A spherical body of mass m and radius r is allowed to fall in a medium of viscosity eta . time in wh

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1.Units, Dimensions and Measurement

medium

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 the above

(AIIMS-1987)

Solution

(d) Time constant $\tau = [T]$ and Viscosity $\eta = [M{L^{ – 1}}{T^{ – 1}}]$

For options $(a)$, $(b)$ and $(c)$ dimensions are not matching with time constant.

Standard 11

Physics

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