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                                                          [AIIMS 1987]

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 the above