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 $\left( \tau \right)$. Dimensionally $\tau $ can be represented by
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 $\left( \tau \right)$. 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 the above
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