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 $2 \mathrm{r}$, 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.
$\mathrm{Mg}=6 \pi \eta \mathrm{rv}$
$\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad$ (as mass is constant)
Now, $\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$
$\mathrm{r}^{\prime}=2 \mathrm{r}$
So, $\mathrm{v}^{\prime}=\frac{\mathrm{v}}{2}$
