Sixty four spherical rain drops of equal size are falling vertica… - Vidyadip

MCQ

Sixty four spherical rain drops of equal size are falling vertically through air with terminal velocity $1.5\, m/s$. All of the drops coalesce to form a big spherical drop, then terminal velocity of big drop is ........... $m/s$

A
$8$
B
$16$
✓
$24$
D
$32$

✓

Answer

Correct option: C.

$24$

c
$\mathrm{R}=\mathrm{n}^{1 / 3} \mathrm{r} \quad \therefore \quad \mathrm{R}=(64)^{1 / 3} \mathrm{r}=4 \mathrm{r}$

$\mathrm{V}_{\mathrm{T}} \propto \mathrm{r}^{2} \quad \Rightarrow \quad \frac{\mathrm{V}_{\mathrm{T}_{1}}}{\mathrm{V}_{\mathrm{T}_{2}}}=\frac{16 \mathrm{r}^{2}}{\mathrm{r}^{2}}$

$\therefore \mathrm{V}_{\mathrm{T}_{2}}=16 \times \mathrm{V}_{\mathrm{T}_{1}}=16 \times 1.5=24 \mathrm{m} / \mathrm{s}$

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