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]

Question

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]

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

$$\frac{m{{r}^{2}}}{6\pi \eta }$$

TuteeHUB · Answer

$$\sqrt{\left( \frac{6\pi mr\eta }{{{g}^{2}}} \right)}$$

TuteeHUB · Answer

0.1 m/s

TuteeHUB · Answer

None of the above

1.	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.	0.1 m/s
D.	None of the above
Answer» E.

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