question_answer

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) is called time constant\[(\tau )\]. Dimensionally \[\tau \] can be represented by:

A) \[\frac{m{{r}^{2}}}{6\pi \eta }\]

B) \[\sqrt{\left( \frac{6\pi mr\eta }{{{g}^{2}}} \right)}\]

C)  \[\frac{m}{6\pi \eta rv}\]

D)  None of these