n small water drops of same size (radius r) f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The terminal velocity $V$ of a drop of radius $r$ is given by $V = \frac{2}{9} \frac{r^2(\rho - \sigma)g}{\eta}$.Since $V \propto r^2$,we have $\f

Vedclass · Accepted Answer

$\frac{VR^2}{r^2}$

Vedclass · Answer

(A) The terminal velocity $V$ of a drop of radius $r$ is given by $V = \frac{2}{9} \frac{r^2(\rho - \sigma)g}{\eta}$.Since $V \propto r^2$,we have $\frac{V_{big}}{V_{small}} = \frac{R^2}{r^2}$.Given that $n$ drops of radius $r$ coalesce to form one big drop of radius $R$,the volume is conserved: $\frac{4}{3}\pi R^3 = n \cdot \frac{4}{3}\pi r^3$,which implies $R^3 = nr^3$ or $R = n^{1/3}r$.Substituting $R^2 = n^{2/3}r^2$ into the velocity ratio,we get $V_{big} = V \cdot \frac{R^2}{r^2} = V \cdot n^{2/3}$.However,expressing the result in terms of $R$ and $r$ as per the options,we use the proportionality $V \propto r^2$. Thus,$V_{big} = V \cdot \frac{R^2}{r^2}$.

$n$ small water drops of same size (radius $r$) fall through air with constant terminal velocity $V$. They coalesce to form a big drop of radius $R$. The terminal velocity of the big drop is

Similar Questions

$A$ small ball of mass $M$,radius $R$ and density $\rho$ moves with terminal velocity through a container filled with glycerine of density $\sigma$. The viscous force acting on the ball is ($g=$ gravitational acceleration).

$125$ small water drops of same size fall through air with constant terminal velocity $4 \,cm/s$. They coalesce to form a big drop. The terminal velocity of the big drop is: (in $\,m/s$)

If the terminal speed of a sphere of gold (density $= 19.5 \times 10^3 \ kg/m^3$) is $0.2 \ m/s$ in a viscous liquid (density $= 1.5 \times 10^3 \ kg/m^3$), find the terminal speed (in $m/s$) of a sphere of silver (density $= 10.5 \times 10^3 \ kg/m^3$) of the same size in the same liquid.

Eight equal drops of water are falling through air with a steady velocity of $10 \,cm \,s^{-1}$. If the drops combine to form a single drop, then the terminal velocity of this big drop is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module