Question

A rod of mass M and length L that is hinged about its end point is released from rest from horizontal position in a vertical plane as shown in figure. Hinge reaction when rod becomes vertical is $\frac{p}{q}$ Mg then p+q is (where p & q are coprime)

Answer 1

By $COE\Rightarrow mg\frac{L}{2}=\frac{1}{2}I{\omega }^2$

$mg\frac{L}{2}=\frac{1}{2}\frac{m{L}^2}{3}{\omega }^2$

${\omega }^2=\frac{3g}{L}$

$N-mg=M{\omega }^{2}R\Rightarrow N=mg+m{\omega }^{2}R$

$N=Mg+m\times \frac{3g}{L}\times \frac{L}{2}=(\frac{3}{2}+1)mg$

$N=\frac{5}{2}$ mg
$\Rightarrow p+q=7$