A solid sphere of diameter A is dropped in vacuum from a variable height H$.$ At the bottom, you have a photosensor that measures the time interval $($DT$)$ between the bottom and top of the sphere passing the sensor$.$ You measure DT for several heights H$.$ If you plot the times DT versus $(1/$ H$0\mathrm{.}5),$ then you will notice the graph is roughly linear in some range of heights. Solve for the acceleration of gravity $($ g $)$ in terms of the slope of the graph in the linear regime $($ m $).$