Question

A uniform rod of mass $m$ and length $l$ hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinged when the rod becomes vertical is

• A. $\frac{mg}{4}$
• B. $\frac{5}{2}mg$
• C. $\frac{mg}{6}$
• D. $\frac{7}{2}mg$

Answer 1

The correct option is B $\frac{5}{2}mg$

$\begin{array}{c}mg\frac{l}{2}=\frac{l}{2}\left(\frac{m{l}^2}{3}\right)w^2\\ \Rightarrow w^2=\frac{3g}{l}....\left(1\right)\\ N-mg=m{w}^2\left(\frac{l}{2}\right)\\ \Rightarrow N=mg+\frac{m.3g}{2}\\ =\frac{5}{2}mg\\ Hence,\\ optionBiscorrectanswer.\end{array}$