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:
Select the correct option:
A
$\frac{v}{2}$
B
$\frac{v}{4}$
C
$4 v$
D
$2 v$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Since density is negligible hence Buoyancy force will be negligible
At terminal velocity.
$$
\mathrm{Mg}=6 \pi \eta \mathrm{rv}
$$
$\mathrm{V} \propto \frac{1}{\mathrm{r}}$ (as mass is constant)
Now, $\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$
$$
\mathrm{r}^{\prime}=2 \mathrm{r}
$$
So, $v^{\prime}=\frac{v}{2}$
Hello 👋 Welcome to Competishun – India’s most trusted platform for JEE & NEET preparation. Need help with JEE / NEET courses, fees, batches, test series or free study material? Chat with us now 👇
