A sperical 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 constant `(tau)`. Dimensionally , `tau` can be represented by

Options

A. `(mr^2)/(6 pi eta)`
B. `sqrt((6pi m r eta)/(g^2))`
C. `m/(6pi eta r)`
D. None of these

Answer

C

Explanation

Dimension of z is dimension of time and only option C has dimension of time.