Question

Two equal drops of water are falling through air with a steady velocity of $10cm/s$. If the drops recombine to form a single drop then the terminal velocity is:

• A. $2^{\frac{2}{3}}$ x $5cm/s$
• B. $2^{\frac{2}{3}}$ x $10cm/s$
• C. $2^{\frac{2}{3}}$ x $15cm/s$
• D. $2^{\frac{2}{3}}$ x $4cm/s$

Answer 1

The correct option is B $2^{\frac{2}{3}}$ x $10cm/s$

From the initial Terminal velocity given,
Let radius of drop = $r$.
So, $V=10cm/s=\frac{2g(T-\sigma )r^2}{9\eta }$
So,If two drops combine
As, $\frac{4}{3}\pi r^3=V\Rightarrow r={\left(\frac{3V}{4\pi }\right)}^{1/3}$
So $\frac{4}{3}\pi r_1^3=2V$
$\Rightarrow r_1=2^{1/3}{\left(\frac{3V}{4\pi }\right)}^{1/3}=2^{1/3}r$
Now,
New Terminal velocity =$\frac{22^{2/3}{r}^2(T-\sigma )g}{9\eta }$
$=2^{2/3}\times 10cm/s$