KVPY Sample Paper KVPY Stream-SX Model Paper-21

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

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