Mechanical Properties Of Fluids Question 9
Question 9 - 2024 (31 Jan Shift 2)
A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity ’ $v$ ‘. Another ball of the same mass but of radius $2 r$, falling through the same viscous medium will have terminal velocity:
(1) $\frac{v}{2}$
(2) $\frac{v}{4}$
(3) $4 v$
(4) $2 v$
Show Answer
Answer: (1)
Solution:
Since density is negligible hence Buoyancy force will be negligible
At terminal velocity.
$Mg=6 \pi \eta rv$
$V \propto \frac{1}{r} \quad$ (as mass is constant)
Now, $\frac{v}{v^{\prime}}=\frac{r^{\prime}}{r}$
$r^{\prime}=2 r$
So, $v^{\prime}=\frac{v}{2}$
