question_answer

A particle of mass m (starting from rest) moves vertically upwards from the surface of earth under an external force \[\overrightarrow{F}\] which varies with height z as,\[\overrightarrow{F}=\left( 2-\alpha z \right)m\overrightarrow{g}\], where \[\alpha \] is a positive constant. If H is the maximum height to which particle rises, then which of the following is/are correct?

A) \[H=\frac{2}{\alpha }\]

B) Work done by \[\overrightarrow{F}\]during motion up to \[\frac{H}{2}\]is \[\frac{3mg}{2\alpha }\]

C) Velocity of particle at \[\frac{H}{2}\]is\[\sqrt{\frac{g}{\alpha }}\]

D) All of these