Small water droplets of radius $0.01 \,mm$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \,cm/s$. Due to condensation, if $8$ such droplets are coalesced to form a larger drop, the new terminal velocity will be ........... $cm/s$.

$A$ copper ball of radius $r$ travels with a uniform speed $v$ in a viscous fluid. If the ball is changed with another ball of radius $2r$,then the new uniform speed will be

The terminal velocity of a liquid drop of radius $r$ falling through air is $v$. If two such drops are combined to form a bigger drop,the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air).

Give two uses of Stoke's law.

$A$ raindrop with radius $R=0.2 \, mm$ falls 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 buoyancy may be neglected. The terminal speed attained by the raindrop is: (in $m/s$)
[Density of water $\rho_{w}=1000 \, kg/m^3$,density of air $\rho_{a}=1.2 \, kg/m^3$,$g=10 \, m/s^2$,coefficient of viscosity of air $\eta=1.8 \times 10^{-5} \, Ns/m^2$]

In an experiment to calculate the coefficient of viscosity of a liquid by measuring terminal velocity, it was observed that a ball of mass $(\frac{\pi}{2}) \ gm$ and radius $0.5 \ cm$ takes $5 \ s$ to fall steadily through a height of $50 \ cm$ inside a long column of liquid of density $1.2 \ gm/cc$. The coefficient of viscosity will be given as: (in $\text{poise}$)