Question

A uniform rod of mass $m$ and length $l$ is fixed from point A, which is at a distance $\frac{l}{4}$ from one end as shown in the figure. The rod is free to rotate in a vertical plane. The rod is released from the horizontal position. What is the reaction at the hinge, when kinetic energy of the rod is maximum?

• A. $\frac{4}{7}mg$
• B. $\frac{5}{7}mg$
• C. $\frac{13}{7}mg$
• D. $\frac{11}{7}mg$

Answer 1

The correct option is C $\frac{13}{7}mg$

KE of the rod is maximum when it is in the vertical position.

From the conservation of energy, we get

$\frac{mgl}{4}=\frac{1}{2}[\frac{m{l}^2}{12}+\frac{m{l}^2}{16}]{\omega }^2$

$\frac{{\omega }^{2}l}{4}=\frac{6g}{7}$

and $R_y-mg=m\left(\frac{l}{4}\right){\omega }^2$

$R_y=mg+m\left(\frac{6g}{7}\right)$

$=\frac{13mg}{7}$