Question

A container filled with viscous liquid is moving vertically downwards with constant speed \(3v_0\). At the instant shown, a sphere of radius \(r\) is moving vertically downwards (in liquid) has speed \(v_0\). The coefficient of viscosity is \(\eta\). There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is

Answer 1

As we know \(F=6\pi~\eta~rv\)
Speed of the container \(=3v_0\)
Speed of the sphere \(=v_0\)
So, the relative speed of the sphere with respect to liquid is \(=2v_0\) upwards.
As the viscous force act on the sphere is given by \(F=6\pi~\eta~rv\)
Here \(v=3v_0\)
Therefore, \(F=6\pi~\eta~r2v_0\) downward
\(=12\pi~\eta~rv_0\) downward

Final Answer: (b)