Question

A thin uniform rod of mass $M$ and length $L$ is hinged at an end and released from rest in the horizontal position. The tension at a point located at a distance $L/3$ from the hinged point, when the rod becomes vertical, will be

• A. $22Mg/27$
• B. $11Mg/13$
• C. $6Mg/11$
• D. $2Mg$

Answer 1

The correct option is D $2Mg$

$2mg$

$0+mg\times 0=\frac{1}{2}I{w}^2+mg(-\frac{L}{2})$

$\frac{1}{2}\left(\frac{m{L}^2}{3}\right)w^2=\frac{mgL}{2}$

$w=\sqrt{\frac{3g}{L}}$

$T=mg+\frac{m{v}^2}{r}$

$=m[g+r{w}^2]$

$=m[g+\frac{2L}{g}\times \frac{3g}{2}]$

$=\frac{2m}{3}(g+2g)$

$=2mg$