question_answer

A uniform stick of mass M is placed in a frictionless well as shown. The stick makes an angle \[\theta \] with the horizontal. Then 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

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