$A$ small metallic sphere of diameter $2 \ mm$ and density $10.5 \ g/cm^3$ is dropped in glycerine having viscosity $10 \ \text{Poise}$ and density $1.5 \ g/cm^3$. The terminal velocity attained by the sphere is . . . . . . $cm/s$. $(\pi = \frac{22}{7}$ and $g = 10 \ m/s^2)$

The terminal velocity $v$ of a spherical ball of lead of radius $R$ falling through a viscous liquid varies with $R$ such that

$A$ solid sphere of radius $R$ acquires a terminal velocity $\nu_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity $\nu_2$ when falling through the same fluid,the ratio $(\nu_1/\nu_2)$ equals:

$A$ solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force, and gravitational force acting on it are $F_{v}$, $F_{B}$, and $F_{W}$ respectively. Then, the correct relation between them is:

$A$ spherical liquid drop of radius $r$ acquires the terminal velocity $v_1$ when falling through a gas of viscosity $\eta$. Now the drop is broken into $64$ identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1/v_2$ is . . . . . . .

$A$ small metal sphere is falling through a viscous liquid. The variation of velocity $(V)$ with time $(t)$ is shown correctly in which graph?