question_answer

Three identical rods are hinged at point A as shown. The angle made by rod AB with vertical is    

A) \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]

B) \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\]

C) \[{{\tan }^{-1}}\left( 1 \right)\]

D) \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\]

Correct Answer: B

Solution :

[b] Vertical line from hinge A must pass through C.M. of rod system.        \[\tan \theta =\frac{OP}{AP}\Rightarrow \frac{\ell /2}{2\ell /3}\] \[\tan \theta =\frac{3}{4}\Rightarrow \theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\]