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CMC Medical CMC-Medical Ludhiana Solved Paper-2015

  • question_answer
    A force, \[F=v\times A\]is exerted on a particle in addition to the force of gravity, where v is the velocity of the particle and A is a constant vector in the horizontal direction. Determine the minimum velocity of projection of a particle of mass m so that it is continues to move in deflected with constant velocity.

    A)  \[\frac{2mg}{3A}\]                        

    B)  \[\frac{2mg}{2A}\]

    C)  \[\frac{mg}{2A}\]                                           

    D)  \[\frac{mg}{A}\]

    Correct Answer: D

    Solution :

                    For the particle to move undeflected with constant velocity, the acceleration of the particle should be zero, i.e. net force acting on the particle should be zero. \[\therefore \]  \[(u\times A)+mg=0\] \[u\times A=-mg\Rightarrow |u\times A|\,=mg\] \[\Rightarrow \]               \[u\,A\sin \theta =mg\] or,          \[u=\frac{mg}{A\,\sin \theta }\] Now, u will be minimum, when \[\sin \theta \] will be maximum (i.e.\[\sin \theta =1\]) \[\therefore \]  \[{{u}_{\min }}=mg/A\,\,\text{along}\,\,Z\text{-axis}\]


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