A small sphere of radius $r$ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

If the terminal speed of a sphere of gold ( density $= 19.5 kg/m^3$) is $0.2\ m/s$ in a viscous liquid (density $= 1.5\ kg/m^3$ ), find the terminal speed (in $m/s$) of a sphere of silver (density $= 10.5\ kg/m^3$) of the same size in the same liquid ...... $m/s$

Which of the following option correctly describes the variation of the speed $v$  and acceleration $'a'$  of a point mass falling vertically in a viscous medium that applies a force $F = -kv,$ where $'k'$  is a constant, on the body? (Graphs are schematic and not drawn to scale)

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 spherical ball of density $\rho$ and radius $0.003$ $m$ is dropped into a tube containing a viscous fluid filled up to the $0$ $ cm$ mark as shown in the figure. Viscosity of the fluid $=$ $1.260$ $N.m^{-2}$ and its density $\rho_L=\rho/2$ $=$ $1260$ $kg.m^{-3}$. Assume the ball reaches a terminal speed by the $10$ $cm$ mark. The time taken by the ball to traverse the distance between the $10$ $cm$ and $20$ $cm$ mark is

( $g$ $ =$ acceleration due to gravity $= 10$ $ ms^{^{-2}} )$

Define coefficient of viscosity.