Eight identical small drops of water are falling down vertically through a medium,each with terminal velocity $v$. If they combine to form a single drop,then its terminal velocity will be (in $v$)

While determining the coefficient of viscosity of the given liquid,a spherical steel ball sinks by a distance $h=0.9 \,m$. The radius of the ball $r=\sqrt{3} \times 10^{-3} \,m$. The time taken by the ball to sink in three trials are tabulated as follows:

Trial No.	Time taken by the ball to fall by $h$ (in second)
$1$.	$2.75$
$2$.	$2.65$
$3$.	$2.70$

The difference between the densities of the steel ball and the liquid is $7000 \,kg \,m^{-3}$. If $g=10 \,ms^{-2}$,then the coefficient of viscosity of the given liquid at room temperature is

State Stokes' law. By using it,deduce the expression for:
$(i)$ Initial acceleration of a smooth sphere.
$(ii)$ Equation of terminal velocity of a sphere falling freely through a viscous medium.
$(iii)$ Explain: Upward motion of bubbles produced in a fluid.

$A$ small spherical ball of radius $0.1 \,mm$ and density $10^{4} \,kg \,m^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering the water the velocity of the ball does not change and it continues to fall with the same constant velocity inside the water,then the value of $h$ will be $m$. (Given $g = 10 \,m \,s^{-2}$,viscosity of water $\eta = 1.0 \times 10^{-5} \,N \,s \,m^{-2}$,density of water $\rho_w = 10^3 \,kg \,m^{-3}$)

$A$ spherical ball of radius $1 \text{ mm}$ and density $10.5 \text{ g/cc}$ is dropped in glycerine of coefficient of viscosity $9.8 \text{ poise}$ and density $1.5 \text{ g/cc}$. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} \text{ N}$. The value of $x$ is (Given, $g = 9.8 \text{ m/s}^2$ and $\pi = 22/7$)

$A$ 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).