$A$ spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta$. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v_t)$ is called the time constant $(\tau)$. Dimensionally,$\tau$ can be represented by:

• A
  $\frac{m}{6\pi \eta r}$
• B
  $\sqrt{\frac{6\pi mr\eta}{g^2}}$
• C
  $\frac{m}{6\pi \eta rv_t}$
• D
  None of the above