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