Question

A rain drop of radius $r$ falls in air with a terminal speed $v_t$. What is the terminal speed of a rain drop of radius $2r$?

• A. $\frac{v}{2}$
• B. $v_t$
• C. $2v_t$
• D. $4v_t$

Answer 1

The correct option is D $4v_t$

$v=\frac{2}{a}{r}^2\frac{(P-T)S}{M}$

$\Rightarrow v\alpha r^2$

$\Rightarrow \frac{v_1}{v_2}={\left(\frac{r_1}{r_2}\right)}^2={\left(\frac{r}{2r}\right)}^2=\frac{1}{4}$

$\Rightarrow v_2=4v_1=4v_t$