question_answer

A force \[\vec{F}=\vec{v}\times \vec{A}\] 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. With what minimum speed a particle of mass m be projected so that it continues to move undeflected with a constant velocity?

Answer:

\[m=V\times d=\left( \frac{4}{3}\pi {{r}^{3}}\times d \right)\]\[\because \] \[\therefore \left( \vec{V}\times \vec{A} \right)+\overrightarrow{mg}=0\] \[VA\,\,\sin \theta =mg\Rightarrow V=\frac{mg}{A\,\,\sin \,\,\theta }\] \[{{V}_{\min }}\Rightarrow \sin \theta =1\Rightarrow \theta =90{}^\circ \] \[\therefore V=\frac{mg}{A}\]