Terminal Velocity

A spherical ball of iron of radius 2 mm is falling through a column of glycerine. If densities of glycerine and iron are respectively 1.3 × 10³ kg/m³ and 8 × 10³ kg/m³. η for glycerine = 0.83 Nm^-2 sec, then the terminal velocity is ______.

A piece of wood is taken deep inside a long column of water and released. It will move up

A solid sphere falls with a terminal velocity of 20 m s⁻¹ in air. If it is allowed to fall in vacuum, 

Two solid spherical balls of radius r₁ and r₂ (r₂ < r₁), of density σ are tied up with a long string and released in a viscous liquid column of lesser density ρ and coefficient of viscosity η, with the string just taut as shown. The terminal velocity of spheres is ______.

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.

(a) Its initial acceleration will be 9.8 m s⁻² downward.
(b) It initial acceleration will be 9.8 m s⁻² upward.
(c) The magnitude of acceleration will decrease as the time passes.
(d) It will eventually stop

A spherical solid ball of volume V is made up of a material of density ρ₁. It is falling through the liquid of density ρ₂(ρ₂ < ρ₁). Assume that, the liquid applies a viscous force on the ball that is proportional to the square of the speed v_t, i.e., `["F"_"viscous" = "KV"_"t"^2]`, then the terminal speed of the ball is ______.

(g = acceleration due to gravity)

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).