Question

What will be the reaction between hinge and rod at point $A$?

• A. $\sqrt{65}\frac{Mg}{4}$
• B. $2Mg$
• C. $\sqrt{17}\frac{Mg}{4}$
• D. $\sqrt{17}\frac{Mg}{2}$

Answer 1

The correct option is D $\sqrt{17}\frac{Mg}{2}$

Mass per unit length $=M/L$

So, mass of length $L=M$

The body is in equilibrium. So, torque about point $A=0$

$Mg\frac{L}{2}=TL\Rightarrow T=\frac{Mg}{2}$

Now, $\sum F=0$

$\Rightarrow F_x+T=0$ So,$F_x=-T=-\frac{-Mg}{2}\Rightarrow F_y=Mg+Mg=2Mg$

So the reaction force$=\sqrt{F_x^2+F_y^2}=\sqrt{(2MG{)}^2+(\frac{Mg}{2}{)}^2}=\frac{\sqrt{17}Mg}{2}$