Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure $p$  at points along the axis is represented by

Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio

Two uniform solid balls of same density and of radii $r$ and $2r$ are dropped in air and fall vertically downwards. The terminal velocity of the ball with radius $r$ is $1\,cm\,s^{-1}$ , then find the terminal velocity of the ball of radius $2r$ (neglect bouyant force on the balls.) ........... $cm\,s^{-1}$

A sphere is dropped under gravity through a fluid of viscosity $\eta$ . If the average acceleration is half of the initial acceleration, the time to attain the terminal velocity is ($\rho$ = density of sphere ; $r$ = radius)

A raindrop with radius $R=0.2\, {mm}$ fells from a cloud at a height $h=2000\, {m}$ above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In ${ms}^{-1}$)

[Density of water $f_{{w}}=1000\;{kg} {m}^{-3}$ and density of air $f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}$ Coefficient of viscosity of air $=18 \times 10^{-5} \;{Nsm}^{-2}$ ]

In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $h$ is proportional to :

(ignore viscosity of air)