what is the dependency of the rate of heat produced in terms of radius $r$ after the drop attains terminal velocity when A small ball of radius $r$ is falling in a viscous liquid under gravity?
My efforts include:
The forces acting on the sphere are its weight $\dfrac 4 3πr^3ρg$ downwards, buoyancy force $\dfrac 4 3 \pi r^3\sigma g$ upwards, and viscous force $6π\eta rv$ upwards. The sphere attains the terminal velocity it when the resultant force on it is zero i.e.,$$\dfrac 4 3πr^3ρg=\dfrac43πr^3σg+6πηrvt$$
I don't know how to Solve the above equation to get the terminal