Two raindrops reach the earth with different | vedclass

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

Question

(D) The terminal velocity $v_t$ of a spherical raindrop of radius $r$ falling through a viscous medium is given by the formula: $v_t = \frac{2}{9} \fr

Vedclass · Accepted Answer

$27/8$

Vedclass · Answer

(D) The terminal velocity $v_t$ of a spherical raindrop of radius $r$ falling through a viscous medium is given by the formula: $v_t = \frac{2}{9} \frac{r^2 g (\rho - \sigma)}{\eta}$,where $\rho$ is the density of the raindrop,$\sigma$ is the density of air,$g$ is the acceleration due to gravity,and $\eta$ is the coefficient of viscosity. Since all these parameters are constant for both raindrops,we have $v_t \propto r^2$. Given the ratio of terminal velocities is $\frac{v_{t1}}{v_{t2}} = \frac{9}{4}$,we can write: $\frac{r_1^2}{r_2^2} = \frac{9}{4}$. Taking the square root of both sides,we get $\frac{r_1}{r_2} = \frac{3}{2}$. The volume $V$ of a spherical raindrop is given by $V = \frac{4}{3} \pi r^3$,so $V \propto r^3$. The ratio of their volumes is $\frac{V_1}{V_2} = \left( \frac{r_1}{r_2} \right)^3 = \left( \frac{3}{2} \right)^3 = \frac{27}{8}$. Thus,the correct option is $D$.

Two raindrops reach the earth with different terminal velocities having the ratio $9: 4$. The ratio of their volumes is

Similar Questions

What is the relation between poise and decapoise?

$A$ particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of its speed $v$ with time $t$ ?

Find the viscosity of glycerine $($having density $1.3 \ g \ cm^{-3})$ if a steel ball of $2 \ mm$ radius $($density $8 \ g \ cm^{-3})$ acquires a terminal velocity of $4 \ cm \ s^{-1}$ in falling freely in the tank of glycerine. $(g = 980 \ cm \ s^{-2})$ (in $\text{poise}$)

$A$ ball of density $\rho$ is released from deep inside a viscous liquid of density $2\rho$. It will move up:

$A$ heavy spherical ball is dropped near the surface in a long column of viscous liquid. Which of the following graphs represent the variation of:
$(i)$ Gravitational force with time
$(ii)$ Viscous force with time
$(iii)$ Net force acting on the ball with time

Vedclass Test Series

Exam Paper Generator

Online Exam Module