Question

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

• A. $\frac{22Mg}{27}$
• B. $\frac{11Mg}{13}$
• C. $\frac{6Mg}{11}$
• D. $2Mg$

Answer 1

The correct option is D $2Mg$

$2mg$

given,

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

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

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

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

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

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

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