A solid sphere moves at a terminal velocity of $20 m{s}^{-1}$ in air at a place where $g=9.8 m{s}^{-2}$.The sphere is taken in a gravity-free hall having air at the same pressure and pushed down at a speed of $20 m{s}^{-1}$[Consider density of air to be negligible]

At terminal velocity , viscous drag is equal to the weight of the ball.In the gravity free place , just after projection the only force acting on the ball is vertically upward  viscous drag which is equal to the weight of the ball.

At any time t, m$\frac{dv}{dt}=-6\mathrm{\pi \eta rv}$ $\Rightarrow v = v_0{e}^{-bt} \Rightarrow Acceleration a =-b{v}_0{e}^{-bt}$

$v_t=\frac{2r^2\rho g}{9\eta }$