}{L}$

So we get $v^2=\frac{3gL}{7}$

Hence, Option $A$ is correct.