1. Tardigrade
  2. Question
  3. Physics
  4. A force, F=v× 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.

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Q. 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.

CMC MedicalCMC Medical 2015

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} $