The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

The viscous force $F$ acting on a sphere moving through a liquid depends on the radius $r$ of the sphere, the velocity $v$ of the sphere, and the coefficient of viscosity $η$ of the liquid. If $F = kη^arv^b$, where $k$ is a dimensionless constant, using dimensional analysis, find the values of $a$, $b$.