Question

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. $\frac{mg}{A}$

Answer 1

Answer: (D)

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. $\therefore$ $(u\times A)+mg=0$ $u\times A=-mg\Rightarrow |u\times A|=mg$ $\Rightarrow$ $uA\sin \theta =mg$ or, $u=\frac{mg}{A\sin \theta }$ Now, u will be minimum, when $\sin \theta$ will be maximum (i.e. $\sin \theta =1$ ) $\therefore$ $u_{\min }=mg/A\text{along}Z\text{-axis}$