a$)$ When a tension force $T$ is applied to a spring the extension $x$ is related to

T by Hooke's law, $T=kx,$ where $k$ is called the stiffness of the spring. What

is the dimension of k$?$ Verify the dimensional correctness of the formula

$t=2\sqrt[\phantom{2}]{\frac{m}{k}}$ for the period of oscillation of a mass $m$ suspended by a spring

of stiffness $k.$

b$)$ Suppose that a sphere of radius $r$ moves at a slow speed $v$ through a fluid

with a coefficient of viscosity $$ and density $.$ Find the way in which the

resistive force acting on the sphere should depend on these three

quantities in two different ways:

I. by omitting $$ from the list of variables

II$.$ by omitting $$ from the list of variables