Question
Three identical rods are hinged at point $$A$$ as shown. The angle made by rod $$AB$$ with vertical is
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.
$${\tan ^{ - 1}}\left( {\frac{4}{3}} \right)$$
Answer :
$${\tan ^{ - 1}}\left( {\frac{3}{4}} \right)$$
Solution :
Vertical line from hinge $$A$$ must pass through $$C.M.$$ of rod system.
$$\eqalign{ & \tan \theta = \frac{{OP}}{{AP}} = \frac{{\frac{\ell }{2}}}{{\frac{{2\ell }}{3}}} \cr & \tan \theta = \frac{3}{4} \Rightarrow \theta = {\tan ^{ - 1}}\left( {\frac{3}{4}} \right) \cr} $$
Vertical line from hinge $$A$$ must pass through $$C.M.$$ of rod system.
$$\eqalign{ & \tan \theta = \frac{{OP}}{{AP}} = \frac{{\frac{\ell }{2}}}{{\frac{{2\ell }}{3}}} \cr & \tan \theta = \frac{3}{4} \Rightarrow \theta = {\tan ^{ - 1}}\left( {\frac{3}{4}} \right) \cr} $$
