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

Answer

d

Explanation

Time constant `tau = [T] ` and viscosity `eta = [ML^(-1)T^(-1)]`
for option (a) , (b) and (c) dimension are not mathing with time constant.