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 $1 \, cm \, s^{-1}$. Find the terminal velocity of the ball of radius $2r$ (neglect buoyant force on the balls). ........... $cm \, s^{-1}$

$A$ spherical ball of radius $1 \times 10^{-4} \,m$ and density $10^5 \,kg/m^3$ 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, then the value of $h$ is approximately: (The coefficient of viscosity of water is $9.8 \times 10^{-6} \,N s/m^2$) (in $\,m$)

$A$ steel ball of radius $6 \ mm$ has a terminal speed of $12 \ cm s^{-1}$ in a viscous liquid. What will be the terminal speed of a steel ball of radius $3 \ mm$ in the same liquid (in $cm s^{-1}$)?

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volumes is

The velocity of a small ball of mass $M$ and density $d_1$ when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is $d_2$,the viscous force acting on the ball is ($g$ = acceleration due to gravity).

Two metal spheres are falling through a liquid of density $3 \times 10^3 \ kg/m^3$ with the same uniform speed. The material densities of sphere $1$ and sphere $2$ are $8 \times 10^3 \ kg/m^3$ and $11 \times 10^3 \ kg/m^3$ respectively. The ratio of their radii is