Rain drop of radius ‘r’ is falling through air starting from rest. The work done by all the force on the drop, when it attains terminal velocity is proportional to

Rain drop of radius ‘$r$’ is falling through air starting from rest. The work done by all the force on the drop, when it attains terminal velocity is proportional to

1. A

${r}^{5}$

2. B

${r}^{7}$

3. C

${r}^{2}$

4. D

${r}^{4}$

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Solution:

Work done by all forces = gain in $\mathrm{KE}\left(\frac{1}{2}{\mathrm{mv}}^{2}\right)$

$\mathrm{W}\propto {\mathrm{mv}}^{2}$

mass of the drop $m\propto {r}^{3}$

As terminal velocity

So $\mathrm{W}\propto {\mathrm{r}}^{7}$

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