question_answer

A uniform stick of mass M is placed in a frictionless well as shown. The stick makes angle \[\theta \] was the horizontal. The force which the vertical wall exerts on right end of stick is -

A) \[\frac{Mg}{2\cot \theta }\]

B) \[\frac{Mg}{2\tan \theta }\]

C) \[\frac{Mg}{2\cos \theta }\]

D)  \[\frac{Mg}{2\sin \theta }\]    

Correct Answer: B

Solution :

The free body diagram of rod is

Where \[{{N}_{x}}\] and \[{{N}_{y}}\] are horizontal and vertical components of reaction exerted by wall on rod. Net torque on rod about left end A is zero

\[\therefore Mg\frac{\ell }{2}\cos \theta ={{N}_{x}}\ell \sin \theta \]\[\Rightarrow {{N}_{x}}=\frac{Mg}{2\tan \theta }\]