Question

Three identical rods are joined and hinged at A as shown. If the angle made by the rod AB with vertical in equilibrium is $\theta$, then $\theta$ is

• A. $30°$
• B. $60°$
• C. $37°$
• D. $53°$

Answer 1

The correct option is C $37°$


Let the length of each rod be L.
Then, the centre of gravity (COG) of the shape will be at the point shown in the figure.


$\tan \theta =\frac{\frac{L}{2}}{\frac{2L}{3}}=\frac{3}{4}\Rightarrow \theta ={\tan }^{-1}\left(\frac{3}{4}\right)=37°$

The line connecting the hinge A and the centre of gravity COG will be vertical (since the net torque about A has to be zero for equilibrium)

Therefore, the angle made by rod AB with the vertical is $37°$